Music Theory for the
21st-Century Classroom
Music Theory for the
21st-Century Classroom
Robert Hutchinson
University of Puget Sound
August 17, 2020
Website: musictheory.pugetsound.edu
©2017
Robert Hutchinson
Permission is granted to copy, distribute and/or modify this document under
the terms of the GNU Free Documentation License, Version 1.2 or any later
version published by the Free Software Foundation; with no Invariant Sections,
no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is
included in the appendix entitled “GNU Free Documentation License.”
Acknowledgements
I owe a huge thanks to Robert Beezer for recommending PreTeXt (formerly
“MathBook XML”) as a means to author Music Theory for the 21st–Century
Classroom. His work creating the “world” of PreTeXt made it easier than
I could have imagined to create this text in all its forms (online, PDF, and
print).
Also of incredible value, and without whom this text would not exist, is
Jahrme Risner, who helped me wrap my head around the nitty gritty of PreTeXt and patiently coached me through entering commands in the terminal.
I wish to thank my colleague, Gwynne Kuhner Brown, for co–piloting the
use of this text at the University of Puget Sound and for suggesting extremely
helpful clarifications and corrections.
Finally, I must thank my wife, Dawn Padula, Director of Vocal Studies at
the University of Puget Sound and musician extraordinaire, for entertaining
my endless questions about my choices for musical examples and the clarity of
explanations and diagrams.
v
Preface
Music Theory for the 21st–Century Classroom is an openly–licensed online
four–semester college music theory textbook. This text differs from other music
theory textbooks by focusing less on four–part (SATB) voiceleading and more
on relating harmony to the phrase. Also, in traditional music theory textbooks,
there is little emphasis on motivic analysis and analysis of melodic units smaller
than the phrase. In my opinion, this led to students having difficulty with
creating melodies, since the training they are given is typically to write a
“melody” in quarter notes in the soprano voice of part writing exercises. When
the assignments in those texts ask students to do more than this, the majority of
the students struggle to create a melody with continuity and with appropriate
placement of harmonies within a phrase because the text had not prepared
them to do so.
In Music Theory for the 21st–Century Classroom, students learn about
motive, fragment, phrase, and subphrase, as well as types of melodic alteration like inversion, intervallic change, augmentation, diminution, rhythmic
change, ornamentation, extension, and retrograde. By understanding motive
and subphrase (also known as “phrase segment” or “phrase member”), I believe
students will better understand the logic and construction of melodies, which
will aid them in creating their own music.
This text is meant to take the student from the basics of reading and writing
pitches and rhythms through twelve–tone technique and minimalism over the
course of four semesters. Whenever possible, examples from popular music
and music from film and musical theater are included to illustrate melodic and
harmonic concepts, usually within the context of the phrase.
Performances of notated examples are linked to legal, copyrighted YouTube
videos with the start and stop time embedded to prevent the instructor the
need to search for the passage. The online nature of the text allows links
between related concepts (including the index) as well as to relevant pages on
the internet.
While I have considered creating a unique curriculum for the theory program at my university since 2001, the impetus to create an online music theory
textbook that could be of use not only to my students but to students at other
colleges came from reading “Transforming Music Study from its Foundations:
A Manifesto for Progressive Change in the Undergraduate Preparation of Music Majors” by the College Music Society’s Task Force on the Undergraduate
Music Major.
The ideas in “the Manifesto,” as it is often called—that colleges need
to train students to be composer–performer–improvisers (and I would add
“arrangers”) like Bach and Beethoven as well as Charlie Parker and Jimmy
Page—resonated with my musical experience growing up, which included writing, arranging, and playing popular music on electric guitar, electric bass,
vi
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keyboards, and drumset in high school—both in my uncle’s home recording
studio and with a garage band I formed. It also resonated with my experiences
playing jazz and fusion as a professional bassist ever since I was in college,
a situation where the majority of the basslines I play are improvised from
lead-sheet symbols.
My Ph.D. is in composition with a supporting area in music theory. I teach
students to write motets and fugues in the upper–division counterpoint class.
I believe in compositional craft. I also acknowledge that there are many things
one can value in music, including lyrics, groove, production, texture, emotion,
harmony, virtuosity, and intellect, to name a few. In this textbook I try to
cover as many as possible of these items that relate to how music is made and
how understanding can enrich one’s experience.
Robert Hutchinson
Tacoma, Washington 2017
Contents
Acknowledgements
v
Preface
vi
1 Basic Concepts
1.1
1.2
1.3
1.4
1.5
1.6
Pitch . . . . .
Notation . . . .
Octave Registers .
Accidentals . . .
Enharmonic Notes
Practice Exercises.
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2 Major Scales and Key Signatures
2.1
2.2
2.3
2.4
Half Steps and Whole
The Major Scale . .
Major Key Signatures
Practice Exercises. .
Steps
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3 Minor Scales and Key Signatures
3.1
3.2
3.3
3.4
Minor Scales . . .
Minor Key Signatures
Scale Degree Names .
Practice Exercises. .
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4 Basics of Rhythm
4.1
4.2
4.3
4.4
4.5
4.6
4.7
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Time Signature . . . . . . .
Durational Symbols . . . . . .
Dots and Ties . . . . . . . .
Meter . . . . . . . . . . .
Tuplets . . . . . . . . . .
Common Rhythmic Notation Errors
Practice Exercises. . . . . . .
viii
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CONTENTS
ix
5 Intervals
5.1
5.2
5.3
5.4
5.5
5.6
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Introduction to Intervals . . . . . . . . . .
How to Identify Perfect, Major, and Minor Intervals
How to Write Perfect, Major, and Minor Intervals .
Inversion of Intervals Explained. . . . . . . .
Augmented and Diminished Intervals. . . . . .
Practice Exercises. . . . . . . . . . . . .
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6 Triads
6.1
6.2
6.3
6.4
6.5
6.6
6.7
Introduction to Triads
Lead-Sheet Symbols .
Inverted Triads. . .
Analyzing Chords. .
Simple “Sus” Chords
Summary . . . . .
Practice Exercises. .
32
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7 Roman Numerals and Cadences
7.1
7.2
7.3
7.4
7.5
Roman Numeral Chord Symbols
Diatonic Chords in Major . . .
Diatonic Chords in Minor . . .
Cadences . . . . . . . . .
Practice Exercises. . . . . .
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Introduction to Seventh Chords. . . . . .
The IV/5 “sus” chord . . . . . . . . .
Roman Numerals of Diatonic Seventh Chords
Practice Exercises. . . . . . . . . . .
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The Circle of Fifths Progression . . . . .
Harmonic Rhythm . . . . . . . . . .
Shorter Progressions from the Circle of Fifths
Harmonic Function . . . . . . . . . .
Exceptions Created by Harmonic Sequences .
The Subtonic VII Chord in Popular Music. .
The Best-Seller Progression . . . . . . .
The i–VII–VI–VII Progression . . . . . .
Practice Exercises. . . . . . . . . . .
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Introduction to Non-Chord
Passing Tones . . . . .
Neighbor Tones . . . .
Appoggiatura . . . . .
Escape Tone. . . . . .
Double Neighbor . . . .
Anticipation. . . . . .
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10 Non-Chord Tones
10.1
10.2
10.3
10.4
10.5
10.6
10.7
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9 Harmonic Progression and Harmonic Function
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
9.9
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8 Seventh Chords
8.1
8.2
8.3
8.4
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Tones
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92
CONTENTS
x
10.8 Pedal Point . . . . . . .
10.9 Suspension . . . . . . .
10.10Retardation . . . . . . .
10.11Incomplete Neighbor. . . .
10.12Adding Non-Chord Tones to a
10.13Practice Exercises. . . . .
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Chord Progression
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11 Melodic Analysis
11.1
11.2
11.3
11.4
11.5
11.6
Motive. . . . .
Melodic Alteration
Fragment . . . .
Phrase . . . . .
Subphrase . . .
Practice Exercises.
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12 Form in Popular Music
12.1
12.2
12.3
12.4
12.5
12.6
Verse-Chorus Form . .
AABA Form . . . .
ABAC Form . . . .
The 12-Bar Blues . . .
Harmonically Closed and
Practice Exercises. . .
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Open Sections
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The Perfect Authentic Cadence . . .
The Sentence . . . . . . . . .
The Period . . . . . . . . . .
The Asymmetrical Period . . . . .
The Double Period . . . . . . .
Phrase Groups and Phrase Chains. .
The Elision . . . . . . . . . .
Summary of Phrases in Combination .
Practice Exercises. . . . . . . .
Texture . . . . . . . .
Chorale Texture . . . . .
Arpeggiated Accompaniments
Block Chord Accompaniments
Afterbeats and Offbeats . .
The 3–2 Son Clave . . . .
Distinctive Bass Lines . . .
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14 Accompanimental Textures
14.1
14.2
14.3
14.4
14.5
14.6
14.7
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118
13 Phrases in Combination
13.1
13.2
13.3
13.4
13.5
13.6
13.7
13.8
13.9
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15 Creating Contrast Between Sections
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15.1 The Elements of Music . . . . . . . . . . . . . . . . 175
15.2 Mozart, Eine kleine Nachtmusik, K. 525, II. . . . . . . . . 176
15.3 “Rude” by MAGIC! . . . . . . . . . . . . . . . . . 178
CONTENTS
xi
16 Figured Bass
16.1
16.2
16.3
16.4
16.5
16.6
Historical Context . . . . . . .
Figured Bass Inversion Symbols . .
The Cadential Six-Four Chord . . .
Other Occurrences of Six-Four Chords
Additional Information . . . . . .
Practice Exercises. . . . . . . .
181
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17 Secondary Dominant Chords
17.1
17.2
17.3
17.4
17.5
17.6
17.7
189
Examples with Secondary Dominants . .
Tonicization . . . . . . . . . . . .
Secondary Dominants in Major and Minor .
Analyzing Secondary Dominants . . . .
Writing Secondary Dominants . . . . .
Irregular Resolutions of Secondary Chords .
Practice Exercises. . . . . . . . . .
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18 Secondary Diminished Chords
18.1
18.2
18.3
18.4
18.5
Secondary Diminished Chords . . . . .
Secondary Diminished Chords in Major and
Analyzing Secondary Diminished Chords .
Writing Secondary Diminished Chords . .
Practice Exercises. . . . . . . . . .
Mode Mixture . . . . . . . . . .
Harmonization of Borrowed Scale Degrees
Analyzing and Writing Borrowed Chords
The Deceptive Cadence with 2 VI . . .
The Picardy 3rd . . . . . . . . .
Practice Exercises. . . . . . . . .
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201
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Minor.
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19 Mode Mixture
19.1
19.2
19.3
19.4
19.5
19.6
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20 The Neapolitan Chord
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20.1 The Neapolitan Chord . . . . . . . . . . . . . . . . 220
20.2 Examples of the Neapolitan Chord . . . . . . . . . . . 221
20.3 Practice Exercises. . . . . . . . . . . . . . . . . . 223
21 Augmented Sixth Chords
21.1
21.2
21.3
21.4
21.5
21.6
21.7
21.8
21.9
Augmented Sixth Chords . . . . . . . . .
Types of Augmented Sixth Chords . . . . .
Analyzing Augmented Sixth Chords . . . . .
Lead-Sheet Analysis of Augmented Sixth Chords
Examples with Augmented Sixth Chords . . .
Distingushing Between Chromatic Harmonies. .
Descending Chromatic Bass Lines . . . . . .
Chromatic Pre-Dominant Chords . . . . . .
Practice Exercises. . . . . . . . . . . .
224
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CONTENTS
xii
22 Modulation
22.1
22.2
22.3
22.4
22.5
22.6
22.7
22.8
237
Modulation . . . . . . . . . . . .
Tonicization versus Modulation . . . . .
Key Relationships . . . . . . . . .
Modulations with Diatonic Pivot Chords .
How to Recognize a Key After a Modulation
Modulations with Chromatic Pivot Chords
Modulations Without Pivot Chords . . .
Practice Exercises. . . . . . . . . .
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23 Enharmonic Modulation
23.1
23.2
23.3
23.4
262
Enharmonic Modulation . . . . .
The V7 and Ger+6 as Pivot Chords .
The Fully Diminished Seventh as Pivot
Practice Exercises. . . . . . . .
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Chord
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24 Binary and Ternary Forms
24.1
24.2
24.3
24.4
24.5
24.6
24.7
24.8
24.9
Binary and Ternary Form . . .
Sectional versus Continuous . .
Balanced Binary . . . . . .
Rounded Binary . . . . . .
Simple Binary . . . . . . .
Binary Principle . . . . . .
Ternary Form . . . . . . .
Distinguishing between Rounded
Practice Exercises. . . . . .
. 262
. 263
. 267
. 271
274
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Binary and
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Ternary .
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25 Sonata and Rondo Forms
25.1
25.2
25.3
25.4
25.5
25.6
. 237
. 237
. 241
. 241
. 244
. 245
. 248
. 257
294
Sonata Form . . . . . . . . . . . .
The Four Structural Functions in Music. . .
Rondo Form. . . . . . . . . . . . .
Rondo Character . . . . . . . . . . .
Standard Forms in a Multimovement Classical
Practice Exercises. . . . . . . . . . .
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Piece
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26 Voice Leading Triads
26.1 Voice Leading . . . . . . . . . . .
26.2 Types of Motion . . . . . . . . . .
26.3 Objectionable Parallels . . . . . . . .
26.4 Voice Ranges . . . . . . . . . . .
26.5 Rules of Melody . . . . . . . . . .
26.6 Rules of Spacing . . . . . . . . . .
26.7 Voice Leading Root Position Triads in Four
26.8 Voice Leading First-Inversion Triads . . .
26.9 Voice Leading Second Inversion Triads . .
26.10Special Situations . . . . . . . . . .
26.11Types of Six-Four Chords . . . . . . .
26.12Summary of Doubling Rules for Triads . .
26.13Practice Exercises. . . . . . . . . .
. 274
. 274
. 276
. 278
. 281
. 282
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. 294
. 296
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.304
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310
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. 310
. 310
. 311
. 311
. 312
. 312
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. 318
. 318
. 319
. 319
. 319
CONTENTS
xiii
27 Voice Leading Seventh Chords
27.1
27.2
27.3
27.4
27.5
27.6
323
Voice Leading Seventh Chords . . . . .
Voice Leading Successive Seventh Chords .
Voice Leading the V7 to I Progression . .
The Special Resolution of vii ◦7 (and vii ø7 )
When to Use Seventh Chords . . . . .
Practice Exercises. . . . . . . . . .
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28 Voice Leading With Non-Chord Tones
28.1
28.2
28.3
28.4
330
Voice Leading With Non-Chord Tones . . . .
Avoiding Objectionable Parallels . . . . . .
Adding Non-Chord Tones to a Chord Progression
Practice Exercises. . . . . . . . . . . .
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29 Voice Leading Chromatic Harmonies
29.1
29.2
29.3
29.4
29.5
Voice Leading Secondary Chords . . .
Voice Leading Borrowed Chords . . .
Voice Leading the Neapolitan Chord . .
Voice Leading Augmented Sixth Chords.
Practice Exercises. . . . . . . . .
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Species Counterpoint . . .
First Species Counterpoint .
Second Species Counterpoint.
Third Species Counterpoint .
Fourth Species Counterpoint .
Fifth Species Counterpoint .
Invention Expositions . . .
Fugue Analysis. . . . . .
Practice Exercises. . . . .
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. 330
. 331
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337
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30 Introduction to Counterpoint
30.1
30.2
30.3
30.4
30.5
30.6
30.7
30.8
30.9
. 323
. 325
. 326
. 328
. 328
. 329
. 337
. 338
. 339
. 339
. 341
343
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31 Introduction to Jazz Theory
31.1 Jazz Chord Basics . . . . . . . . . .
31.2 Chord Symbol Specifics . . . . . . . .
31.3 Altered Dominant Seventh Chords . . . .
31.4 Chord Labels . . . . . . . . . . . .
31.5 How to Write Jazz Chords . . . . . . .
31.6 How to Analyze Jazz Chords. . . . . . .
31.7 Jazz Chord Voicings . . . . . . . . . .
31.8 Standard Chord Progressions . . . . . .
31.9 Scales . . . . . . . . . . . . . . .
31.10How to Determine Chord-Scale Relationships.
31.11Harmonizing the Bebop Scale . . . . . .
31.12Practice Exercises. . . . . . . . . . .
. 343
. 343
. 345
. 347
. 348
. 349
. 349
. 353
. 357
364
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. 364
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. 371
. 372
. 374
. 377
. 378
. 379
CONTENTS
xiv
32 Impressionism and Extended Tonality
32.1
32.2
32.3
32.4
32.5
Impressionism . . .
Pandiatonicism. . .
Quartal, Quintal, and
Polychords . . . .
Practice Exercises. .
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Secundal Harmony
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382
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33 Set Theory
33.1
33.2
33.3
33.4
33.5
33.6
33.7
33.8
33.9
Set Theory . . .
Normal Form . .
Prime Form . . .
Interval Vector . .
Forte Numbers . .
Lists of Set Classes
Transposition (Tn )
Inversion (Tn I). .
Practice Exercises.
392
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34 Serialism
34.1
34.2
34.3
34.4
34.5
34.6
34.7
. 382
. 386
. 387
. 388
. 390
Twelve-Tone Technique . . . .
Determining Row Forms . . .
Writing Row Forms . . . . .
Twelve-Tone Matrix . . . . .
Row Form Presentation in Music
Non-Twelve-Tone Serialism . .
Practice Exercises. . . . . .
. 392
.395
. 396
. 399
. 401
. 401
.404
. 405
. 406
408
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35 Minimalism
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. 408
. 410
. 411
. 411
. 412
. 413
. 414
417
35.1 Additive Minimalism . . . . . . . . . . . . . . . . 417
35.2 Phase Shifting . . . . . . . . . . . . . . . . . . . 418
35.3 Homework Assignments . . . . . . . . . . . . . . . 420
A Answers to Practice Exercises
421
B GNU Free Documentation License
452
Index
459
Chapter 1
Basic Concepts
1.1 Pitch
& 51
Pitch has to do with notes. On the piano there are 88 notes. As you move to
the right on a piano, the notes sound higher. Notes sound lower as you move
to the left. Try it on a piano with a smaller range at the following website.
lower
higher
1
2
3
1.2
Notation
4
2
&
8
7
9
10
F
Fine
œ
œ
E
œ ledger lines
F
Every
E
staff with7 the dots
the
5 a five-line
1 The2 F clef,
3 when 4placed on
6
9 lines
œsurrounding
8
10
ledger
2
3
2
E
B
B
D
D
Good
F Every
Good
Boy
Boy
Does
F
Fine
Does
A
A
C
C
E
w
wE G
?
Grass
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w Do wFine? w
w
Cows
C
wG B D F B
Boys
B
w
All
A
w Eat Grass
A Goodw
Always w
&
?
G
Fine
F w
E
Do
D
Cows
C
second line from the top, creates the bass clef . See the example for the names
of lines and spaces,
remember them.
A and for mnemonics toAlways
1
3
G
G
G
B
Good
2
3
4
Boys
5
All
A
6
7
8
9
11
10
1.3 Octave Registers
3
7
4
6
Notes are written on a five-line staff . A clef orients the lines to a reference
point. For example, the G clef, when placed on a five-line staff, becomes the
treble clef , the most well known clef. In treble clef, the notes on the lines are
E–G–B–D–F from lowest to highest, often remembered through the traditional
mnenomic “Every Good Boy Does Fine.” The spaces are F–A–C–E from lowest
to highest. Staves (the plural of “staff” in musical terminology is “staves”) are
extended by the ledger lines.
&
&
HW
5
HW
4
11
12
& œ
The note
w names used inwmusic are ABCDEFG (knownw as thew“musical alphabet”).
note A returnswand
& After G, the
B again and again.
?ABCDEFG
w occurs
& œ w w B
w w
w
w
œ
? 1 2 3 4 5 6 1 7 8 9 10 11 12
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1
2
4
3
& w bœ ‹œ w
bw
w
#w
?
?
&
&
?
?
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2
?
&
CHAPTER 1. BASIC CONCEPTS
A
Always
ledger lines
G B
E
D
F
2
Grass
Eat
E G
D
C
Cows
Boys Do
B
A
All octave (which means the
G
Good
The distance
from the first A to the second
A is an
F
Fine
Every
Boy
Good
notes are eight steps apart.)
A
1
?
half step whole step
B0 C1
2
D
4
E
5
F
6
F
G
7
?
A
8 (octave)
Fine
?
whole step
D
G B
C2
C3
C4
& œ
Good
B4C5
C6
Boys Do
C7
A FC
Do
A C
E
C8
Note that the register number changes after the noteB each time (B4 is
followed by C5 ).
In treble clef, middle C is notated on the ledger line below the staff. In
bass clef, middle C is notated on the ledger line above the staff.
3
7
C
3
The distance from any note to a note
register
D of the same name in the next Boy
A Does
F
above or below is called an octave
“8ve”). Good
G B (abbreviated
How can the piano keyboard
have 88 notes Every
when there areB
onlyD
seven note
E
BoysF
G
Good
names? The musical alphabet repeats 7 times (with an extra ABC at the
top), which means we have at least seven octave registers. (There are also five
chromatic notes in each register, which we will learn about when we discuss
Accidentals.) When learning about octave registers, we will focus on the note
C for reasons that will soon become clear when we learn about the major scale.
We use octave registers (C4 , D5 , etc.) to specify the exact register of
a note. The note C4 is known as “middleAC” and is an important reference
Always
point. See the keyboard 3in the example
Fine
F below.
4
2
2B
&
half step
?
3
œ
?
4
& œ
7
B œ
œ
?
Figure 1.3.1 Middle C (C4) in treble clef and bass clef
4
The other two commonly used clefs are alto clef and tenor clef . Each
use a C clef that, when 8placed on a staff, designate the placement of middle C.
B œ
B œ
B0 C1
C2
C
Figure 1.3.2 Middle C in alto clef and tenor clef
The grand staff , which is a treble and bass clef joined together by a
bracket, is how piano music is written.
8
B œœ
& 44 œ œ œ œ
? 44
œ œ œ œ
Middle C
5
&
?
œ œ œ œ
œ œ œ
œ œ ˙
œ œ C2œ œ ˙ C3
œ
œ
œ
B0
C1
œ
œ œ
Middle C
Note that middle C is always clearly notated in either the upper or lower
staff and never floats between the two staves.
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
C4
B4C5
to A Major key signature
w
& w
w
w
ww
CHAPTER 1. BASIC CONCEPTS
1.4 Accidentals
m6
195
A is below F
M3
w
w
3
A is above F
b ww w ww w ww w # ww w
b
w
w
w
w
w
w
&
#w
b w a pitchwa half step. w
b w• The sharpwsymbol—4—raises
There are five types of accidentals; accidentals are characters that can be
placed before notes to raise or lower them.
m2
• The
pitch am6
half P4
step. P5
M2flat symbol—
M7
m7
m32—lowers
M6 aM3
°4
+5
• The double sharp symbol—5—raises a pitch two half steps, or a whole
step.
How Intervals Invert
• The double flat symbol—3—lowers a pitch two half steps, or a whole
1 8
M
m
step.
2
7
P
P
• The natural symbol—
3 66—cancels
+ out° any other accidentals that may have
occurred earlier in4a measure
or in Major Key Signatures or Minor Key
5
Signatures.
201
&w
bw
nw
#w
nw
G
Figure 1.4.1
1.5 Enharmonic Notes
4
2
Observe that C and D are the same note on the piano but are written as
different notes on the staff.
&
#œ bœ
Figure 1.5.1
4
2 4
2 4
2
This occurs with all the black keys on the piano (C =D , D =E , F =G ,
2
4
2
G =A , A =B ). When two notes sound the same but are written as two
4
2 CHAPTER
&
1. BASIC CONCEPTS
4
different notes on the staff, the written notes are said to be enharmonic.
Notes on the white keys of the piano can be written enharmonically as well
4
2
5
(C=B , E=F , D=C , etc.).
HW
5
& 1.6
1 Practice Exercises
& 51 1 2 3
5
4
1.
3
6
7
8
10
For each note on the piano keyboard,
specify the
note
name and9octave
register.
&
1
1
1
2.
&
6
&
2
2
2
3
w Bw
3
3
w
4
4
w
5
w ?w
5
6
5
4
6
6
7
7
7
w
w
8
8
9
Bw
10
8
w
9
11
9
w
10
12
10
w w
w Bw w w
B
w w
For each note on the staff, specify the note name and octave register.
2
7
2
w
w
HW
w
&
&
w
2
1
3.
11
1
Provide
two2
Example
Bw
ww B
3
4
3
4
enharmically
1
& w bœ ‹œ w
w
w
5
w ?w
w?
w
6
6
5
equivalent
bw
2
7
7
notes
w
11
12
each9 given10note.11
12
8
for8
9
3
w
10
4
#w
1
2
3
4
versions of the textbook,
homework
exercises, and
practice exercises
can
b
œ
‹
w
?
#
œ
be found at
musictheory.pugetsound.edu
‹
w
w
bw
HW
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16
PDF
Example
Chapter 2
Major Scales and Key Signatures
5
2.1 Half Steps and Whole Steps
?
A half step on a piano keyboard is the distance from one note to the next
nearest note. A whole step is made of two half steps.
half step whole step
2.2 The Major Scale
A major scale contains a specific succession of whole and half steps. It is helpful
to think of the pattern as consisting of two tetrachords. (A tetrachord is a
four-note scale segment.) The lower tetrachord consists of the pattern whole
step, whole step, half step. A whole step joins the lower tetrachord to the
upper tetrachord. The upper tetrachord duplicates the pattern in the lower
one: whole step, whole step, half step. If we use W for whole step and H for half
step, the major scale pattern is W–W–H, Whole–step connection, W–W–H.
5
B
9
CHAPTER 2. MAJOR SCALES AND KEY SIGNATURES
&
tetrachord
W
#œ bœ
6
tetrachord
W HW W
W H
12
Figure 2.2.1 The D major scale on a keyboard
B
10
&œ
tetrachord
W
œ #œ
W
H
œ
W
œ
tetrachord
W W H
œ #œ
œ
Figure 2.2.2 The D major scale in treble clef
All major scales use the notes of the musical alphabet in order; no notes are
skipped and no notes occur twice. In the example above, the first four notes
4
2
2
are D–E–F –G, not D–E–G –G. In D–E–G –G, G erroneously occurs twice
4
and the F between E and G is skipped.
2.3 Major Key Signatures
A key signature is placed at the beginning of a piece (or the beginning of a
section) and is written with the clef on the beginning of each line of music.
The key signature reminds the performer which sharps or flats are in the
scale (or key) of the piece and prevents the composer or arranger from writing
every sharp or flat from the scale every time it occurs.
W
W
& œH œ # œ
W
œ
œ
W W H W
CHAPTER 2. MAJOR SCALES AND KEY SIGNATURES
13
## 2
## 2
œœ œœ ˙
œœ
&
& 4 œ œ œ œ œ œ 4˙ œ œ œ œ œ œ œœ œœ œ˙œ œ œœ œ˙ œ œ œ œœ œœ œ ˙˙
25
#
& # œœ œœ œœ ˙
œœ ˙
œœ œœ
7
œœ œœ
œœ ˙
##
œ œLittle˙ Star"œin Dœ major
œ œTwinkle,
& œ œ œ œ œ Figure
œ ˙ 2.3.1œ "Twinkle,
œœ œœ ˙
œ
There are 15 major key signatures. The key of C major has no sharps or
#
##
##
b
& #
37
50
&
62
&
##
##
flats in the key signature. The other key signatures can have between 1 to 7
sharps and 1 to 7 flats, giving us the other 14 key signatures.
# # # # ## # ## # # # # # # # # # # # # # # # #
&
#
#
#
G
G
D
D
A
A
E
E
B
B
Figure 2.3.2 Major Key Signatures using Sharps
&b
F
bb
Bb
bbb
Eb
bbbb
Ab
bbbbb
Db
F#
F
C#
C
bbbbbb
bbbbbbb
Gb
Cb
Figure 2.3.3 Major Key Signatures using Flats
It is important to memorize the order of sharps and flats, since you will be
writing key signatures regularly.
The order of sharps is F–C–G–D–A–E–B, often remembered by a mnemonic.
One common mnemonic for the order of sharps is “Fast Cars Go Dangerously
Around Every Bend.”
The order of flats is B–E–A–D–G–C–F. It is the reverse of the order of
sharps. It is easy to remember since the first four letters make the word BEAD,
and GCF is something most students learn as “Greatest Common Factor” when
studying math in elementary school.
A mnemonic that works forward and backward is “Father Charles Goes
Down And Ends Battle,” which reversed is “Battle Ends And Down Goes
Charles’ Father.”
A helpful learning device to remember the order of keys in relation to
the order of sharps and flats is the circle of fifths. As you ascend in fifths
(clockwise), key signatures get one degree “sharper.” (C to G is a fifth because
C=1, D=2, E=3, F=4, and G=5.) As you descend in fifths (counterclockwise),
key signatures get one degree “flatter.”
B bbbbbbb
B bbbbbbb
52
CHAPTER 2. MAJOR SCALES AND KEY SIGNATURES
1b
2b
0b
C
0#
F
Bb
1#
G
b
3b E
A
4b
8
D
#
2
3# A
b
7#
C#
Db
5b
6#
F#
Gb
6b
5#
B
4#
E
Cb
7b
Figure 2.3.4 Circle of Fifths for Major Keys
Note the overlapping keys at the bottom of the circle. B major is enhar2
4
2
monically the same as C major, F major is enharmonically the same as G
4
2
major, and C major is enharmonically the same as D major.
2.3.1 Identifying Key Signatures
While it is preferable to memorize key signatures, use the following method
to determine major key signatures based on the sharps or flats in the key
signature.
1. For key signatures withs sharps: Go up a half step from the last sharp
to find the key.
2. For key signatures with flats: The second-to-last flat is the key.
?
&
CHAPTER 2. MAJOR SCALES AND KEY SIGNATURES
B¯≤ major scale
E major scale
HW
1.
25
2
?
&
2.4 Practice Exercises
23
2.
27
23
HW
34
25
41
27
& 55
3.
HW
48
60
53
&
Using the WWHWWWH pattern, write the specified major scales without
using
key scale
signatures.
C˜ major
A¯≤ major scale
D¯≤ major scale
A
?major scale
&
&
21
9
?
DOuble bars? new clefs?
Given the key signature, specify the major key.
E?
major
#
#
b scale # #
b B¯≤ major scale
&
b bb
#
____
1
C˜ major
# scale
&
&
____
2
## #
bb
____
8
____
9
____
3
bbbb
b
____
10
____
4
#### #
##
#
bb ? b
____
5
____
6
# # scaleb b
# # # # # A¯≤ #major
#
# ? # b b bbb
____
11
____
12
____
13
____
7
bbbbbb
____
14
Write the major key signature for each key given. Be sure to use the
? b b order
# # # #flats. b b
#
b b for #sharps
correct
and
#
bb b
bb b
?
bb
____
1
1. A major
&
###
____
6. C¯≤ major
8
____
____
____
2
3
4
2. B¯≤ major
3. F˜ major
bbbbbbb
#### ##
#
b
____
____
____
9 7. E¯≤ major 10 8. B major
11
b
bb
3
____
____
____
5
6
7
4. D¯≤ major
5. D major
####
#
bbb
#### #
#
____
____
____
9. F major
10. C˜ major
12
13
14
? to download the homework.
# # # # #Click here
# PDF versions of the textbook, homework exercises, and practice exercises
&
&
can be found at musictheory.pugetsound.edu
65
55
61
#### #
#
&
&
69
63
69
74
77
&
85
&
?
83
?
107
79
?
&
?
b
3b E
4
b
bA
3# A
Db
54
55
5#
6#
C#
5b
53
7#
F#
B
Gb
E
Cb
7b
6b
Chapter
3
Major scale
3̂
4̂
5̂
w
6̂
w
w
3ˆ
4̂
w
5̂
6ˆ
7ˆ
8̂
4̂
w
w
w
w
& w
w
w
w
w Scales
Minor
and
Key Sigb
b
b
natures
w
bw
bw
&
w
1̂
2̂
Natural Minor scale
1̂
2̂
w
w
Harmonic Minor scale
1̂
2̂
bw
b 3ˆ
w
w
bw
w
w
& w
w
bw
w
w
w
5̂
7̂
b 6ˆ
bw
3.1
& Minor Scales
56
4#
8̂
7̂
8̂
There are three minor scales: the natural minor scale, the harmonic minor
Melodic
Minor
scale (ascending
scale,
and
the melodic
minorversion)
scale. Play or sing through each one and notice
b 3ˆ
1̂
2̂
4̂
6̂
7̂
8̂
5̂
the differences.
The melodic minor scale has an ascending version, shown above, and a
descending version that is the same as the natural minor scale.
57
Melodic Minor scale
1̂
2̂ b 3ˆ
4̂
b 7ˆ b 6ˆ
b 3ˆ
& w w bw w w w w w bw bw w w bw w w
5̂
6̂
7̂
8̂
ascending
5̂
4̂
2̂
1̂
descending
So far, we have looked at minor scales in relation to the major scale. However,
we will typically encounter minor scales in music using minor key signatures.
3.2 Minor Key Signatures
Minor key signatures agree with the notes of the natural minor scale. Since
2 2
2
the C natural minor scale had E , A , and B , the key signature of C minor
2 2 2
has three flats, written in the order of flats—B , E , A .
10
b 4
œœœ
œ
œ
& b b 4 ‰ œ nœ œ œ œ œ œ œ œ œ nœ œ œ œ œ œ œ œ œ nœ nœ œ œ œ œ
œ
bSCALES
b 6ˆ
7̂
7̂
7̂ 6̂
6ˆ
CHAPTER 3. MINOR
AND KEY
SIGNATURES
Natural Minor scale written with major key signature
b 3ˆ
4̂
5̂
1̂
2̂
72
&
73
w
bw
w
w
b
&bb
w
b
&bb
bw
b
& b b 44
b
& b b w œ bœ
w
&b
95
&b
b
Bb
b
83
b
& b bbbbb
bb
& b b bbb
99
F#
bb
add 3 flats
subtract 3 sharps
&
bbb
E b major
b 7ˆ
w
8̂
w
w
8̂
###
f#
#
G
subtract 1 sharp
and add 2 flats
bb
g
b
& b&b
Below are the minor key signatures.
#
a
a
b
e
d
##
bb
b
g
C minor
w (œ) ( b œ ) w
half steps between: 1
&
91
w
Note on uppercase versus lowercase: When writing below the five-line staff
to designate keys, we will use the shorthand of upper case for major ( C ) and
lowercase for minor ( c ). When writing prose, we will use uppercase: C major
and C minor.
We use the term relative minor when referring to a minor key that has the
2
same key signature as a major key. For example, the relative minor of E major
is C minor because both have three flats in the key signature. Conversely, one
2
could say the relative major of C minor is E major. The relative major is
three half steps above the relative minor.
95
75
#### #
#
bbbbb
94
6
b 6ˆ
bw
Therefore, a minor key signature will have three lowered notes—the 3rd,
7
6th, and 7th—in relation to the corresponding major key signature. We use
b major when referring to a minor scale that has the same
94 term parallel Eminor
the
C minor
1st scale degree (in this case C) as the major. We say, “The parallel minor of
E major is E minor,” and
) parallel major of F minor is F major.” One
( ) (“The
method of half
figuring
out
a
minor
steps between: 1
2 key
3 signature is to add three flats to the parallel
major key signature. This is the same as subtracting three sharps.
75
101
w
w
w
w
w
b 7ˆ
b 6ˆ
Natural Minor scale written with minor key signature
b 3ˆ
4̂
5̂
1̂
2̂
74
11
2
3
###
####
####
#
#### #
#
#### #
##
bbb
bbbb
bbbbb
bbbbbb
bbbbbbb
f#
c
c#
f
g#
bb
d#
eb
a#
ab
Here are circle of fifths diagrams for both major and minor, for comparison.
7
B bbb
93
CHAPTER 3. MINOR SCALES AND KEY SIGNATURES
1b
2b
0b
a
0#
d
g
1#
e
b
#
2
3b c
4b
f
bb
5b
Figure 3.2.1
12
7#
a#
6#
d#
eb
6b
5#
g#
4#
ab
7b
#
3# f
c#
B bbbbbbb
52
CHAPTER 3. MINOR SCALES AND KEY SIGNATURES
1b
2b
0b
C
0#
F
Bb
1#
G
D
#
2
b
3b E
75
3# A
A
4b
6
&
13
#
a
e
b
7#
C#
D b# #
##
5bb
#
f#
6#
F#
#### b ####
G #
c#
6b
5#
4#
E
b
C
#
B
## # #
#### ##
b
#7
#
a#
d#
g#
b minor
b b minorb b band melodic
b b b b minor
b b b bscales
b b b b busing
b b b b b bkey
&Writingb harmonic
b when
b
83
bb
signatures requires you to raise scale degrees.
a
B bbbbbbb
91
92
b
&bb
93
b
&bb
115
b
&bb
123
d
g
c
f
Harmonic Minor scale: raise 7̂ in minor
b 3ˆ
1̂
2̂
4̂
b
&bb
w
w
w
w
w
5̂
eb
b 6ˆ
w
Melodic Minor scale (ascending version): raise 6̂ and 7̂ in minor
b 3ˆ
4̂
2̂
5̂
6̂
1̂
b
&bb
w
w
w
w
w
nw
ab
nw
w
nw
w
7̂
7̂
8̂
8̂
Compositions in minor typically do not strictly use only one of the three
minor scales, however. The three minor scales are distillations of composers’
actual practice.
CHAPTER 3. MINOR SCALES AND KEY SIGNATURES
bb 4 ‰ œ n œ œ œ œ œ b œ œ œ œ œ œ n œ œ œ œ œ œ œ œ
b
& 4
œ
œ
harmonic minor
58
7̂
58
14
5
harmonic minor
natural minor
b 6ˆ b 7ˆ
7̂ b 6ˆ
7̂
bb 4 ‰ œ n œ œ œ œ œ b œ œ œ œ œ œ n œ œ œ œ œ œ œ œ
b
& 4
œ
œ
harmonic minor
bb
&
10 b
60
natural minor
b 6ˆ b 7ˆ
7̂
Figure 3.2.2 J.S. Bach, C Minor Invention
7̂ b 6ˆ
YT: HFeLqgVLxBM
148
58
60
152
harmonic minor
5
7̂ 5
harmonic minor
harmonic minor
# 4
minor œ
œ œnatural
#
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
& b 44
œ œ œœ œœ œœ
œ minor
natural
œ œ œ n œ œ œœ œœ œ wœ œ œ
œ
b
‰
n
œ
b
œ
b
œ
œ
& 4
œ
œ œœ
œherœwedœ œ- dingœ has
where
b C El -Óean - orŒRigœ-œby, œ picks
œ œupœtheœriceœ œin the church
œ been,
œ œ Œ œœ
b
Œ
&
b 6ˆ b 7ˆ
without syncopation
7̂
7̂
7̂ b 6ˆ
# 4
œ # œ œ # œ œ œb 7ˆ œb 6ˆ œ
p
œ
œ
œ
œ
œ
w
& 4
œ œ œ
œ
church where her wed - ding has been,
bb b œ œ œ œ œ œœ œœ œ œ œ œœ œ Œ œ œ œ œ #œœ œœ œœœ œ œ œœ œœ œ œœ œ
Œ
Œ
& b C Ó Œ156 incorrect rhythmic notation
&
p & 68 œ œ œ œ œ œ œ7̂œ œ œbb6ˆ7ˆ œb 6ˆœ œ œ œ . œ œ
J
harmonic minor
69
œ
œ
œ
bb œ
notation # œ œ œ œ œ œ œ œ
œ correct rhythmic
Œ
&
& bb œ44 œ 158œ œ œ YT:
1 O0PChj-uQPo
2
1
2
ˆ
b
Figure 3.2.3 Mozart, Symphony
No. 40 in G Minor,
K.
7̂
6 550, 1st movement
& 68 œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ . œ œ
65
El - ea - nor Rig - by
60
65
natural minor harmonic minor
picks up the rice in the
melodic minor
harmonic minor
œ œ œ œ interval
b b b 44horizontally
‰ œ n œ œ œ=œ"melodic"
measured
&
œ œ nœ œ œ œ œ œ
œ b ˆ# œ œ .
7̂
? 44 œ
#6 œ œ . 7̂ # # œœ b 6ˆ
J
J
J
69
160
b
&bb
72
œœ
œœ
J
œœœ
œ nœ nœ œ œ
œ
œœ œ
œ . 7̂ 6̂ ˙
œ.
˙
measured vertically = "harmonic" interval
YT: xp3zPzDnTEk
162
Figure 3.2.4 J.S. Bach, Well-Tempered Clavier, Book One, Fugue 2 in C
Minor
?w
w
w
w
w
3.3 Scale
Degree
major Names
major perfect
perfect
w
w
w
w
perfect major major perfect
third
fourth
fifth
sixth seventh octave
unison second
(M3)
(P4)
(P5)
(M6)have(M7)
Scale degrees,(P1)
though(M2)
often referred
to
by numbers,
also
names.(P8)
163
?
164
tonic
? w1̂
supertonic
mediant
subdominant
dominant
2̂
3̂
4̂
5̂
w
w
w
w
submediant
w6̂
leading tone
w7̂
These names will be used throughout this text to refer to scale degrees,
chords built on these scale degrees, and keys associated with these scale degrees.
Another way to understand why some scale degrees have “sub-” in their
names is through the following example.
mediant
tonic
E majorsupertonic
scale
1̂
HW? &
w
163 23
w
w
w6̂
w
w?
5̂
4̂
3̂
2̂
subdominant
B¯≤ major scale
CHAPTER 3. MINOR SCALES AND KEY SIGNATURES
25
C˜ major scale
?
&
tonic
55
164
27
____
1
Notice that
b ww
###
#
subtonic
bbb
####
HW
74
48
79
# # # # #2.
& #
55
83
# # #3.
&8589 # # #
63
HW
94
87
4.
99
?
HW
89
104
7. E¯≤ major
8. B major
9. F major
____
____
____
____
____
6
2
4
5 the tonic,
subtonic
is a3 whole step
below
bb
#### #
#
bbbbb
#### #
####
#
##
subdominant
10. C˜ major
____
7
while the
leading
bbbbbbb
10
11
12
13
9
? 8
Specify the minor key for each key signature given.
? bb b b
#2.# C˜ major# # # # 3. G¯≤ major
#
1. E¯≤ major
bb
b b4.b bD major
bb
&
____
1
###
&
?
6. B major
____
8
11. C¯≤ major
____
2
____
3
____
____
4
____
5
# # # # # #8. F˜ major
b
#
bbbbbbb
____
____
6
# #9.# #A¯≤ major b b
#
b
7. D¯≤ major
____
____
____
9 12. A major 10 13. B¯≤ major
11
____
____
12 E major 13
14.
bbbbbb
____
14
bbbbb
5. F major
____
7
#### #
#
10. G major
____
14
Write the minor key signature and specified minor scale in each example.
&
?
F harmonic minor scale
(include key signature)
B melodic minor scale
(include key signature)
?
&
?
Write the minor key signature for the given key in each example.
A¯≤ harmonic minor2.scale
1. D minor
F˜ minor
(include key signature)
&
6.&
B minor
3. F minor
C˜ melodic
minor scale 5. A¯≤ minor
4. D˜ minor
(include key signature)
?
8. G˜ minor
9. B¯≤ minor
10. E minor
2
minor:
is the subtonic
2. EDminor
3. A˜ minor
4. G minor
5. B¯≤ minor
9. G˜ minor
10. A¯≤ minor
7. C minor
Specify
the minor
key from
G natural
scale the scale degree name.
F˜ melodic minor scale
(include key signature) 2
(include key signature)
(a)
minor: A is the mediant
?
1.(b)
F minor
(c)
&
(d)
109
w
w
5. D major
##
b
submediant
3.4 Practice
Exercises
____
____
____
____
411.
HW
dominant
ww 4. D¯≤ major
3. F˜ major
the
?
34
tone
is only a half step below the tonic.
&
69
4
&
? bb
bb
6. C¯≤ major
?mediant
supertonic
2. B¯≤ major
DOuble bars? new clefs?
60
65
?1. Awmajor
A¯≤ major scale
15
3
6. F˜ minor
?
(e)
11.(f)
E¯≤ minor
(g)
major: B is the dominant
major: C is the submediant
7. A minor
8. B minor
4
minor: D is the subdominant
2
major:
B˜ minor
is the leading
tone
12. C
13. C minor
4
minor: E is the supertonic
Click here to download the homework.
14. D˜ minor
w7̂
CHAPTER 3. MINOR SCALES AND KEY SIGNATURES
16
PDF versions of the textbook, homework exercises, and practice exercises
can be found at musictheory.pugetsound.edu
Chapter 4
Basics of Rhythm
bb
E b major
7
b w inœ music,
In relation &
to rhythm
we will discuss time signatures, durational
( ) (b œ ) w
symbols, meter, beat, pulse, tempo.
94
C minor
half steps between: 1
2
3
#### #
bbb
4.1b bTime bSignature
#
95
&
###
b
add signature,
3 flats
subtract 3 of
sharps
In a time
the topF #number
the# time
bb
f
Bb
many” and the bottom number tells you “of what.”
## 4
4
3
&b 2
"How many?" 3
101
"Of what?" 1/2 notes
(half notes)
b b b b 85
4
106
107
& 44 ˙
G
5
### 6
16
110
“how
6
1/16 notes
(sixteenth notes)
˙
& 44 œ
œ
œ
œ
œ
œ
œ
œ
J
œ
J
eighth notes (equal 1/8 of a whole note) (can be beamed or flagged)
109
g
half notes
(equal
of a whole
note)
In the present
day,
the1/2most
common
time signature is 44 (also known as
“common time”). It makes sense to introduce durational symbols in the context
of 44 because a whole note takes up a whole measure in 44 , a half note takes up
4 , a quarter note takes up 1 of a measure, and so on.
half a measure
ofnotes
quarter
4 (equal 1/4 of a whole note)
4
& 44 œ
108
bb
subtract 1 sharp
and add
2 flats
signature
tells
you
1/8 notes
(eighth notes)
1/4 notes
(quarter notes)
whole note
4
4 w
4.2&Durational
Symbols
105
#
œ
J
œ
J
sixteenth notes (equal 1/16 of a whole note) (can be beamed or flagged)
4
& 4 œ œ œ œ œ œ œ œ œ œ œ œ œR œR œR œR
4
& 4 œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œR œR œR œR œR œR œR œR
ÔÔÔÔÔÔÔÔ
thirty-second (32nd) notes (equal 1/32 of a whole note) (can be beamed or flagged)
111
&
whole rest half rest
∑
17
Ó
quarter
rest
Œ
eighth sixteenth 32nd
rest
rest
rest
‰
≈
®
half notes (equal 1/2 of a whole
b 3note)
˙
101
& 2
the measure
## 4
4
˙
the measure
b b b b 85
CHAPTER
OFnote
RHYTHM
1/2 note is4. BASICS 1/4
is
beat value
œ
106
œ
œ
œ
œ
1/8 note is
beat value
beat value
note
105
quarter notes (equal
1/4 of a whole
note)
4 whole
&4 w
œ
& 44 œœ
œœ
J
notes (equal 1/2 of a whole note)
4 half
˙
&4
˙
œ
J
the measure
eighth notes (equal 1/8
of a whole note) (can be beamed or flagged)
107
œ
quarter notes (equal 1/4 of a whole note)
1/16 note is
beat value
18
œ
œ
J
4 œ
œ
œ
œ
œ
4 note)œ (can be
sixteenth notes (equal 1/16 of&a whole
beamed or flagged)
J
J
108
# # # 6 the measure
16
eighth notes (equal 1/8 of a whole note) (can be beamed or flagged)
œ
œ
J
œ
J
œ
J
œ œ œ œ œ œ4 œ œ œ œ œ œ œ œ œ œ
& 4 œ œ œ œ œ œ œ œ œ œ Rœ œR œR RœR œRR œR
sixteenth notes (equal 1/16 of a whole note) (can be beamed or flagged)
109
4
œ œ œ œ œ œ œ œ œ œ &œ 4œ œœœ œœ œœœ œœ œœœ œœœœœ œœœ œœ œœœ œœ œœœ œœœ œœ œœœ œœRÔ œRÔœœRÔ œœRÔ œRÔœœRÔ œRÔœœRÔ
RÔ RÔ RÔ RÔ RÔ RÔ RÔ RÔ
110
thirty-second
(32nd) notes
(equal (can
1/32 of be
a whole
note) (canor
be flagged)
beamed or flagged)
thirty-second (32nd) notes (equal 1/32
of a whole
note)
beamed
Figure 4.2.1
111
&
111
Here are durational symbols for rests.
&
whole rest half rest
∑
Ó
quarter
rest
Œ
eighth sixteenth 32nd
rest
rest
rest
‰
≈
®
To put this information into practice, listen to the durational values double
in speed in each measure of the following example.
? 44
œ œ œ œ
œ œ ˙
œ œ œ œ
œ œ œ œ
Middle C
CHAPTER 4. BASICS OF RHYTHM
44
19
eighth notes are twice
as fast as quarter notes
sixteenth notes are twice
as fast as eighth notes
4
& 4 œ œ œ œ œ œ œ œ .. œ œ œ œ œ œ œ œ .. .. œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ ..
5
? 44 ˙
this pattern of 8 notes
takes 8 beats
˙
˙
˙
sixteenth notes are four times
faster than quarter notes
˙
.. ˙
˙
.. .. ˙
..
this is another way of notating
32nd notes, showing 4+4
32nd notes are twice as fast as sixteenth notes
(there are eight 32nd notes for each quarter note)
& œœœœœœœœœœœœœœœœœœœœœœœœœœœœœœœœ w
9
this pattern of 8 notes
takes 1 beat
˙
? ˙
˙
˙
Two rare durational values are the double whole note (also called a “breve”)
and the 64th note, which is twice as fast as a 32nd note.
∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
& ∑ ∑ ∑two∑ways
of notating the
double whole
64th notes
64th
11
rest
œ
œ
œ
œ
œ
∑ ∑ ∑ ∑ R ∑ ∑ Ù∑
ÔÔ
›
„
? ∑ ∑&∑ ∑ W
∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
double whole note (or breve)
4
4
rest
4.3 Dots and Ties
8
We have a whole note, which lasts for four beats, and a half note, which lasts
for two beats, but we don’t have a durational value that lasts three beats. To
do so requires using a dot or a tie.
A tie links two notes together to create a new duration. Ties occur between
notes of the same pitch. A slur, which looks like a tie, is placed over or under
notes of differenttwo
pitches
and means
to
play
them in
a notes
connected
ways of notating
the
double
whole
64th
64thmanner.
noteincreases
(or breve)
rest duration of that note
restby half. A
A dot addeddouble
to awhole
note
the
second dot represents half the value of the first dot, or a quarter of the original
duration. (These are known as “double-dotted notes.”)
W ›
&
112
& ˙.
113
tie joins notes together
to create a new duration
=
˙
dot equals half of
the note's duration
& 44
118
œ
œœœœ œ
RÔÔ
„
˙ ..
=
˙
second dot equals half of
the first dot's duration
œ œ
J ˙
Ù
j
œ
œ
slur means to play with no
audible gap between the notes
?
CHAPTER 4.11.BASICS
OF RHYTHM
E¯≤ minor
12. C˜ minor
4.4 Meter
8
113
112
&
& ˙.
113
116
117
112
120
?
119
123
118
j
œ
œœ œ œœ œœRÔ œ Ùœ œ œ
64th notes
64th
˙
œ
˙ ..
˙
œ œ œ
Ô
j
œ œ
œ œ
J ˙
œœ
œœœœœœ
œ œ œœœœ œ œ œ œ œ œ œ œ œœœœœœ
œœœœ œ Ù
W ›
„
&
= œ œfour œbeats="quadruple"
RÔÔ œ
4.
three beats="triple"
two beats="duple"
j tie joins
j notes together
2
œ
œ
32 ˙œ œ ˙œ œ ˙œ œ 44 œœ œ œœ œ œœ œ œœ œ
& 8 œ œ to œcreateœa new duration
j
. = ˙
œ ˙ .. = beats˙in each bar
œ naturally
œ divide into two parts
& ˙each
œ
of these meters is "simple" because the
œ
J ˙
j j
6 œ . œ . 9 œ . œ . œ . 12 ˙ . ˙ . ˙ . ˙ .
& 16 œ œ œ œ œ œ 8 œ œ œ œ œ œ œ œ œ 4 œ œ œ œ œ œ œ œ œ œ œ œ
3 these meters
Meter
beats
œ œis "compound"
œ œ œ œbecause
œ theœ ___________________________
œ in œeachœbarœnaturally
œ œ divide
œ œ œintoœthree
œ œparts
&each4 =ofœ_____________________
second dot equals half of
equals half of
2 is “simple
Thedot
time
signature
duple meter.” The time signature 32 is
8three beats="triple"
beats="duple"
the first dot's duration four beats="quadruple"
thetwo
note's
duration
slur means to play with no
4
“simple triple meter.” Finally, 4 is “simple quadruple meter.”
audible gap between the notes
When describing meter, we say how the beat is divided before the number
of beats in the measure.
3
5
6
("simple" or "compound")triplet
("duple,"quintuplet
"triple," or "quadruple")
sextuplet
(how the beat is divided)
(the number of beats)
126
&
˙ ..„
3
&4 œ
118
113
W ›
double whole
Meter describesdouble
the number
measure (also know as rest
a “bar”) and
whole note of
(or beats
breve) in arest
how the beats are normally
divided.
=
Example
Beat is "[t]he basic pulse underlying measured music and thus the unit by
which musical time is reckoned..." according to Barry Kernfeld in The New
Grove Dictionary
ofnotes
Jazz,
2nd edition. Pulse and beat are synonymous.
tie joins
together
to create
Tempo refers
toa new
the duration
speed 1.
of the beat or=pulse. Tempo can be referred
to in beats per minute (bpm), such as 60bpm (where the rate of the beat
= to a second), or, in classical
=
would be equal
music, with terms like Allegro,
Andante, and Adagio, sometimes in combinations with "M.M." for Maelzel’s
second dot equals half of
dot equals half of
=
2.
Metronome.
the first dot's duration
the note's duration
slur means to play with no
Meters with two beats in a bar are described as duple.
If there
are the
three
audible
gap between
notes
beats in a bar, the meter is described as triple, and if there are four beats in a
bar, the meter is described as quadruple.3
5
6
=
3.
If the beats are normally divided into two parts, the meter is described
two ways of notating the
double whole
64th notes
64th
as simple.118If the
beats
divided
into three parts, rest
the meter is
double
wholeare
note normally
(or breve)
rest
sextuplet
triplet
quintuplet
described as compound.
115
8
two ways of notating the
14.20
D˜ minor
13. C minor
120
j
j
2
œ
œ
&8 œ œ œ œ
two beats="duple"
four beats="quadruple"
32 ˙œ œ ˙œ œ ˙œ œ
44 œœ œ œœ œ œœ œ œœ œ
j j
. .
. . .
.
.
.
.
6
œ
& 16 œ œ œ œœ œ œ 98 œœ œ œ œœ œ œ œœ œ œ 12
4 ˙œ œ œ ˙œ œ œ ˙œ œ œ ˙œ œ œ
two beats="duple"
123
three beats="triple"
With compound meters the bottom number specifies the division of the beat.
6 is “compound duple meter” because
The beat value is a dotted note. We say 16
6
it has two beats. The time signature 8 is also compound duple. Compound
time signatures have a top number greater than four that is divisible by 3 (6,
9, 12).each of these meters is "simple" because the beats in each bar naturally divide into two parts
three beats="triple"
four beats="quadruple"
each of these meters is "compound" because the beats in each bar naturally divide into three parts
126
&
The following table summarizes meter and time signatures.
Top number of time signature:
Top number of time signature:
Number of beats:
2
6
Duple
3
9
Triple
4
12
Quadruple
= Simple
= Compound
8
112
118
120
113
j
equals
˙ half ofœ 118 ˙ .. = ˙
œ œ
3
=dot
& ˙ .second
œ
the first
dot's duration
œ
slur means
to play with no J
˙
3
audible
gap
œ of theœnotesœ œ œ œ œ œ œ œ œ œ
&equals
464thbetween
second
dot
half
dot equals half of
two ways of notatingthe
thenote's duration
double whole
64ththe
notes
first dot's duration
CHAPTER 4. BASICS
OF
RHYTHM
21 slur means to play withtriplet
no
qu
double whole note (or breve)
rest
rest
audible gap between the notes
3
5 œ
6
œ
œ
œ
W
›
„
œ
3 œ &œ œ œ œ œ œ œ œ œ œ 120œ œ œ Rœ œ œÙtwo
œj œ 5 three beats="triple"
& 4Tuplets
ÔÔ 3 œ jœbeats="duple"
118
4.5
6
2
œ
œ
3
˙
˙
3 œ triplet
sextuplet
quintuplet
œ aœgrouping
œ œ œ ofœ notes
œ &œthat
œ 2œ œ œ œœ œœ œ œ œ ˙œ œ 44
8 œœwould
œœ œœœnot
&that4 describes
tie joins notes
together
Tuplet is a generic
term
to create a new duration
beats="triple"
four beats="quadruple"
twooccur
beats="duple"
sextuplet
triplet
quintuplet
normally
within three
a beat.
j
j
j
each
of
these
meters
is
"simple"
because the beats in each b
. œ =œ note˙ 3naturally
A ˙quarter
into
eighth
sixteenth
œ divides
˙˙two.. beats="duple"
˙ three
œ œnotes
œ œor four
= ˙ two
&
œ
2
˙
4
œ
œ
beats="triple"
four beats="quadruple"
120
œ
J œ occurs
notes.
& 8 Aœ triplet
œ œ œ is2 a œgrouping
œ œofj three
œ j œeighth
œ notes
4 œthat
œ˙ œ œ within
œ beats="duple"
œ œthe three beats="triple" four beats="
two
span ofdotthe
quarter
would
be123a grouping
of˙five sixteenth
second
dot
equals
half
of
equals
half of note. A quintuplet
2
œ
œ
3
˙
˙
j j44 œœ œ œœ œ œœ œ œœ œ
the
first
dot's
duration
theoccur
note's duration
&
8
œ
œ
œ
œ
2
œ
œ
œ
œ
œ
œ
. toœparts
. 9 œ . œ . œ . 12 .
notes each
to
within
the
span
of
one
quarter
note.
It
is
not
uncommon
see
slur
means
to
play
with
no
6
œ
of these meters is "simple" because the beats in each bar naturally divide into two
audible
the notes8 œ œ œ œ œ œ œ œ œ 4 œ̇ œ œ
&gap16between
œœœœœœ
quintuplets, sextuplets, and septuplets.
dot equals half of
the note's duration
123
118
36 œœj. œjœ. 9œ œœ. œ œœ. œ œ . œ œ12 œ˙ . œ œ ˙œ. œ œ ˙œ. œ œ ˙œ. œ œ
& 16
4 œœœœœœ
&
8 œ œ œ œ œ œ œ œj.œ j4. œ œ. œ œ. œ .œ œ œ œ .œ œ œ .
123
6 œœœœœœœ
œtriplet 98 œœ œ2œquintuplet
œœ œ œ œœ œ œœ 12
œ sextuplet
œ˙ œ œ ˙œ œ œ ˙œ . œ œ ˙œ . œ œ
&
16
4
&
4
each of these meters is "compound" because the beats in each bar naturally divide into three parts
each of these meters
"simple" because the beats in each bar naturally divide into two parts
fourisbeats="quadruple"
two beats="duple"three beats="triple"
3
5
each of 6these meters is "compound" because the beats in each b
126
four beats="quadruple"
two beats="duple"three beats="triple"
If you write a piece of music that naturally has a triplet division to the
3
beat, you should use 68 , 98 each
or 12
depending
on the number
of3beats
beats
in each
of
meters is "compound"
because the
in each
bar naturally divide into three parts
8 these
126
measure.
126
& 42 œ œ œ œ œ œ
&
120
3
3
& 68 œ œ œ œ œ œ
& 42 œ œ œ œ œ œ
3
3
128
œ
& 68 œ œ œ œ Inœ compound
a duplet is a grouping of two eighth notes to occur
6 œ meter,
œ œ œquarter
œ note and&a quadruplet is a grouping 9of
&span
8 of œa dotted
within the
Figure 4.5.1 Two measures that sound 127
the same
four eighth notes to occur with the span of a dotted quarter note.
127
128
4
& 4 4œ œ œ œ œ œ œ œ œ œ œ œ
127
6
& 8 œ128.
&
œ
œ
œ
œ
duplet
œ
œ œ œ9 œ
quadruplet
&4 œ œœœœœ œœ œ œœœ
2
4
4.6 Common Rhythmic Notation Errors
The standard practice when notating rhythms is to use beaming to show where
the beginning of each beat occurs.
Consider the following example:
4 4œ œ œ œœœœœ œœ œœ œœœ œ œ œœ œœ œ
& 4& 4J J
It is difficult to discern where the downbeats are.
downbeats?
?
?
?
?
?
?
4
4& 4œ œJ œ œœœœœ œœ œœ œœœ œ œ œœ œœ
downbeats?
&4 J
œ
Here is the same rhythm correctly notated. The downbeats provide a reference point, matching the conductor’s beat pattern or your tapping toe.
&
# 4
œ œ# œ œ œ œ œ œ œ œ œ œ
œ BASICS
œ
4 œ œ œ œ œ œ CHAPTER
œ
œ
4.
OF RHYTHM
œ
El - ean - or Rig - by,
# 4
& 4 œœ œ œ œ
picks up the rice
without syncopation
El - ea - nor Rig - by
156
130
158
in the church
1
9
where her wed - ding has been,
2
3
4
4œ
œ œ&œ 4 #œœ œœ œ# œœ œ œœ œœ œœ œœ œœ
w
22
œ wœ
picks up the rice in the church
where her wed - ding has been,
In compound meters like 68 , the beat is the dotted quarter.
6
& 8 &œ 44œ œJ œ œ œœœœœ œœ œœ œ œ œ œ œœ œ œœ. œ œJ
incorrect rhythmic notation
1
2
3
9
4
& 44 œ œ1 œ œ œ œ œ œ2 œ œ œ œ
?
?
?
correct rhythmic notation
1
2
downbeats?
& 68 &œ 44œ œœ œ œ œœœœœ œœ œœ œ œ œœ œ œœ œœ œœ. œ œ
J
131
44 œ œ œ œ œ œ œ œ œ œ œ
&
The exception to this practice of “showingJthe beats” involves syncopation.
Syncopation occurs when notes on weak beats and on weak parts of beats
are emphasized and nearby strong beats are deemphasized. Syncopation is
downbeats?
?
?
?
common in popular music.
2
3
Strong beats are the first beat of each measure (in 4 and 4 ) and beats 1 and
3 in 44 . Syncopation at the beat level involves ties across those strong beats.
Numbers in parentheses in the example below are beats that are obscured
through syncopation.
132
& 44 œJ œ œ œ œ œ œ œ œ œ œ
133
137
2
&4 œ
& 43 œ
& 44 œ
141
144
&
158
&
166
&
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
(1)
œ
œ
œ
˙
œ
œ
(1)
(3)
˙
œ
˙.
œ
œ
(1)
œ
˙
Syncopation can also occur at the division of the beat level. Below are two
syncopation figures that don’t show the beat but are acceptable because they
are common and to write them out correctly involves more symbols (beamed
eighths and ties) for the performer to comprehend.
4
&4 œ
141
œ
œ
œ
œ
˙
œ
(3)
CHAPTER 4. BASICS OF RHYTHM
144
exceptions to rhythmic notation rules
& 44 œJ œ
œ œ œ
J J
44 œ œ
J
œ
J
2-beat
syncopated pattern
146
œ
œ
(1)
œ
˙
23
œ
œ
J
4-beat
syncopated pattern
& 44 œ œ œ œ œ œ œ œ
44 œ œ œ œ œ œ œ œ
this "proper" rhythmic notation of the above syncopations is not required
An example of syncopation at the eighth-note level (the division of the
beat) can be found in the following example from “Eleanor Rigby.”
148
&
148
152
&
# 4
œœ
4 œ œ œ œ œ œ œ œ œ œ #œ œ œ
El - ean - or Rig - by,
picks up the rice
#
& 44 œ œ œ œ œ
without syncopation
El - ea - nor Rig - by
œœ œ œ œœ œœ
in the church
where her wed - ding has been,
œ œ œ œ #œ œ #œ
picks
up the rice
in the
w
œ œ œ œ œ w
church where her wed - ding has been,
Notice how syncopating notes gives them emphasis and creates a “pull”
incorrect rhythmic notation
against the rhythm
156 of the accompaniment.
6
& 8 œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ . œ œJ
4.7 Practice Exercises
1.
correct rhythmic notation
After listening to each example,
specify2 the meter (e.g.,
triple”).
1
1 “compound
2
158
(a) Lin-Manuel
Miranda, “First Burn”
6
& 8 œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ. œ œ
YT: r2ys-AimNbE
œ
Al Green,= Willie
Mitchell,
measured(b)
horizontally
"melodic"
intervalAl Jackson Jr., “Let’s Stay Together”
? 44 œ
J
160
œ ..
œ
#œ
# œ
J
#œ
œ œœ ..
# œ
œ
J
J
YT: uSu6tcbMOu0
˙
˙
measured
vertically
= "harmonic" interval
(c) Kenny
Kirkland,
“Dienda”
162
wFarjeon,w“Mornw
? w (d) Traditional
Scottish
w Gaelicw tune, wtext by Eleanor
w
w
ing Has Broken”
YT: ko1gUVP461A
perfect
unison
(P1)
major
second
(M2)
major
third
(M3)
perfect
fourth
(P4)
perfect
fifth
(P5)
major
sixth
(M6)
major perfect
seventh octave
(M7)
(P8)
YT: qH0iFkxQba4
submediant
leading
tone
dominant
subdominant
Guy Lawrence,
James Napier,
and Sam
Smith,
mediantHoward Lawrence,
tonic (e)supertonic
? w1̂
163
w
“Disclosure”
2̂
164
?w
tonic
w
3̂
w
w
5̂
4̂
w6̂
supertonic
mediant
dominant
subtonic
submediant
subdominant
b ww
ww
w
w
w7̂
46
˙. #œ
& # ˙˙ .. # œœ ‰ Œ ‰
p
? ˙. œ ‰ œ œ
nœ
f
# w
& # ˙˙
˙˙
2.
? 2142# # ˙
49
&
˙
&
19
YT: 93ASUImTedo
˙ ww
˙ ˙
œ
bb ˙ œ w œ ≈ ≈ b œr œ ˙
&
œ
˙ ˙
˙
˙
poco cresc.
˙˙
œ
˙
Ó
∑ ˙
∑
œ
œ #œ œ œ œ œ œ œ
∑ ˙˙˙ ∑ ˙˙˙˙˙˙∑ ∑˙˙˙˙˙ ∑ wwww ∑ ∑
ww
˙
n œœ
˙˙ ‰˙ ˙
J
‰
‰
˙˙
## ˙˙ ˙˙ ˙˙
15
15
Meter:
1. D minor
94
# œ
∑& œJ&
∑
˙‰ ˙
∑
∑
&b
∑
?
∑
25
b
113
115
∑
3.
? # ∑ ∑
6. F˜ minor
??
b
∑
Meter:
#
∑
‰
∑
4. D˜ minor
5. A¯≤ minor
œ
∑ # ∑ ∑Jn b œ ∑
&
p
23
œ
Mozart, K. 283, III, mm. 187-190
9. B¯≤ #minor
10. E minor
j ‰ j
n
‰ & œj ?
∑
œ
& œ œ b œœ
∑ p ∑ ∑
# 5. B¯≤ minor
& ∑
# ∑?
œ œœ
&
9. G˜ minor
10. A¯≤ minor
23
œ œ œ œ œ
˙
œ˙
7. A minor
11. E¯≤ minor
d. Time
∑ Signature:
∑
8. B minor
œœ
Meter:
∑
∑
12. C˜ minor
˙œ
b œœ
13. C minor
œœ
œœ
∑
14. D˜ minor
∑
Use one note value (with one or two dots as necessary) to show the sum
of all the rhythmic values given.
∑∑
∑
∑
Example
1.
2.
118
4.
?
‰
œ œ œ˙ œ # œ œ œ
œ
3.
119
œ œ
8. G˜ minor
∑
œœ œœ œœ œœ œœ
œœœœœ
? ## #
∑ ?
œ Corelli,
5, No. 1, mm. 12-15
œ Op. Op.
5, No. 1, mm. 12-15
J Corelli,
œ
˙
˙
˙
˙
˙
˙
˙
w
∑˙˙ ˙˙ ∑ ˙ ˙˙∑ ∑˙˙p˙˙ ∑w w∑ œ ∑œ œ∑n #
w
˙
˙
j
j
˙
‰
˙ œj Ó Ó n #
& œ Ó Ó œœ
˙ œ˙
˙œ˙
∑ p ∑ ∑ ∑ ∑ ∑ ∑ ∑
# œ ∑œ œ œ∑ œ
∑
###
#
n # ∑
&
3. F minor
‰
œ œ ≈ œ œ
Beethoven, Op. 110, III, mm. 124-125
2. E"Pavane
minorPassamaize"
3. A
˜ minor
4.Danceries,
G minor m. 7
Gervaise,
from
Sixième Livre de
&& b œ˙
∑
116
117
∑
1. F minor
24
109
#
∑
∑ œ
? Signature:
HWc. Time
104
&
∑
2. F˜ minor
œ # œ œ œ œ7. C minor
6. B minor
n œœ
?# œ
J
? 99# # ∑
24
‰
j
œœ
∑
œw œ œ .
œ
J 14
Ócresc.
p˙
&
œœœ œœœ œœœ œœœ # œœœ œœœ œœœ
Mozart, K. 283, III, mm. 187-190
∑Ó Ó
? b b œR≈≈Œ‰. . ∑ ∑ ∑? ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
b. Time Signature:
Meter:
89
19
rK
œ
? b œœ œœ œœ œœ œœ b œœœœ œœœ œœœ œœœ œœœ œœœ œœœ
b b n œœ œœ œœ œœ œœ
nœ œ œ œ œ œ
j
# œ
‰
œœ
& 51 œJ
# ww˙
b
& b4 œ ∑ ∑œ &&∑ # ## œ∑˙˙
#œ
œ
?# œ
? ##
?
#
& # ∑
24
œn œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ
f
∑ ?œ . # œ .
&
œ œœ #
œ
.
˙.
œ . n œ œœ
a. Time Signature:
19
∑
Op. 5, No. 1, mm. 12-15
For each example, specify the implied timeCorelli,
signature
and the meter (e.g.,
˙˙
˙˙
œ œ n#
˙duple”).
˙
“simple
˙
Ó
˙ w
˙
˙
##
Beethoven, Op. 57, I, mm. 78-80
CHAPTER 4. BASICS OF RHYTHM
15
? ## #
& ∑
14
2
∑ ˙ .. ∑= œ œ ∑œ ∑ œ œ œ ∑œ∑j
∑
=œ
=œ
œ œ
œ
∑
=œœœœœœ
=œ
œ œ œ
∑
∑
CHAPTER 4. BASICS OF RHYTHM
4.
5.
25
Specify the meter of each time signature.
(a) The meter of
4
2
(b) The meter of
9
16
(c) The meter of
3
4
is:
is:
is:
Correct the incorrect rhythmic notation in each example in order to show
the beats. The subdivisions grouped into beats are shown in parentheses11
above the rhythms to be corrected.
Example
1.
ã 43 œJ .
(œ œ œ œ œ œ œ œ œ œ œ œ )
2.
œ
ã 68 œ
6 œ˙
ã8
(
381
3.
œ
3 (œ œ œ
ã4 œ œ œ
(
379
Incorrect
œ
œœ
œ œ œ œ œ œ œ œ œ)
œ œ
œ œ
œ œ œ œ œ œ œ œ œ œ œ)
œ œ œ.
œ œ
œ
J
3 (œ
4
68 ( œ
œ œ 68
œ œ œ œ œ œ œ œ œ œ œ)
œ
(œ œ
43 œ .
Correct
œ œ œ œ œ œ œ œ œ œ)
œ œ.
œ œœœ
œ œ œ œ œ œ œ œ œ œ œ)
œ œ œ œ œ œ œ œ œ œ œ)
(œ œ œ œ œ œ œ œ œ œ œ œ )
Click here to download the homework.
versions of the textbook, homework exercises, and practice exercises
44 PDF
be found at musictheory.pugetsound.edu
ãcan
383
Chapter 5
10
10
148
148
152
152
# 4
Intervals
& # 44 œ œ œ œ œ œ œ
&
œœ
œ œ œ œ #œœ# œœ œ œ œ œœ œ œ œ œ œ œ w
œ
œ
œœ œœ w
4 Elœ- eanœ- or Rigœ - œby,œ œpicksœ upœthe rice in theœchurch whereœher œwed œ- ding
has been,
# 4 towithout
œ œ in# œthe œnextœ chapter,
In&order
œ œ œwe wwill focus
œ œ syncopation
œ œ ofœ œ#triads
44 œ prepare
œ forœ theœ study
#
#
œ
#
œ
primarily
on
major
and
minor
seconds,
thirds,
and
sixths,
œ
œ
œ
œ
œ œperfect,
œ
œ
œ
œ
& 4 - ea - nor Rigœ- byœ picksœ up the rice in the church where her wedand
œ been,wdimin- ding has
ished, andElaugmented
fourths and fifths. We will leave discussion
of augmented
El - ean - or Rig - by,
without syncopation
picks up the rice
in the church
where her wed - ding has been,
El - ea - nor
Rig - by
up the rice
the chapters
church whereon
herSeventh
wed - ding has
been, and
and diminished
sixths
andpicks
sevenths
forinthe
Chords
incorrect
rhythmic
notation
Augmented Sixth156Chords. We will return to Section 5.5 at that time.
incorrect rhythmic notation
156
6
& 86 œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ . .œ œJ
œ œ œ œ œ œ œ œ œ œ œœ œ œœ œœ
5.1 Introduction&to8 Intervals
J
correct rhythmic notation
1of scales,notation
2
1
2 melodies.
Intervals are the 158
building correct
blocks rhythmic
chords
(or harmonies),
and
Intervals are a measurement between
two
pitches,
either
vertically
1
2
1
2 or hori158
zontally. When measuring
vertically, we refer to harmonic intervals because
the two notes sound simultaneously. When measuring horizontally, we refer to
melodic intervals because the notes occur one after the other.
& 686 œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ . œ œ
& 8 œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ. œ œ
œ
œ
measured horizontally = "melodic" interval
? 44 œ
? 44 Jœ
J
160
˙
˙
˙˙
When you measure
fromvertically
the tonic=up
to each scale
degree of a major scale,
measured
"harmonic"
interval
you find the following intervals:
?
162
162
?
.
#œ
œ œœ ..
# # œœ œœ . .
#
œ
œ œ.
#
œ
J
J œœ œ .
# #Jœœ œœ .
#
œ
measuredJvertically = "harmonic"
J interval
J
measured horizontally = "melodic" interval
160
?w
w
perfect
unison
(P1)
w
major
second
(M2)
w
major
third
(M3)
w
perfect
fourth
(P4)
w
perfect
fifth
(P5)
w
major
sixth
(M6)
w
w
major perfect
seventh octave
(M7)
(P8)
163
All intervals in the example above are either “perfect” or “major.”
5.1.1 Numeric Size of Interval
There are two elements to naming intervals: the quality and the number (for
example, “major sixth,” abbreviated as “M6”). Let us first focus on the numeric size of intervals.
26
?
CHAPTER 5. INTERVALS
11
11
Odd-numbered intervals will always be a line to a line or a space to a space.
165
165
?
?
2
?
9
?
ww
3rds
3rds
ww
ww
5ths
5ths
w
w
ww
ww
w
w
7ths
7ths
w
w
Even-numbered intervals will always be a space to a line or a line to a space.
168
168
165
? w
w
?
ww
?
2nds
2nds
w
w
ww
ww
4ths
4ths
ww
ww
w
w
w
w
6ths
6ths
w
w
w
w
w
w
8ves
8ves
11
172
5.1.2
Interval
Quality: Perfect
172
5ths versus Major/Minor
7ths
3rds
168
ww
? ww
4
27
3rds
ww
174
2nds
ww
Intervals such as the unison, fourth, fifth, and octave can be classified11
as
“perfect” but never “major” or “minor”. Conversely, the intervals of the
second, third, sixth, and seventh can be major or minor but never perfect
in quality.
? ww ww
ww ww
185
185
2nds
ww4ths
w Perfect Intervals:
?
172
Major or Minor Intervals:
?
w
w
w
w
w
w
6ths
w
w
w
w
Unison, 4th, 5th, 8ve
2nd, 3rd, 6th, 7th
bw
w
w
w
8ves
w
w
w
#w
Perfect intervals5ths
are always natural to natural, sharp
to sharp, and flat to
7ths
4
flat except for the fourths and fifths between B and F, which involve B to F
2
192 B to F.
192
and
M7
m7
M7
m7
?
w w
?w b w # #www
bw
?
199
199
?
4ths
?
?
206
206
?
199
n b ww # n ww
perfect fourths
177 Minor
172
w
w
w
w ww
w# # ww b b ww b n ww
perfect fifths
6ths
exceptions between B and F
w
w
bw
w
#w
n w
wb w w n w
wb w ## www n w
w
w
w
#w
perfect octaves
8ves
intervals are one half step smaller than major intervals.
M7
m7
M7
m7
5.2 How to Identify Perfect, Major, and Minor
Intervals
206
?
Here are two methods for identifying intervals.
The first method involves thinking of the lower note of an interval as the
tonic (the first note of the scale). Remember that all the notes above the tonic
in a major scale are perfect or major. Determine if the upper note is in the
major scale. If it is not, determine if the interval is a half step smaller than a
major interval, in which case it is a minor interval.
? b w # # ww n b ww # n ww
bw
174
#w bw nw #w
# w bw bw n w
CHAPTER 5. INTERVALS
exceptions between B and F
28
bw
w
&
177
bw #w nw
bw #w nw
Interval: m7
quality
size
(P, M, m) (number)
178
think of lower
note as tonic
179
&
w
b w7
œ
œ
& w
1
both notes are on spaces,
so count in odd numbers to
determine the numeric size
of the interval
(3) (5)
E¯≤ is not in the F major key signature,
so the interval is not major
œ œ
œ œ œ Aœ œ
key signature of F major
180
&b
m7
E¯≤
E
F
M7
If the lower note of an interval has a sharp or flat on it, cover up the
accidental, determine the interval, then factor the accidental back in.
12
#w
& #w
182
Interval: ?7
186
&
#
#w
w
cover sharp on lower
note to think in G major
instead of G˜
#
w
w
#w
#w
F˜ is in G major, raising G to G˜ makes
so this is a M7
this a half step smaller,
therefore it is a m7
The second method is to memorize how many half steps there are in each
interval. To determine the size of an interval, count the number of half steps
between the two notes then refer to your memory.
Number of half steps
1
2
3
4
5
6
Name of interval
m2
M2
m3
M3
P4
Tritone∗
Number of half steps
7
8
9
10
11
12
Name of interval
P5
m6
M6
m7
M7
P8
∗ A “tritone” is a generic name for an augmented fourth ( + 4) or diminished
fifth ( ◦ 5). These two intervals are enharmonic. Augmented and Diminished
Intervals are discussed later in this chapter.
#w
& #w
#w
w
#
CHAPTER 5. INTERVALS
w
w
#w
#w
29
8
9 10
bcover
w sharp on lower1 so2 this3 is a4 M7b œ5 n œ6thisœ7a bhalf
bw
step
smaller,
œ
n
œ
& notew to think inwG major
bœ nœ bœ nœ
therefore it is a m7
instead of G˜
counting half steps
186
Interval: ?7
F˜ is in G major,
raising G to G˜ makes
10 half steps = m7
5.3 How to Write Perfect, Major, and Minor Intervals
counting half steps
#w
& #w
#w
1 #2
3 w 4 5 6 7 8 # w9 10
b
w
bw
b œ given
nwœ below.
To write an intervalwabove a given note,w
use the
two
methods
#
œ
b
œ
n
œ
b
œ
n
œ
&
n œ sixth above the note A, start with the A
w asked to write
w b œa minor
If you are
186
4 G to G˜ makes
G major,
major scale and key signature. F˜
In is
A in
major,
there is raising
an10Fhalf
, which
steps is= am7major
6
cover sharp on lower so this
M7 sixth
thisabove
a halfA.step smaller,
sixth above the note A. Therefore,
F isisa aminor
Interval: ?7
12
note to think in G major
instead of G˜
188
& w## ww
&
182
###
?
m6 up = ?
&
w
#ww
w
#
w
w
M6 up is F#, according
F˜ is in G major,
to
A Major
key so
signature
cover sharp
on lower
this is a M7
Interval: ?7
186
therefore it is a m7
bw
w
Nw
#ww
#w
m6
above A = F
raising G to G˜ makes
œ bœ nœ bw
w bœ nœ bœ nœ bœ nœ
counting half steps
note to think in G major
this a half step smaller,
therefore
is10
a m7
Alternatively, you can simply
know
1 2count3 the4number
5 of
6 half
8
9Ifityou
7 steps.
instead of G˜
there are 8 half steps in a minor sixth, you can count from A up to F.
Writing small intervals up to a major third below a given note is straightforward using a combination of whole and half steps. However,
to write
10 half steps
= m7larger
intervals below a given note, it is sometimes helpful to invert the interval first
186
(Inversion
of Intervalscounting
Explained
is discussed in the next section).
half steps
1 2
3 4 5 6 7 8
bw
b œ n œ9 b10w
œ
b
œ
n
œ
b
œ
n
œ
#
& #w
nwœ
Nw
w b œ Explained
5.4 Inversion
of# Intervals
10
half
w
w
wsteps = m7
&
188
?
There are
an up
interval,
one lower and onem6
higher.
m6188only
up = two
? notes inM6
aboveTo
A =invert
F
is F˜, according
an interval, change the position
of
the
notes
so
the
note
that
was
lower
is now
?
to A Major key signature
higher.
w
& w
m6
&w
w
m6 up = ?
w
###
w
ww
w
M6 up is F˜, according
to A Major key signature
w
& Awis below wF
w
ww
M3
w
Nw
w
m6 above A = F
w
A is above
w F
w
In the above example,
to a FM3. ThisM3
is true for
notes
m6a m6 inverts
A is below
A isall
above
F a M3
(or m6) away from each other. Below are examples of how intervals invert.
195
& b ww b ww ww
m2
201
&
210
&
M7 M2
w b ww w ww
bw
w
m7
m3
M6
M3
w ww
w
m6
P4
ww # ww # ww
P5
°4
+5
Note that the symbol ◦ represents “diminished” (one half step smaller
than perfect or minor) and the symbol + represents “augmented” (one half
step larger than perfect or major).
Below is a chart of how intervals invert.
CHAPTER 5. INTERVALS
30
(larger)
Augmented
HowMinorIntervals
Invert
Major
Perfect
(smaller)
Diminished
203
&
8
7
6w
#w
5
m3
diminished
third
b ww
m
P
°
‹
# ww
+3
M3
minor third
augmented
third
major third
ww
º4
&
M
P
+
#
# ww
# ww
+4
P4
To write a small interval below a given note, you should be able to combine
whole steps and half steps up to the interval of a perfect fourth (two whole
fourth
steps plusdiminished
one halffourth
step). To write perfect
a larger
interval belowaugmented
a given fourth
note, invert
the interval size, determine the note above, then write it below the given note.
210
& w
202
º3
&
207
214
1
2
3b w
#w
4
&
w
w
?
invert interval:
m7 down = M2 up
#w
w
M2 above E is F˜
m7 down = ?
w
#w
m7 below = F˜
5.5 Augmented and Diminished Intervals
A is above F Augmented intervals are one half step larger than perfect or major intervals
219
&
and diminished intervals are one half step smaller than perfect or minor
intervals.
Remember that perfect intervals (unisons, fourths, fifths, and octaves) can
never be major or minor, and major and minor intervals (seconds, thirds,
sixths, and sevenths) can never be perfect in quality. However, any size of
interval can be augmented or diminished.
(larger)
Perfect
(smaller)
Diminished
Minor
Augmented
Major
Here are musical examples illustrating the continuum of interval quality.
202
&
13
Diminished
203
&
# b ww
º3
Minor
CHAPTER
5. INTERVALS
diminished
144
207
ID # only
& &
150
203
210
&
6
156
ID # & Qual
&
wwbº4w
w &
202
3
Ex. ____
# b ww
1. ____
diminished
w
& third
w
w
w
2. ____
# ww
w +4
w # ww
ww P4
ww ? ww
1. ____
diminished fourth
& wwº3
w
w
2. ____
3. ____
ww
#4.# ww____
# ww
minor third
2. ____
3. ____P4
13. M3↑
Incorrect
14.
m2↑
31
w
w
5. ____
w
w
augmented fourth
? ww
M3
# ww 3. ____
m3
augmented
third
4. ____
perfect fourth
1. ____
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called a chord as well as a harmony. (Harmony also refers to chord progressions.)
invert interval:
45
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The lowest ?note
a triad
The middle note is the third and the highest note of the triad is the fifth. (We
m7 below = F˜
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6.2 Lead-Sheet Symbols
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&
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b
51
Lead-sheet symbols (also known as “lead-sheet notation” and “lead-sheet
chord symbols”) are often used as shorthand for chords in popular music and
jazz. These symbols allow a guitarist or pianist to choose how to “voice” the
chords, i.e., how they want to arrange the notes.
52
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CHAPTER 6. TRIADS
33
Lead-sheet symbols for triads communicate the root and quality of a chord.
44
44
Lead-sheet Symbol
F
Gm
D◦
C+
Chord Quality
major
minor
diminished
augmented
Notes in the Chord
F–A–C
2
G–B –D
2
D–F–A
4
C–E–G
Here is a musical example with lead-sheet symbols and guitar tablature.
A
A
422
422
422
422
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Fire”
426 (2012)
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As#you
#
&
&
uppercase
letter ( A , E , and D ) while minor triads are represented with the
4
root in uppercase followed by a lowercase “m” (e.g., F m ). Diminished triads
#
?
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are?represented
by including the diminished symbol ( ◦ ) after the chord root
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426
426
symbol after the root ( C+ ).
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CHAPTER 6. TRIADS
34
Sara Bareilles
"Love Song"
6.3
Gm
F/A
B bsus2
Inverted
Triads
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67
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An inverted triad does not have the root as the lowest note. It is important
to distinguish between root and bass. The root of a chord is the lowest note
when the notes are stacked in thirds. The bass is the lowest note, which might
be the root, third, or fifth.
A triad is in “root position” when the root is the lowest note, “first inversion” when the third of the chord is the lowest note, and “second inversion”
when the fifth of the chord is the lowest note.
71
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(also Csus9)
(also Csus)∑
∑
∑
6.3.1 "Slash" Chords
Fifth
Fifth
Fifth
In lead-sheet notation, an inverted chord has the triad before the slash (/) and
the bass note after Third
it. “ C/E ” means a C triad with Fourth
an E as the lowest note.
Second (or
∑
∑ note that is not the root of∑ the chord. In
Therefore,
a slash chord has a bass
Root
Root
Root
fact, it is possible to
.have slash chords where the bass note is not one of the
C Major
root of chord is lowest note
77
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slash
chord
C/E
bass note
Remember, in a slash chord, the first letter you see represents the root of
the chord. The letter after the slash is the lowest note (the bass).
Lead-sheet Symbol
F/A
Dm/A
. 2
G◦ D
. 4
C+ G
Root of Chord
F
D
G
C
Notes in the Chord
F–A–C
D–F–A
2 2
G–B –D
4
C–E–G
Bass Note (Lowest Note)
A
A
2
D
4
G
˙
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474
CHAPTER 6. TRIADS
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6.4 Analyzing Chords
When a three-note chord is represented by four or more notes (some of which
are duplicates of the original three notes) and spread out across a grand staff,
we can arrive at a lead-sheet symbol by answering three questions:
˙˙
˙
˙˙˙
˙˙
1. What is the root of the chord?
2. What is the quality of the chord (i.e., is the chord major, minor, diminished, or augmented)?
3. What is the bass note (i.e., is the chord inverted)?
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476
476
Lead-sheet:
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You could also choose to write all the notes only on the spaces in a staff.
401
Subphrases:
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To determine the root of the chord, write all the notes only on the lines of the
staff in treble clef (you may need to use ledger lines).
22
410
35
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12 3
The bottom note is the root when the chord is stacked as a triad. In this
case, the root is D.
Next, determine the quality of the triad (major, minor, diminished, or
augmented) by analyzing if there is a M3 or m3 from the root to the 3rd, and
D
F
if there is a M3 or m3 from the 3rd to 5th.
12 3
D
F
#
1 2 34
F
A
Since there
411is a m3 (3 half steps) from D to F and a M3 (4 half steps) from
F to A, the triad is minor.
Finally, determine if the chord is inverted by checking to see if a note other
than the root is the lowest note. Since the bass note (lowest note) is the root
&
411
&
#
V
D
CHAPTER 6. TRIADS
36
35
D, the chord is not inverted. The chord is in root position,
so the lead-sheet
symbol is Dm .
Now, try the process again.
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478
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Lead-sheet:
22
___
___
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On scratch paper, stack theSubphrases:
notes only on lines in the treble clef to determine the root.
Motives:
411
479
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The root is E.
Analyze the quality of the triad by measuring from E to G and from G to
2
B.
492
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∑
∑
∑
∑
&
&
478
411
∑
∑
∑
E
G
∑
D
F
35
1 2 34
It is an E diminished triad ( E◦ ).
Finally, determine if the chord is inverted. Is the root (E) the lowest note?
499
?
12 3
B¯≤
∑
∑
w
bw
bw
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w
F
A
∑
Since the lowest note is G, the chord is inverted. Our lead-sheet symbol is
E◦ /G , which means we have an E◦ chord with a G in the bass.
506
479
&
6.5 Simple “Sus” Chords
? ∑ ∑ ∑
∑ ∑ ∑
Common in popular music are “sus” chords, with “sus” being a shortening of
“suspended,” a term we will study in the chapter on non-chord tones.
The two basic sus chords are the sus4 and sus2 chords. In the sus4 chord
(also labeled simply as “sus”), a perfect 4th replaces the 3rd of the chord. In
the sus2 chord (sometimes called “sus9”), a major 2nd replaces the 3rd of the
chord. Both of these sus chords have a perfect 5th from the root to the fifth.
∑∑ ∑
∑
∑ ∑∑
∑
∑
∑
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∑ ∑ ∑
∑
∑
492
&
?
∑
∑
i
iv
V
CHAPTER 6. TRIADS
59
222
59
63
63
65
65
67
67
71
71
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254
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242
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242
260
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2.
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272
290
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284 298
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EXER
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290
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302
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326
103
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2. ____
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and
sus chords.
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ww
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6. Gº/D¯≤
7. Dº/F
b b www
6. ____
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## w‹ www
w
12. ____
5. ____
____
18.
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6. ____
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18. ____
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&
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b
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∑
b # www∑
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____
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303
&
290
98
?
5. ____
sheet notation. All of the examples are in root position (the lowest note
9
is the root).
296
278
311 308
# ww
38
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b ww ?
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b www
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b
b
b
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10. ____
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2. ____
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____
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6.7 Practice
Exercises
1. Bm
2. E+
3. A¯≤sus2
254
272
79
b www
Correct
2. ____
Click here to download the homework.
Click
& here to download the Unit 1 Practice Test.
∑b # www
∑
Incorrect
Correct
∑
∑
3. ____
∑ &
∑
∑
∑
∑
∑
∑
∑
∑
∑
&
&
Chapter 7
Roman Numerals and Cadences
7.1 Roman Numeral Chord Symbols
Music is full of patterns that are similar from one piece to the next. As we
saw with minor scales, we were able to use scale degree numbers to show
the different patterns for harmonic, melodic, and natural minor, despite the
fact that there are 15 minor key signatures. Using numbers instead of note
names helps us see these patterns. Thinking of music in terms of numbers is
also helpful with transposition, which means moving melodies and/or chord
progressions from one key to another. Thinking of music in terms of numbers
also helps us to analyze it and to spot similar patterns between many different
pieces in different keys.
We will use Roman numerals to represent chords within a specified key.
The Roman numeral “ I ” represents a triad built on 1̂ , or the 1st note of the
scale. Uppercase Roman numerals represent major triads and lowercase Roman
numerals (e.g., “ i ”) represent minor triads. Uppercase Roman numerals with
a “ + ” are augmented (e.g., “ III+ ”), and lowercase Roman numerals with a
“ ◦ ” are diminished (e.g., “ vii◦ ”). (There is also the Nashville Number System,
which uses Arabic numbers for chords instead of Roman numerals.)
Key
Lead-Sheet
G 230 Bm
f
G◦
2
c
E
&
Root
Scale Degree of Root
Roman Numeral
B
G
2
E
3̂
2̂
3̂
iii
ii◦
III
Notes15in Chord
4
B–D–F
2 2
G–B –D
2
2
E –G–B
For inversion of Roman numerals, we will use a modified “slash chord”
notation until we study Figured Bass. For now, we will write “ I /3rd” if the
3rd of the I chord is the bass note, for example.
G: ii/5th
C: I/3rd
the 3rd of the I chord
(C-E-G) is in the bass
the 5th of the ii chord
(A-C-E) is in the bass
The following table offers more examples.
31
&
39
CHAPTER 7. ROMAN NUMERALS AND CADENCES
Key
14
Roman Num.
g
a
222
D
Root
Scale Deg. of Root
V/3rd
D
iv/5th C MajorD
4
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ww
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5̂
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Fourth
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www
&
Third
Root
40
Notes in Chord
4
D–F –A
Csus2
D–F–A
(also
4 Csus9)
C –E–G
Fifth
Bass Note
4
F
A
E
ww Second (or Ninth)
w
& Root
7.2 Diatonic Chords in Major
slash
Observe the pattern ofchord
diatonic chords in major represented by Roman numerals. (Diatonic means notes within a key signature and can be contrasted
with the term “chromatic.”) One C/E
sees the pattern M-m-m-M-M-m- ◦ in triad
bass note
quality.
Lead-sheet symbols
225
Dm
Em
F
G
www
Am
www
Bº
I
ii
iii
IV
V
vi
viiº
& ww
w
C:
ww
w
C
ww
w
www
www
Roman numerals
(require key designation)
226
&
240
&
Figure 7.2.1
7.3 Diatonic Chords in Minor
248
&
Because there are three versions of the minor scale, there are more than seven
diatonic chords in minor. The sixth and seventh scale degrees affect all of the
triads except the tonic, making 13 possible diatonic triads in minor.
C:
I
ii
iii
IV
V
vi
viiº
Roman numerals
(require key designation)
CHAPTER 7. ROMAN NUMERALS
AND CADENCES
226
227
NATURAL MINOR
Am
Bº
& ww
w
a:
i
iiº
HARMONIC MINOR
Am
Bº
& ww
w
a:
228
i
www
iiº
MELODIC MINOR
Am
B
& w
ww
a:
i
# www
ii
rare
www
www
wwwG
v
VI
VII
ww
w
E
# www
F
# www
www
C
Dm
III
iv
www
www
# www
C+
Dm
III+
iv
rare
# ww
w
C+
Em
# www
V
ww
w
VI
viiº
# www
# www
# www
G˜º
˜viº
V
rare
G˜º
F˜º
E
IV
rare
F
rare
D
III+
41
viiº
rare
Most Commonly Used Chords (Roman numerals) in Minor
from the natural minor scale
229
Am
Bº
C
Dm
# www
ww
w
n www
i
iiº
III
iv
V
VI
VII
& ww
w
a:
www
www
ww
w
E
F
G
# www
G˜º
and viiº
from the harmonic minor scale
Figure 7.3.1
However, when one analyzes a large amount of tonal music, one finds the
following Roman numerals are most commonly used in minor.
& w
ww
Am
B
# ww
w
D
# www
# www
F˜º
# www
# www
# ww
w
C+
E
G˜º
CHAPTER
7. ROMAN
NUMERALS
AND CADENCES
a:
i
ii
III+
IV
V
˜viº
rare
rare
rare
42
viiº
rare
Most Commonly Used Chords (Roman numerals) in Minor
from the natural minor scale
229
Bº
C
Dm
i
iiº
III
iv
& ww
w
a:
ww
w
Am
www
www
# www
ww
w
n www
V
VI
VII
E
F
# www
G˜º
G
and viiº
from the harmonic minor scale
Notice that both VII (the “subtonic triad”) and vii◦ (the “leading-tone
triad”) are included. The subtonic triad ( VII ), built on the lowered 7̂ that
occurs in natural minor, regularly occurs in circle of fifth progressions in minor
and in rock and pop music, while the leading-tone triad ( vii◦ ), built on raised
7̂ , is usually either a passing harmony or has dominant function.
7.4 Cadences
We’ve been studying harmony—triads and chords. A cadence is a harmonic
arrival point, a harmonic moment of stasis. A cadence can be compared to
a comma or period in written language—the ear gets a moment to process a
short passage of music, then the music continues. We will differentiate between
four basic cadences now, adding more specificity in a later chapter.
1. Authentic Cadence (AC): a phrase ending with the chords V – I
2. Plagal Cadence (PC): a phrase ending with the chords IV – I
3. Deceptive Cadence (DC): a phrase ending with the chords V – vi
4. Half Cadence (HC): a phrase ending on the V chord
? ###
j
œ.
œ œ
œ
w
CHAPTER 7.
ROMAN NUMERALS AND CADENCES
.
œ
w
43
Francis Scott Key and John Stafford Smith
7.4.1
Examples
of Authentic Cadences
"The Star-Spangled
Banner"
F
b 3
&b 4 œ œ
5
O'er the
b
& b 43 œ œ
5
B b/D
œ.
B b/D G m C ø7/G b B b/F
œ œ (œ ) ˙
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j
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land
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b 4 œ œ
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F Bb
free
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and
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J
home
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brave!
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œ
J
œ bœ
œ bœ
j
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the
Bb
F7
˙˙
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˙
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V7
I
authentic
cadence
YT: LGvW6jHUHiY
Figure 7.4.1 Francis Scott Key and John Stafford Smith, “Star-Spangled
Banner”
In the example above, the notes surrounded by parentheses are non-chord
tones, which will be studied later. Also, there are seventh chords in this example, which we will study in the next chapter.
Here is another example ending with an authentic cadence.
2
"I Want to Hold Your Hand"
C#
F#
D #m
Lennon–McCartney
C#
F#
## #
œœ
œ œ . œ œ . œ œ œ œ Œ ‰ œJ œ œ œ
V # # # 44 ‰ J œ œ
œ ˙
B
10
# ## # 4
& # # 4 ‰ œj œ Œ
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? # # # # # 44
j
#
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I want to hold your
10
F˜: IV
V
œœ
œ
j
œ
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j
œ. œ œ.
B
hand,
I
vi
14
Œ œ ‰ œj œ Œ œ
œœ œœ œœ œœ
I want to hold your hand.
‰j
œœ œœ
œœ
œœ
œ
j
œ
"Just Give Me a Reason"
G
14
œ.
IV
j
jœ
œ œœœ œ
œ œ. œ
V
I
authentic
cadence
Pink, Jeff Bhasker, Nate Ruess
Em
# 4 œ œ œ . œ œ œ YT:‰ jenWdylTtzs
j œ œ œ œ œ œ Œ ≈
V
4
œ
œ
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Figure 7.4.2R Lennon-McCartney, “I Want to Hold Your Hand”
C
4 ≈
7.4.2 #Examples
of Plagal Cadences
I
& 4
let you see the parts
œœ ..
of me that weren't all that pret - ty
j
œœ œœ œ œ œ ˙˙˙
œ ˙
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œ
G: I
# œ.
C
V
œ
˙˙
IV
œ
J
œ
( )
œ
And with
œœœ œ
Here are examples with plagal cadences.
17
Ó
vi
œ
( )
G
œ
Œ
Score
CHAPTER 7. ROMAN NUMERALS AND CADENCES
Lyrics: John Newton, Harriet Beecher Stowe
Tune: "New Britain" (traditional)
G
C
G
Lennon–McCartney
"Amazing Grace"
2
C#
F#
D #m
B
C#
F#
## 3
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V
˙ ˙.
˙
˙
"I Want to HoldG/B
Your Hand"
Em
B
10
7
&
#
?#
18
&
#
?#
18
27
&
#
?#
27
G/D
Was
∑
∑
∑
14
∑
∑
17
∑
#
& 44 ≈
I
∑
∑
∑
∑
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I
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Figure 7.4.4 Pink, Bhasker, and Ruess, “Just Give Me a Reason”
Œ
∑
∑
∑
∑
CHAPTER 7. ROMAN NUMERALS AND CADENCES
"Take Me to Church"
19
#
j œ
V 43 œ œ œ œ œ œ œ œ ‰ œ . œ œ œ œ œ ‰Œ œ œ œ . œ œ œ ≈Œ œ b œ œ . œ œ ‰Œ
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B¯≤: I
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19
45
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Wolfgang Amadeus Mozart
7
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Figure 7.4.6 Mozart, The Marriage of Figaro, “Voi che sapete”
3
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CHAPTER 7. ROMAN
NUMERALS
AND
CADENCES
w
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"True Colors"
Kelly and Billy Steinberg
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33
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33
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Figure 7.4.8 Wagner, Tristan und Isolde, Prelude to Act I
A deceptive cadence means V did not go to I . This means that “ V to
not- I ” is technically a more correct description for a deceptive cadence than
V - vi , which is the most common realization of “ V to not- I .”
In the example below, V goes to IV/3rd .
Wolfgang Amadeus Mozart
CHAPTER
7. ROMAN
NUMERALS
AND CADENCES
47
Ave
Verum Corpus,
K. 618 (textural
reduction)
100
100
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108
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7.4.4
Examples
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"Eine kleine
Nachtmusic,"
525 (reduction)
D
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œ œ œ œ œ #Aœ œ œ œ œ œ œ œ #Aœ
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# œœœ œ œ œ œ Œ
E m7/G
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K.I/5th
618
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#
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ii7/3rd
V
V
7
Wolfgang Amadeus Mozart
A
A
half cadence
(phrase ends on V)
œ œ œ œ œ œ œ# œ œ œ œ œ œ œ œ œ œ œ œ œ œ Œ
œœœœ
half cadence
(phrase ends on V)
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Figure 7.4.10 Mozart, Eine kleine Nachtmusik, K. 525, I.
7
C: IV/5th I
w
IV/5th I
vi7
Vsus
V/3rd
I
œ ˙
IV
deceptive cadence
CHAPTER 7. ROMAN NUMERALS AND CADENCES
33
# 4 œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œœ œ œ œ œ ˙
Œ
V # 4
E m7
G
A
Bm
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me I fall in lovewith you ev - 'ry sin-gle day
33
48
Ed Sheeran and Amy Wadge
"Thinking Out Loud"
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& # 44 ˙
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half cadence
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Figure 7.4.11 Sheeran and Wadge, “Thinking Out Loud”
You may encounter chords with no thirds in rock and pop music. If you
encounter a chord that has only a root and fifth, label it with a “5” after the
root in lead sheet labeling (e.g., B5 , as in the next example).
Additionally, you may encounter incomplete chords, which are chords
containing only the root and third but no fifth.
5
CHAPTER 7. ROMAN NUMERALS AND CADENCES
49
"Love Yourself"
Justin Bieber, Benny Blanco, and Ed Sheeran
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∑
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∑
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1. Label the following chords with lead sheet symbols (above) and Roman
?numerals
4
(œ œ œ œ œ œ œ œ œ œ œ œ )
b b b3b (4œ œœ (below).
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2
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b
n
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1
379
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381
3.
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Given the Roman numeral and key, write the key signature, notate the
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CHAPTER 7. ROMAN
NUMERALS AND
w
w CADENCES
3.
ww
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Thomas a’Becket, “Columbia, the Gem of the Ocean”
"Columbia, the Gem of the Ocean"
130
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David T. Shaw
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Bob Marley, “Could You Be Loved”
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Bob Marley
"Could You Be Loved"
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Chapter 8
15
Seventh Chords
230
&
8.1 Introduction to Seventh Chords
G: ii/5th
C: I/3rd
A seventh chord adds to a triad another note a third higher than the fifth.
Chords, being the
built3rd
in thirds,
members that are odd
fifth,
of the Ihave
chord
the numbers—third,
5th of the ii chord
seventh, and we
will
eventually
discuss
extensions
of
the
ninth,
eleventh,
and
(C-E-G) is in the bass
(A-C-E) is in the bass
thirteenth. The fifteenth would be the double octave, so chords only extend as
high as the thirteenth.
15
230
root
Rt
231
& fifth
third
3rd
& w
w
seventh
7th
5th
230
ninth
9th
C: I/3rd&
w
w
w
w
w
eleventh thirteenth
11th
13th
15
(this
is for later)
G:
ii/5th
In classical and popular
music,
there are five types of
chords
comthe 3rd of
the I chord
theseventh
5th of the
ii chord
monly encountered: (C-E-G) is in the bass
(A-C-E) is in the bass
232
&
G: ii/5th
C: I/3rd
• the major seventh
chord
• the major-minor the
seventh
(also known as a dominant
seventh
chord)
3rd ofchord
the I chord
the 5th of
the ii chord
root
third
fifth
seventh
ninth
eleventh thirteenth
(C-E-G) is in the bass
(A-C-E) is in the bass
• the minor
Rt seventh
3rd chord 5th
7th
9th
11th
13th
• the&half-diminished seventh
w chord w
231
w
w
w
w
9th
11th
w
(this
is for later)
root
third seventh
fifth
ninth
eleventh
thirteenth
• the fully-diminished
chord seventh
(often called
diminished
seventh
chord)
231
232
232
Rt
3rd
5th
& w
w
w
b www
& wwww
w m7seventhm
Full name: M major
seventh
major-minor
M7
M
Full name:
major seventh major-minor seventh
Primary abbrev:
maj7
7
Other labels: Maj7, Δ7, MM7
Mm7, Dom7
7th
w
minor seventh
m7
-7, mm7
Primary abbrev:
triad
maj7
7
triad
triad
Other labels: Maj7, Δ7, MM7
Mm7, Dom7
b www
bminor
w seventh
m7
m7
-7, mm7
Lead-sheet symbols:
237
&
242
&
242
&
w
13th
b b b wwww
b b ∫ wwww
(this is for later)
half-diminishedm7
seventh fully-diminished seventh
º
º
º7
ø7
triad
triad
º7
b
m7( 5), -7(-5), dm7
dim7, dd7
C7
Cm7
Cø7
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b www
b www
b www
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b
b
b
b
b
Another way Mw
typesb w
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m bw
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m7
m7
M3M7
m3
M3
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º b ∫ w
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triad
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m3
M3
m3
b
triad
triad b w
triad b w
learning howtriad
thirds
are
in
each
one.
w stacked
w
m3
m3
M3
m3
M3
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8.1.1
Lead-sheet
symbols
: Cmaj7
237
w
w
half-diminished seventh fully-diminished seventh
ø7
º7
m7( b5), -7(-5), dm7
dim7, dd7
Cmaj7
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w
M3
m3
M3
C7
b www
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Cm7
m3
m3
M3
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m3
M3
m3
b b b wwww
Co7
M3
m3
m3
b b ∫ wwww
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m3
m3
CHAPTER 8. SEVENTH CHORDS
52
In later chapters we will discuss other seventh chords built on augmented
triads and minor triads.
8.2 The IV/5 “sus” chord
An additional four-note chord that sounds like and functions similar to a V7
chord is the IV /5̂ (or F/G in C major) chord. In popular music this chord
often is substituted for the V7 chord
16
F/G
244
or
F
w
w
major
& w
w basstriad
note is G
G9sus4
www
w
a variant: Dm7/G
or
www
w
w
sus4
9th
7th
Root
2
Here is a musical example with the IV /5̂ chord in A major.
248
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Another example of this chord is found in the opening to the Beatles’ “The
Long and Winding Road”. In the key E2 major, the chord is A2/B2.
G9sus4
www
w
w
230 3rd of the I chord
the
(C-E-G)
& is in the bass
the 5th of the ii chord
(A-C-E) is in the bass
CHAPTER 8. SEVENTH CHORDS
231
53
root
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fifth
seventh
ninth
eleventh thirteenth
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C: I/3rd
Rt
3rd
5th
7th
9th G: ii/5th
11th
13th
Figure 8.2.2 Beatles, “The Long and Winding Road”
& w
(C-E-G) is in the bass
w
w
w
w I chordw
the
w 3rd of the
the 5th of the ii chord
(A-C-E)
is in the bass
(this
is for later)
8.3 Roman Numerals of Diatonic Seventh Chords
232
231
237
232
242
Full name:
major seventh major-minor seventh minor seventh half-diminished seventh fully-diminished seventh
ø7 there are a few 7conWhen notating
seventh7 chords with m7
Roman numerals,
Primary abbrev:
maj7
º
b
Other labels:
Maj7,
Δ7,
MM7
Mm7,
Dom7
-7,
mm7
m7(
5),
-7(-5),
dm7
dim7,
dd7a
ventions to follow. An uppercase Roman numeral means
a major
triad
and
ww
ww
&
&
w
www
w
& wwww
&triadwwww
maj7
&
Lead-sheet symbols:
C
C: IM7
237
243
242
244
&
243
b ww
ww
bw
b www
w
b b b wwww
b b ∫wwwww
root Roman
third
lowercase
numeral fifth
means a seventh
minor triad.ninth
Addingeleventh
“7” after thirteenth
a Roman
Rt means 3rd
5th seventh
7th between9th
13th
numeral
there is a minor
the root 11th
and seventh
of the
7
m
M
M7
chord. Therefore, V
M means
m7 a major triad
m7 withºa minor seventh
m7
º between the
º7
triad
triad vi7 means
triad
roottriad
and seventh and
a minor triadtriad
and a minor seventh
between
the root and seventh. Add “M7” for a major seventh chord
(e.g.,
IM7 ). The
(this
is
for
later)
maj7
7
m7
ø7
o7
Lead-sheet symbols
: C
C ( ø7 ) means C
C triad with a C
half-diminished
symbol
there is a diminished
minor
seventh
rootmajor-minor
to seventh.
Theminor
diminished
symbol ( ◦7 )seventh
on a seventh
chordseventh
Full name:
majorfrom
seventh
seventh
seventh
half-diminished
fully-diminished
m3
m3
M3
m3
M3
means maj7
the triad
is diminished
from the
ø7 root
Primary abbrev:
m3
m3 and the
M3
m3 to seventh
7
m7distance
7 is am3
º
m3
m3
M3
m3
M3
Other labels:
Maj7, Δ7, seventh.
MM7
Mm7, Dom7
-7, mm7
m7( b5), -7(-5), dm7
dim7, dd7
diminished
Below are the diatonic seventh chords used in major and minor and their
Roman numerals.
m
M
M7
M
m7
m7
m7
º
º
º7
&
& ww
ww
&a: wwwwi7
www
w
M3
m3
M3
w
b www
w
b www
w
wwwtriad
w C7
ii7
ww
ww
wwwiiø7
w
b www
w
w
ww
ww
w
b b wwww
b b b wwww
b b wwww
www
triad
w
Cm7
IVM7
ww
ww
www M7
III
w
b b wwww
ww
ww
wwwiv7
w
www
w
www
w
iii7
m3
m3
M3
w
m3
M3
m3
b b b wwww
w
triadw
ww
Cø7
b b b wwww
# wwww
V7
b b ∫ wwww
www
w
b b ∫ wwww
www
triad
w
vi7
wwwV7
w
www
w
www M7
VI
w
# wwww
www
w
M3
m3
m3
Co7
viiø7
b b ∫ wwww
w
# www
www o
vii
w7
C: IM7
ii7
iii7
IVM7
V7
vi7
viiø7
Figure 8.3.1 Roman numerals for diatonic seventh chords in major
& www
w
a: i7
www
w
iiø7
IIIM7
iv7
V7
VIM7
244
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Figure 8.3.2 Roman numerals for diatonic seventh chords in minor
w
# www
viio7
m3
m3
m3
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____
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CHAPTER 8. 5.SEVENTH
CHORDS
391
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153
9
Chapter 9
Harmonic Progression and Harmonic Function
In this chapter we will look at common harmonic progressions and examine
the principle of harmonic function that underlies progressions.
9.1 The Circle of Fifths Progression
The circle of fifths progression ( I – IV – vii◦ – iii – vi – ii – V – I ) was a stalwart of
the Baroque era in music. You will find many examples of this progression in
the music of Bach, Handel, and Vivaldi, especially in minor ( i – iv – VII – III – VI – ii◦ – V – i )
with the subtonic VII .
55
CHAPTER 9. HARMONIC PROGRESSION AND HARMONIC FUNCTION56 11
Gm7
Dm
˙
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Dm
∑ ∑ œ∑œ œ∑œ œ∑œ œ∑ œ ∑ ∑ ∑ ∑ ∑ œ ∑ œ ∑œ œ∑œ œ∑œ ∑ ∑ ∑ ∑ ∑ ∑
& b ∑ ∑ ∑ ?
œ œ dHrvGOd6G20
œœ œ
b
œ œ œ œYT:
j
œ œ œ œ œ œ œ œ 1047,
Figure 9.1.1 J.S. Bach, Brandenburg Concerto No. 2 in F Major, BWV
œ
I.
M7
M7
iiø7
V7
i
? ∑ ∑ ∑ ∑ ∑ III∑ ∑ ∑ ∑ VI
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
b
Gm
Cm/E¯≤ F
B¯≤
E¯≤
Ao/C
D
Gm
162
162
C7
b 4 œ. œ œ œ. œ œ. œ
& b 4 œ . œ œœ .. œ œ . œ œ . œ
f
˙
˙˙
? b b 44 ˙˙
˙
g: i
iv/3rd
œœ .. œœ œœ . œœ œœ .. œœ œœ .. œœ œœ . œœ # œœ . œœ œœ .. œœ œœ . œœ # œœ . œœ œ . œœ œœ œ œ ..
.
. .
.
. nœ.
˙˙˙
VII
˙˙
˙˙
III
˙˙
˙
VI
˙˙
˙
iio/3rd
œ
V
œ
˙
i
..
b
∑ f6jvsEb-Usk
∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
& b ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ YT:
166
Figure 9.1.2 George Frideric Handel, Suite in G minor, Passacaglia
? b ∑ ∑ the∑ circle
∑ of∑ fifths
∑ for
∑ key
∑ signatures
∑ ∑ ∑because
∑ ∑this∑circle
∑ of∑ fifths
∑ for∑ harmonic
∑ ∑
b
progression contains diatonic notes only. The circle of fifths for key signatures
This circle (the circle of fifths for harmonic progression) is different than
(Figure 2.3.4) contained all 12 notes of the chromatic scale.
f
˙
˙˙
˙˙˙
˙˙
˙˙
˙˙
? b b 44 ˙˙
˙
˙ AND HARMONIC
..
˙˙
œ FUNCTION57
˙
CHAPTER
9. HARMONIC PROGRESSION
œ ˙
g: i
iv/3rd
VII
III
iio/3rd
VI
V
i
Major
I
V
V
iv
minor
iiº
ii
IV
i
VI
VII viiº
III
iii
vi
Figure 9.1.3 Circle of Fifths for Harmonic Progression
The circle of fifths (for harmonic progression) is sometimes known as the
“circle of descending fifths.”
12
166
&
?
œ
œ
begins on C
descending fifths
œ
œ
œ
œ
œ
œ
ends on C
∑ circle
∑ of∑ fifths
∑ progression
∑ ∑ ∑has been
∑ ∑used ∑regularly
∑ ∑since∑the Baroque
∑ ∑
& ∑ ∑ ∑ The
168
Figure 9.1.4 Circle of descending fifths occurring diatonically on the staff
era.
? ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
œ
?
œ
œ
œ
CHAPTER 9. HARMONIC PROGRESSION AND HARMONIC FUNCTION58
œ
G/B
168
&
≈
œœœ
C
≈ œ œ œ
œ
& ≈ œ œ œ
œ
G: I/3rd
œ
Em/G
170
&
& ≈
œ
œœ
≈
œœœ
& ∑
8
& ∑68
∑
∑
∑
∑
#œ
œœ
œ
≈ œ œ œ
∑
œœœ
œ
D/F˜
≈
#œ
V/3rd
≈
œ
iii
≈
œ œœ
#œ
œœ
œ
œœ
œ
≈
I
∑
œ
œœ
iv7
œ
∑
∑
∑
∑
∑A 7 ∑ D˙∑7
Œ œJ œJ
∑
œœ. œ. œ. œ.
b œœ œ œ œ ˙˙˙˙
b
&
f
? bb ˙
œœœœ
œ. œ. œ œ
˙
. .
g:
œ
œ
≈ œ œ
G
Figure 9.1.5 W.A. Mozart, Piano Sonata in C, K. 545, I (1780s)
7
F7
∑ Cm
œ∑ œ œ∑ œ ∑
? bb J J J J ˙
≈ œ œ œ
∑ YT: 5NkzTTkqTB4
∑ ∑ ∑
Hal - la - hal - lo - he!
68
Bm
Am
ii
∑
≈
œœ
≈ # œ œ
viio/3rd
≈
œ
œ
IV
œ
vi/3rd
172
œ
≈ œ œ
œ
F˜o/A
ends on C
VII7
∑ œ ∑ E¯≤maj∑7
Œ
˙
B¯≤maj7
œœ. œ. œ. œ.
˙
œœ œ
œ œ ˙˙˙
O - ho!
ø
œœ. œ. œ. œ. # ˙
œœ œ œ ˙˙
œ #˙
Tra - la - lei!
œœœœ ˙
œ. œ. œ œ ˙
. .
˙
˙
IIIMA7
VIMA7
iiø7
œœœœ
œ. œ. œ œ
. .
7
V
? bb
∑
&b
b
∑
∑
∑
∑
∑
? bb
∑
∑
∑
∑
∑
71
∑
∑
YT: PiIblkOtm3g
∑
∑
Figure 9.1.6 Richard Wagner, Die Meistersinger, Act II, Scene 6 (1860s)
71
F
& www major
w basstriad
note is G
16
www
w
www
ww
sus4
9th
7th
Root
www
ww
CHAPTER 9. HARMONIC PROGRESSION AND HARMONIC FUNCTION59
G9sus4
or
7
Dm
G7
F/G
AmF7
244
&
? 44www major
w triad w
w bass
note is G
248
a: i7
16
Am7
16
Dm7
i7
a:
F/G
Am7
?256
244
7
wG7
iv7
VII7
iv7
VII7
77
Fmaj
Fmaj
7
w
V7
i7
B
Bøø77
E
E77sus4
7 7
E
Am
Bø7
E7sus4
E7
w 7 Bwø7
Fmaj
w
w
w MA7 iiwø7
IIIMA7 VI
G7
wDm7
w
Cmaj7
Fmaj7
Cmaj7
w
IIIMA7
iiø7
VIMA7
a variant:Dm7/G
Cmaj7 Fmaj7
www w
w
w
C˜m
c˜: i
Am7
A
or
wwww
w
w
wE7
w
w7
V
Am7
w
V7sus4
V7
i7
G9sus4
E7sus4
w
F˜m
w
www
w
w
w
7
7
B7
iv
G7
Cmaj7
ø7
D˜
VII
Fmaj7
G ˜7
7
ø7
7E
III
E7sus4
C˜m
7
w
?4
w
w
w
w
? #4# # #w ‰ j‰ j‰ j‰ j ‰ j‰ jw‰ j‰ j ‰ j‰ jw‰ j‰ j ‰ j‰ j‰ j‰ j
ø7
MA7
MA7
7
7
7
7
a: i7
œ œiv œ œVII œ œIII œ œ VI œ œ ii œ œ V œsus4œ Vœ œ
C˜m
F˜m
B
E
? # # # # 44VI ‰ j‰ j‰ j‰ iijø7‰ j‰ j‰ j‰ jV7‰ j‰ j‰ j‰ ji ‰ j‰ j‰ j‰ j
œ œ œ œ œ œ œ œ œ œ œ œ
œ œ œ œ
268
? 264
286
294
? ####
272
294
Dm7
c˜: i
? ####
Bø7
ivYT: EgT_us6AsDg
VII
E7
III
Figure 9.1.9 Antonina Armato,
Tim James, 7Adam Schmalholz, “Love You
A
D˜ø7
G˜
C˜m
Like A Love Song” (2010s) (bass and chords only)
268
? ####
292
272
276
?The
# # # #circle
‰ jof‰ fifths
‰ j ‰ j‰ jhas
‰ ja‰feeling
‰j
j‰ jprogression
j ‰ jof‰ inevitability
j‰ j‰ j ‰ about
j‰ j‰it jbecause
it consists of harmonic sequences. To understand harmonic
œ œsequence
œ œ we
œ œ œ œ œ œ œsince
œ
œ
œ
œ
will first look at melodic sequences,
the
bass
line
is
the
“melody”
in a
œ
harmonic sequence.
Ask yourself
idea:
VI
iiø7 what happens
V7 after this melodic
i
U
b 2 ‰
b
b
& 4
œ œ œ ˙
ƒ
?
œ
œœ œ œ
?
œ
œ œ œ œ isœœa musical
œ œ œ idea
œ œ pitch
b b C Ó a Œsequence
Œ repeated œat aœ œdifferent
Πlevel.
?
&Therefore,
Figure 9.1.10 Beethoven, Symphony No. 5, Op. 67, I.
p
b
iiø7
VIMA7
Am7
Am
Dm
G
Cmaj
Fmaj
B
E
Am
?
? #44# # # 44 ‰ jw‰ j‰ j‰ j ‰ j‰w j‰ j‰ j ‰ j‰ wj‰ j‰ j ‰ j‰ j‰ j‰ j
w œ œ œ wœ
w
w œ œ œ œw
a: i7
iv7
VII7 œ IIIœMA7œ œVIMA7 iiø7
V7 œ œ i7 œ œ
278
286
&b
Cmaj
Cmaj77
G9sus4
or
Dm7
G7
?
& 44www
ww
?264
248
281
IIIMA7
w
www
ww
Bø7
E7
F
sus4 YT: FHhZPp08s74
major
9th
7th
triad Freddie Perren
Figure 9.1.8
and Dino Fekaris, “I Will Survive” (chords only)
Root
note is G
(1970s) bass
a: i7
iv7
VII7
IIIMA7 VIMA7 iiø7
V7sus4 V7
270
278
284
VII7
Dm77
G
G77
orDm G9sus4
? 44 Am7
? 44 w
a: iw7
?248
?
w
www
ww
w
G9sus4
E7
Dm /G or
G9sus4
w a variant:
? 444 F ww
?
w
ww
w
www wsus4
wwww
wwww
w
YT: K8wE58PTIkw
& 4www wwmajor
9th
ww Moon”
ww 7 (1950s)
7th
triad
Figure
Me
to the
(chords
only)
MA7
MA7
ø7
MA7
MA7
77 Howard,
77“Fly III
w bass
w
a:
i77 noteBart
iv
i77
a:
i9.1.7
iv
VII
VI
ii
V sus4 V
Root
is G
264 256
?256
www sus4
9th
7th
w wRoot
iv7
Am77
F/GAm
248
256
244
264
270
a variant:Dm7/G or
Cmaj7 Fmaj7 Bø7
268
272
272
276
&b
281
b
œ œ œ œ G ˜7
C˜m
? # # # # ‰ j‰ j‰ j‰ j ‰ j‰ j‰ j‰ j ‰Vj7‰ j‰ j‰ j ‰ i j‰ j‰ j‰ j
CHAPTER
PROGRESSION
AND HARMONIC FUNCTION60
U
b 2 9.‰œ HARMONIC
b
œ
œ
œ
& b 4
œ œ œ œ˙ œ œ œ œ œ? œ œ œ œ ?œ œ
Sequences can be short orø7long. For example,
look at this familiar idea and
VI ƒ
ii
V7
i
notice how all four bars are sequenced down a step in the following four bars.
U
b
& bbb bC 42Ó ‰ Œœ œ œœ œ œœ œœ ˙ œ œ œ œ Œ œ œ œ ? œ œ œ œ œ œ œ ?Œ ?
&
ƒp
D˜ø7
iiø7
A
VI
Figure 9.1.11 Mozart, Symphony No. 40,
œ I. œ
œœœ œœ œ Œ œ œ œœœ œœ œ œ Œ
œ bass
b b Clook
Ó again
Œ œatœ the
?
line in “Love You Like A Love Song” and notice
&Now
how it can be thought
of
a
two-note
idea
treated
as
a
descending
sequence.
p
276
281
? #### ˙
↓2nd
↓2nd
˙
œ
↓5th
œ
↓2nd
˙
↓5th
↓5th
œ
˙
↓5th
œ
Figure 9.1.12 “Love You Like A Love Song” bass line sequence in groups of
two notes
Sometimes we will hear a circle of fifths sequence where some of the chords
are not in root position, as in the Handel and Mozart examples. In these two
examples, we are hearing the sequence of the roots, even though they are not
clearly presented in the bass.
17
282
œ
? b b œ̇
Gm
g: i
? bb
Cm/E¯≤
F
œœ̇
B¯≤
E¯≤
œœ̇
Ao/C
iv/3rd
VII
III
VI
iio/3rd
œ̇œ
œœ̇
œ̇œ
D
Gm
V
i
# œœ̇
œœ̇
283
YT: f6jvsEb-Usk
Figure 9.1.13 Handel Passacaglia with roots as open note heads
We will return to the idea of harmonic sequence later in this chapter.
9.2 Harmonic Rhythm
You will find that all of the progressions we discuss can have different harmonic rhythm. Harmonic rhythm is a term for how long each chord lasts.
For example, in “Fly Me To The Moon” (Figure 9.1.7), “I Will Survive” (Figure 9.1.8), and “Love You Like A Love Song” (Figure 9.1.9), each chord lasts for
four beats and has whole-note harmonic rhythm. In the Mozart (Figure 9.1.5)
and Wagner examples (Figure 9.1.6), on the other hand, each chord lasted for
two beats, and so had a faster harmonic rhythm.
Listen to the following example to hear four-beat harmonic rhythm change
to two-beat harmonic rhythm.
? bb ˙
œ̇
œœ
œ̇
œœ̇
# œœ̇
œ̇œ
o
œœ̇
g: i
iv/3rd
VII
III
VI
/3rd
V
i
CHAPTER
9. HARMONIC
PROGRESSION
ANDiiHARMONIC
FUNCTION61
? ### 4 w
4
283
A: IV
w
I
w
w
vi
V
˙ ˙
IV I
w
˙ ˙
V
IV I
w
V
half-note harmonic rhythm
whole-note harmonic rhythm
? ###
291
YT: F90Cw4l-8NY
Figure 9.2.1 Dan Smith, “Pompeii”
In some music, harmonic rhythm will remain consistent, while in other
pieces there will be an infinite variety to the length of harmonies. Throughout this text, we will be examining harmonic rhythm and the placement of
harmonies within the phrase.
9.3 Shorter Progressions from the Circle of Fifths
9.3.1 II-V-I
The “ ii – V – I ” progression can be found in many pieces of music in all styles—classical,
popular, but especially jazz, since the Great American Songbook (popular
songs from the 1930s, 40’s, and 50’s) on which jazz repertoire is built contains 13
many examples of this progression.
175
Dm7
& 44 w
G9
C: ii7
V9
œ #œ œ œ œ bœ œ œ
w
? 44 www
&
∑
?
∑
178
∑
www
w
∑
∑
∑
∑
œ
www
w
œ ˙.
I
∑
YT: MENQyu4D7Ig
∑
Figure 9.3.1 Duke Ellington, “Take the ‘A’ Train”
∑
C6
∑
∑
∑
∑
∑
∑
w
? 44 www
www
w
www
w
CHAPTER 9. HARMONIC PROGRESSION AND HARMONIC FUNCTION62
C: ii7 7
V9
I
Cm
F7
B¯≤maj7
E¯≤maj7
Aø7
D7
Em7
A7
Dmaj7
8
œ œ œ œ ˙
? b#b# 4J J J J
& 4 ˙.
œ
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. w
? # # 44œœœ œ.www œ. œ. ˙
b œ œ œ œ ˙˙˙
&b
68
178
68
f
? b
∑ b ˙
˙
œ
Œ
˙
b˙
n˙
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œœ. wwœ. œ. œ. ˙
œœ wœ
œ œ ˙˙˙
D: ii7
181
&
##
? ##
∑
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œœœœ ˙
∑ œ œ œœ œ ˙∑
œ. œ. œ ∑œ ˙
. . . œ. YT:˙ sUg1Dpsd6fw
. .
∑E bm
w
œ. wwœ.
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iiø7
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bb 4
&bbb 4 ‰
œ.
? bb 4 ‰ œ
bbb 4
œ
? bb b
bb
œœ
j
nœ ˙
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œ
D¯≤: ii
∑
∑
? bb b
∑
b –V–I
• vib– ii
b
& b bbb
A b 13
œœ
J œ
œœ
œ. # ˙
œ # ˙˙˙
œœœ œ
œ
œœ
ii7
b
b #
V
∑D b6
˙
V13
I
V+9
Ó
Ó
I
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
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∑
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∑
YT: d22CiKMPpaY
Ó
sigh is just a sigh
76
Figure
9.3.3 Herman Hupfeld, “As Time Goes By” (1931)
9.3.2 VI-II-V-I
œ ∑œ œ œ
œ. œ. œ œ
. .
7
œœ
œœ n œœœœœœ ˙˙˙˙
n œœœ œ
œ
œ
œœ
œ
œœ
œ œ œœ œœ
˙
œ
œ
œ
˙
œ
œ
kiss is just a kiss, a
œœ ..
V7
∑
76
∑ E bm7
˙
œ œJ
a wJ
œD∑ 6œ œ œ ˙A 9( 5)
œ
œ
œ
œ
œ
œ
.
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œ œ œ œ. J
œœ J
bbb 4 J
A b7
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71
œœ.
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V7
Figure
g: 9.3.2
iv7 Miles Davis,
VII7 “Tune-Up”
IIIMA7
71
Œ
This progression can occur in one of the following three ways (or orderings):
• I – vi – ii – V
• ii – V – I – vi
One can think of these reorderings as rotations, as shown in the example below.
˙ ˙
˙ ˙
# 4f w
w
? b b A:˙ IV Iœ œ œ viœ ˙ V IV
œ œ Iœ œ V ˙ IV Iœ œ Vœ œ
œ
half-note
rhythm
œ. AND
harmonic
œ. œharmonic
œ. œ. œ œ
CHAPTER
9. HARMONIC
FUNCTION63
. œ. œrhythm
˙ whole-note
œ. ˙
. PROGRESSION
˙
. œHARMONIC
.
. .
ø7
7
7
MA7
MA7
7
g:
71
iv
start
? ###
291
? ###
III
E bm
A b7
b
start
VI
ii
b
V
b
b #
start
E m7ii
A 13 D 6
œ œ œ œ ˙A 9( 5)I
œ
œ
œ
? b b 4 œ œ œ œ œ œ. J œ œ œ œ. J
bbb 4 J
vi
I
71
VII
ii
œœ
œœ
bb b 4 ‰
J œ
œœ
b
& b 4V
j
œ
œ
.
œ
œ.
nœ ˙
œ. I
œ
œœ
œœœœ
œ œœ of the œviœœ – iiœ – V –œœ I progression
? b b9.3.4
4 ‰Rotations
Figure
œ
œ
bbb 4
œ
œ
œ
œ
œ
œ
œ
9.3.2.1
vi
You must re - mem - ber this a
D¯≤: ii
vi-ii-V-I
V
kiss is just a kiss, a
V7
ii7
V13
V
D b6
˙
vi
sigh is just a sigh
I
n œœ œœœ ˙˙˙
n œœœ œœ ii ˙
œ
œœœ
˙
œ
˙
œ
V+9
Ó
Ó
Ó
I
The vi – ii – V – I progression contains the last four chords of the circle of fifths
progression.
295
76
175
76
178
bb 4
& b b 47
B b m7
F m7
˙.
œ œ œ œ Cœ6
œ the prom - isedœ kiss œof
You
œ # œare œ
& 44b b w4
œ bœ œ
∑
& b b 4 Œ ‰ œj Ó Œ ‰ œj Ó
œœ
œœ
w
wwww
? 44 www
www
w
? bb 4
˙
bC:b ii74 ˙
˙
˙ V9 ˙
˙ I
Dm
w
E b7
G9
#
j
& # 44 ˙ .
œ
b˙
nœ. aœ
www
YT:wOPapxr8GvGA
w
?
#
4
w
Figure #9.3.5
4 Jerome Kern, “All the
w Things You Are”
A¯≤: Em
vi77
ii7
A7
V7
±
Ab 7
13
œ ˙.
spring - time,
œ Œ ˙. ‰ Ó
j
œœ
œ
˙
˙
DmajI7MA7
w
ww
w
Here isD:another
example from more
ii7
V7 recent popular music.
IMA7
C˜m
#
& # 44 ˙˙˙
181
? ## 4 ˙
4
E: vi
#
& #
185
? ##
F ˜m
˙˙
˙
˙
ii
B
E
C˜ m
˙
˙
˙˙
˙
˙˙
˙
˙
V
I
∑
F ˜m
˙˙˙
˙˙
˙
vi
ii
˙
Bsus4
˙˙˙
˙
B
˙˙
˙
˙
Vsus4 V
YT: ZyhrYis509A
Figure 9.3.6 Søren Rasted, Claus Norreen, René Diff, and Lene Nystrøm,
“Barbie Girl” (chords only)
∑
CHAPTER 9. HARMONIC PROGRESSION AND HARMONIC FUNCTION64
9.3.2.2
I-vi-ii-V
Here are examples of the I – vi – ii – V progression, sometimes called the 1950s
progression because of its prevalence during that decade, although this progression was also widely used in the 1930s and ’40s.
bb
&bb
80
80
A b66
A
4
4 œ w
Blue
Blue
moon
moon
b
& b b b 44 Œ Œ œœœ Œ
œ
? b b b 44 Œ
b
˙ ˙
80
80
A¯≤¯≤::
A
II
B bm9
m9
B
F m7
m7
F
E b 99
E
A
A b 66
œœ œ œ œ œ œ œ
w
you saw
saw me
me stand
stand--ing
you
ing aa-- lone,
lone,
œœœœ Œ œœœ
œ
˙
vi77
vi
ii99
ii
Œ
˙
F
F m7
m7
œœœ
œ
V99
V
II
‰
E
E b 99
œ œœ œ œœ œ
with
with--out
out aa dream
dream in
in my
my heart
heart
œœœ Œ œœœ Œ
œ
œ
Œ œœ Œ
œœ
˙
B
B b m9
m9
˙
7
vi
vi7
˙
˙
9
ii
ii9
œœœ
œ
9
V
V9
b bb b bb
&
?
& bb b b b ∑∑w
b
85
85
85
85
YT: WTj7DvlptAc
Figure 9.3.7 Richard Rodgers, “Blue Moon” (1934)
86
86
86
86
Vb
F 66
F
44
œ w
D m7
m7
D
Some--where
where
Some
G m7
m7 C
C 77
G
Œ ‰ œj œ œ ˙
œ
be -- yond
yond the
the sea
be
sea
j
4
& b 4 Œ Œ ‰ œjœ œœœ œœ œœœ ... œœœ Ó
œœ œ œœ œ . œ
? 4 Œ
b 4
œ œ œ œ œœ œ œ
F:
F:
II
vi77
vi
F
F 66
ii77
ii
V77
V
D
D m7
m7
G
G m7
m7
C
C 77
Œ œ œ . œjj œ
œ
œ œœ
some
wait -- ing
some -- where
wherewait
ing for
for me
me
Œ ‰ jœ
jj Ó
œ
.
œ
œ
œ
œ
œ
.
œ
œœ œœ œœ œœ .. œœœœœ
œ œ
œ
œœ œ œ œ œ œ œ
II
vi
vi77
ii
ii77
V
V77
∑ ∑ C ∑13 C ∑7(13b9)∑F ±9∑ ∑ A m7
∑ /E∑D m9∑ ∑ ∑ ∑
V b ∑ G∑m7 ∑ ∑ ∑ C 13sus
44 œ œ ˙ œ œ YT:
œ œ_R8HhlaMvko
œ œ œ
˙.
b
Œ Sea”
œ œLasry,
œ œ“Beyond
V
œ
Figure
9.3.8
Charles
Trenet
and
Albert
The
(1945)
91
Take
my∑ bass
hand
a∑stran
next
b ∑ for
∑this
∑ line
∑ inI'm
∑ the
∑- gerrecording.
∑in ∑par - a∑- dise∑ ∑ ∑ All
∑ lost∑ in∑ a ∑
&Listen
˙˙˙
œœœ b œœœ ˙˙ ..
& b 44 w
œœœ ww
www
˙
œ œ ˙˙ ..
œ w
? b ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑w ∑ ∑ ∑ ∑
˙ ˙
? b 44
˙
œ œ ˙ ˙
˙
˙
91
91
91
F: ii7
V7
IMA7
authentic cadence
vi7
connects to next phrase
99
? bb 4 Œ
bb 4
˙
˙
V
˙
˙
I
˙
˙
˙
˙
ii
CHAPTER A
9.¯≤: HARMONIC
PROGRESSION
AND
HARMONIC
FUNCTION65
I
vi7
ii9
V9
I
vi7
ii9
V9
291
F#
? # # # # # 44
#
˙
? # # # #86#
#
86
G #m
C#
F#
D #m
vi
ii
V
I
vi
F6
D m7
˙
F˜: I
295
D #m
F6
˙
˙
D m7
G m7 C 7
˙
b bb b bb
&
? ˙b b b b ∑∑w
˙ &
bb
G # m 85 C #
85
˙
ii
G m7
Some-where
be - yond the sea
some - where wait - ing for me
4
jÓ
Œ ‰ jœ
& b 4 Œ Œ ‰ œjœ œœœ œœ œœ .. œjœ Ó
œ
.
œ
œ
œ
œ
œ
.
œ
œ
œ
9.3.2.3 ii-V-I-vi œ œ œ œ
œœ œ œœ œœ .. œœœ
œ œ œ .. œœ
Below is an example of the ii – V – I – vi progression. In this example, the vi
? acts
4 asŒ a link between the Vœ– I cadence in the middle of the
chord
phrase
b
4
œ of the next œphrase.
œ œ activity
œ
œ
œ
and the ii chordœ at
This
harmonic
œ theœ beginning
œ
œ
œ
œ
œ
after the arrival on the I chord is like a “turnaround” in jazz. We discuss
Fools Fall in Love” (1955)
G m7
V b 44 œ œ ˙
91
C7
4
ΠYT:
‰ j mEHcTciiXQY
Œ œ œ. j
Vb 4 œ w
œ œ œœ ˙
œ œœ œœ
Figure 9.3.9 Frankie Lymon, Herman Santiago, Jimmy Merchant, “Why Do
F: I
vi7
ii7
V7
I
vi7
turnarounds more in a later chapter on jazz harmony.
91
V
Take my hand
4
&b 4 w
www
? b 44
˙
˙
F: ii7
C 13sus
±
C 13 C 7(13
b9) F 9
œ œ œ œ œ œ œ œ ˙.
˙˙
˙˙
˙
I'm a stran - ger in
œœ œœ
œœ b œœ
˙
V7
ii7
A m7/E D m9
Œ œ œ œœ
par - a - dise
˙˙˙ ...
˙.
˙
IMA7
authentic cadence
V7
All lost in a
œœœ
œ
œ œ
www
w
˙
˙
vi7
connects to next phrase
YT: WFrUsa5SUv0
Figure 9.3.10 Robert Wright, George Forrest, Alexander Borodin, “Stranger
in Paradise” (1953)
If you view this video on YouTube, you will briefly see the double bass part,
which has lead-sheet symbols on it.
9.3.3 III-VI-II-V
The iii – vi – ii – V circle of fifths segment is sometimes repeated (or looped)
within a song.
CHAPTER 9. HARMONIC PROGRESSION AND HARMONIC FUNCTION66
10
95
10
95
95
95
97
97
97
97
##
& # ∑
99
C # m7
##
& # ##
& #
? ###
###
&
###
&# #
& #
? ###
##
& #
? # # # ∑
99
99
œ ˙
44 Cœœœ #m7œœœ ... œ Fœ #.m7œ
œœ .. œ
44
œ œ œœ ˙
44 great
˙ - test ˙
44 œœœ 7 œœœ ... œ œ 7. œ
A: iii
vi
œœ .. œ
great
-
test
C # m7
# ###
?
#
& # 44w ˙
œœ
œ
w
˙
œœ
œiii7
A: iii7
C # m7
∑? # #∑# ˙∑
### œ
&
J ‰ŒÓ ∑
99
F # m7
### 4
& 4 œ œœ
F # m7
Bm
E
œ œ œ œ.
Bm
˙
Œ
ii
˙
œœ .. œ œ˙ œ œ œ œ œ œ
œ . viœœ ...7 œ œ œ œ iiœ œ
˙
∑
∑
∑
is hap - pen - ing to me
‰ œj œœ
E
œœ .. œ Fœ #m7 œ œ œ œ Bœ m œ
œ.
œœ ... œ œ œ œ œ œ
Œ
vi7
∑
œ œ œ œ œœ
œ
œ . œœE œœ œœE/Dœ œœœ
œ œœ œœ Bœœ m
œ.
œ
œ œ œ œ œœ
œ œ œ œ.
œ - pen - ingœ to me
love of all
is hap
˙
œ
œ . œœ œœ œœ 7 œ œœœ
œ œ œœ iiœœ
V /7th
œ. V
œœ
love of all
˙
∑
E/D
∑ ∑
˙
E/D
œœ œ
œ œ œ Vœ/7thœ
œœ
œE œ œE/Dœ
œœ j
‰ œ œ
œ œ
œ
I've found
the
œ œ œ œœ œ
œœ
œ œ Vœ 7/7thœ
V
œœ
YT: IYzlVDlE72w
I've V
found
∑
7
the
∑ œ ∑
∑œ ∑
∑
∑ ∑
Figure 9.3.11 Michael Masser and Linda Creed, “Greatest Love of All” (1977)
iii7
vi7
ii
V
V7/7th
Sometimes, this progression is rotated to ii – V – iii – vi , as in “September,”
the well known song by Earth, Wind, and Fire.
∑
∑
∑
∑
##
∑& #∑ 44 ∑œ œ ∑œ Ó∑
B m7
##
j
& # 44 œœ .. œœ
œ. œ
? # # # 44 œ œ œ
E
Ba - de - ya
A: ii7
∑
∑
C # m7
∑
F # m7
∑
∑
B m7
∑
E
∑
C # m7
F # m7
∑œ œ ∑œ œ ∑œ œ ∑ œ ∑œ œ ∑Ó ∑ œ ∑œ œ ∑œ œ ∑œ
say do you re-mem-ber
˙˙
˙
œœ
œ
œœ
œ
V
iii7
Œœ #œ œ œ
œ
Ba - de - ya
j
œœ .. œœœ ˙˙˙
œ.
œ œ Œœ #œ
œ
œ
œ
œ
˙˙
˙
vi7
ii7
V
danc-ing in Sep-tem-ber
œœ
œ
œœ
œ
œ œ
œ
iii7
˙˙
˙
œ œ
vi7
YT: Gs069dndIYk
Figure 9.3.12 Maurice White, Al McKay, Allee Willis, “September” (1978)
This ii – V – iii – vi progression is also seen in the following song.
CHAPTER 9. HARMONIC PROGRESSION AND HARMONIC FUNCTION67
b
& b bbb c œ .
œœ ..
? bb c
b b b œ.
214
j
œœœ ... œœœ ˙˙˙
j
œ
˙
œ.
j
œœœ ˙˙˙
j
œ ˙
D¯: ii7 V
iii7 vi
b
& b bbb
j
œœœ ... œœœ ˙˙˙
j
œ
˙
œ.
j
œœœ .. œœœ ˙˙˙
.
j
œ
˙
œ.
ii7 V
iii7 vi
205
YT: dQw4w9WgXcQ
Figure 9.3.13 Mike Stock, Matt Aitken, and Pete Waterman, “Never Gonna
Give You Up” (1987)
? bb
bbb
9.4 Harmonic Function
Now we will address non-circle-of-fifths progressions. Notice that we have not
included the vii◦ or IV chord in any of the shorter circle of fifths progressions
above. However, it is a common axiom that Rock ‘n’ Roll is made up of
three chords: I , IV , and
V . This is because each of those chords represents
¯/F
Gø7
a harmonic function. Harmonic function refers to the tendency of certain
chords to progress to other chords, or to remain at rest. Many texts on music
theory enumerate three harmonic functions. In this text, we will discuss four.
1. Tonic function (abbreviated “ton.”): The I chord has tonic function,
which is a state of stability and rest. Tonic chords do not demand progression to other chords.
2. Dominant function (abbreviated “dom.”): The V and vii◦ (chords containing the leading tone 7̂ and supertonic 2̂ ) tend to progress to tonic ( I ).
Special note: The I/5th chord has dominant function when it resolves
to the V chord, as in the third chord from the end of the “Star-Spangled
17
Banner.”
F
152
152
b
& b 43 œ œ
b
& b 43 œ œ
O'er the
B b/D F B b
œ.
land
œœ ..
? b b 43 œ ( œ ) œ .
œ ( œ) œ .
B b/D G m C ø7/G b B b/F
œ œ (œ ) ˙
J
j
œœœ œœœ ( œœœ ) ˙˙˙
of the
free
j
˙
œ œœ ( œœ ) ˙
œ ( )
F7
œ œ œ . ( œJ ) œ
œœ œœœ œœœ ... ( œœœ ) œœœ
œ
J
and the home
of the
œ bœ œ. j
œ bœ œ. œ œ
œ œ
B¯≤: I/5th
V7
dom.
Figure 9.4.1 Key and Smith, “The Star-Spangled Banner”
Bb
˙
brave!
˙˙
˙
˙
˙
I
ton.
? bb
œ
A: IV
˙
I
œœ̇ V
vi
whole-note harmonic rhythm
g: i
iv/3rd
VII
˙IV
œœ V
I
# œ̇IV
I
half-note harmonic rhythm
III
iio/3rd
VI
V
œœ̇ V
i
CHAPTER 9. HARMONIC PROGRESSION AND HARMONIC FUNCTION68
start
I
# vi
?3. #Pre-dominant
w(abbreviated
w ii “pre-dom.”):
w
ii (chords
˙ ˙ w The IV˙ and
# 44 w function
w
containing the subdominant 4̂ and submediant 6̂ ) tend to˙ progress to
283
start
chords
A: of
IVdominant
Iii function.
vi vi
V
I
start
IV VI
VV
IV I
half-note harmonic rhythm
whole-note harmonic rhythm
Vvi
4. Tonic prolongation function (abbreviated “ton. prol.”): The vi and iii
(chords that share two common tones with 1̂ –3̂ –5̂ from the tonic triad)
V
Iand progress to chords ofstart
iipre-dominant
tend tostart
occur after the tonic chordstart
function.
vi
ii
I
291
#
Harmonic function
next section.
F # is represented
D #m
G # mon aCflowchart
F # in the
D #m
G #m
C#
? #I# # # # 44
ii ˙
vi
˙
#
˙
˙
9.4.1 The Harmonic Flowchart
F˜: I
vi
V
FUNCTION:
291
Tonic
F#
? # # # # # 44 I
#
˙
ROMAN
NUMERALS:
F˜: I
ii
V
D #m
˙
vi
#
iiiG m
vi
˙
ii
I
I
Tonic Prolongation
C#
˙V
˙
V
vi
Pre-Dominant
˙
V
F # IV
˙
I
ii
D #m
˙
vi
˙ vi
˙
ii
ii
V
Dominant
C#
G #viiº
m
˙
V
ii
˙
Tonic
I
V
(dashed lines represent possible movement within a functional area)
Tonic
Prolongation
FUNCTION:
Pre-Dominant Dominant Tonic
Figure
9.4.2Tonic
Harmonic
Flowchart
in Major
iii I in the plagal cadence
IV
ROMAN
Remember that
IV goes to
and Vviiº
goes to viI in
I
NUMERALS:
the deceptive cadence. When IV goes to I , label IV as having tonic prolongavi
ii
V
tion function. The plagal cadence and deceptive cadence are exceptions to the
harmonic flowchart.
(dashed lines
representin
possible
movement
withinaddition
a functional
Here is the Harmonic
Flowchart
minor.
Note the
ofarea)
the subtonic
VII chord, which has one function—to progress to III .
FUNCTION:
Ton.
ROMAN
NUMERALS:
i
VII
Ton. Prol.
Pre-Dom.
Dom.
III
iv
viiº
VI
iiº
V
Ton.
i
Figure 9.4.3 Harmonic Flowchart in Minor
The tonic chord I can progress directly to a chord of any other function and,
in fact, many pieces begin with a I – V – I progression, representing harmonic
function of Tonic-Dominant-Tonic.
9.4.2 Tonic-Dominant-Tonic Progression
This is the most elemental progression in music, often realized with I – V – I .
181
185
185
190
190
V7
? # # cD: ˙ii7 ˙
˙ IMA7
˙
˙
˙B
˙
˙B
C˜m F˜m
E
C˜ m
F ˜m
Bsus4
# 9. HARMONIC PROGRESSION
CHAPTER
AND
HARMONIC
V
I
vi
ii
Vsus4
V
˙˙˙ FUNCTION69
˙˙
˙˙
& # E:c vi˙˙˙ ii˙˙˙
˙˙
˙˙˙
˙˙˙
˙
˙
˙
G
D 7/A
D 7/F #
G
œ . œ œ˙
? ### 3c œ˙. œ œ ˙ Œ ˙
˙
Œ œ˙ œ ˙ Œ
& 4
œ œ Œ ˙
E:p vi
ii
V
I
vi
ii
Vsus4 V
œ
œ
œ
œ
œ
œ
œ
? # 3 Œ œG œ œ œ Dœ7/Aœ œ œ Dœ7/Fœ# œ œ Gœ œ œ
œ. œ œ
# 43 œ . œ œ Œ
Œ œ œI Œ
& G:4
œ Vœ7/5th Œ
I
V7/3rd
tonic
dominant
tonic
C p
G
G7
C
œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œÓ œ œ
&?c# 4˙3 Œ œ œ œœ œ œœ œ œ œœ Ó
˙˙ # œœ œœ œœ œœ œœ. œœ n œœ œ.
˙ œ œ œ œ . œ. œ.YT:œ. OmQQoohTW80
. .
7/5th
7/3rd
p
G:
I
V
V
I
Figure 9.4.4 W.A. Mozart, Piano Sonata, K. 283, I.
.
w
tonic
dominant
œ œ Ó
œœ œœ. tonic
? c wwC
Ó
G
G7
C
œ. œ.
w
&C:c I˙ œ œ œ œ œœ œ Vœ œ Ó V˙˙ 7 œ œœ œ œœ œœ œœ œI œœ Ó
˙ œ œ œ œ . œ. œ. œ.
# œ œ . . n œ. .
p
w
œ œ Ó
œœ. œœ. Ó
? c ww
œ. œ.
w
C: I
V7
V
tonic
I
dominant
tonic
YT: o1iUR3GG4DQ
Figure 9.4.5 Ludwig van Beethoven, Piano Sonata in C major, Op. 2, No. 3, 11
I.
103
#### 3 œ œ œ
& # 8 J J J
B
con brio
##
& # # # 38 ‰ œœ œœ
œ œ
La
103
don na è
? # # # # 38 œj ‰ ‰
#
B: I
F#
œ. œ œ
R RÔ
‰
qual
œœ œœ
œ œ
œ œ
œ
V
‰
œ
œ
J
œ. œ œ
œ
J
più
ma al
œœ
œ
œœ
œ
œ
B/F #
ven
to,
‰
œ
œœœ œœœ
j ‰ ‰
œ
V
I/5th
dominant
tonic
œ œœ œ œ œ œ
œ ˙
œ˙
œ œ œ œ
œ œ
œ
? 4
‰J
Œ
YT: Œ4iUwkJuRdiY
b 4
F
107
œ
J
mo - bi - le
tonic
107
F#
C
C 7sus
F
Figure 9.4.6
Giuseppe
Verdi, Rigoletto, “La
donna è mobile”
Hey Jude,
don't make it bad
take a sad song and make it
4
&b 4 Œ œ
œœ œœ œœ œœ
œœ œœ
œœ œ
œœ
? 4 Πj
j
b 4
œ œœ œ
œ œj œ œj
œ œœ œ
œ œ œœ
F:
I
V
œœ œœ œœ œœ œœ œœ
œœœ
j
œ œ.
œ œ.
j
œ œœ œ
œ œœ œ
V7sus4
œ
œ
bet - ter
œœ
œœ œœ
j œj œ œ œj
œ
œ œ œ œœ
I
? # # # # 38 œj ‰ ‰
#
œ œ
œ
œ
œ
œ
j ‰ ‰
œ
I
V
V HARMONICIFUNCTION70
/5th
CHAPTER 9.B:HARMONIC
PROGRESSION
AND
tonic
107
107
? 4
b 4
F
œ ˙
Hey Jude,
dominant
C
œ œ œ œ
‰J
Œ
don't make it
bad
4
&b 4 Œ œ
œœ œœ œœ œœ
œœ œœ
œœ œ
œœ
? 4 Πj
j
b 4
œ œœ œ
œ œj œ œj
œ œœ œ
œ œ œœ
F:
I
V
tonic
tonic
œ œœ œ œ œ œ
œ˙
œ œ
œ
Œ
C 7sus
take a
sad song and make it
œœ œœ œœ œœ œœ œœ
œœœ
j
œ œ.
œ œ.
j
œ œœ œ
œ œœ œ
V7sus4
dominant
YT: A_MjCqQoLLA
Figure 9.4.7 Lennon-McCartney, “Hey Jude”
F
œ
œ
bet - ter
œœ
œœ œœ
j œj œ œ œj
œ
œ œ œ œœ
I
tonic
12
CHAPTER 9. HARMONIC PROGRESSION AND HARMONIC FUNCTION71
œ œ œ
J œ œ œ œ œ. Œ
? # # # 44 œ .
A
112
E7
### 4 ‰ j ‰ j ‰
& 4 œ œ
œœ œœ
? ### 4
4 œ œ œ
All
112
my ex - es live in Tex
j‰ j
œœœ
œœœ
œ œ
A: I
-
œ œ
≈ œ
Œ
as
‰ j‰
œœœœ
œ
œ
j‰ j‰
œœœœ œœœœ
œ œ
V7
tonic
? ### œ œ œ œ œ ‰ œ œ œ œ ˙
J
###
‰
&
114
? ### œ
A
I
hang my
j ‰
œœœ
œ
V7
œ
hat
in
Ten - nes - see
j ‰ j ‰
œœœ
œœœ
œ
œ
œ
œ
j
œœœ
œ
116
Db
bb 4
&bbb 4 œ
œ œœ w
Ó
‰ œj ‰
œœ
œ œ
j
œœ ‰
œ
j
œœ ‰
œ
œ œ
I
(dominant)
116
j
œœœœ
dominant
E7
114
And that's why
j
œœ
œ
tonic
Db
Œ
YT: Jk7uXaNuWNE
œ œ œ
œ
E b m7 A b 7
w
E b m7 A b 7
Œ
Db
œ œ œ œ
Figure 9.4.8Startspreading
Sanger
D.news
Shafer and Linda
J. toShafer,
- the
I'm lea - ving
day, “All My Ex’s
I want Live
to bein
Texas” (1986)
œ œœ
œ
œ œ œ
œœ œ
œ
4
b b b bprinciple
&The
b 4 Œ Óof
œ œ œ œ œ œ œ œ œ œ œœ œœ œœ œ œ œœ Œ Ó
œ
“Tonic-Dominant-Tonic” could also be represented with
I – vii◦ – I . Even though we learned that “dominant” means “5̂ ” (and also
œ
œ in terms
œ
œ
“ V?
”) in
4 sections,
b b earlier
∑ to “dominant
œ Œ Œ function”
œŒ
Œ œ Œ of harmony
Œ œ Œ means
Œ œ“a
b b 4progresses
chordb that
the tonic chord.” We will revisit this concept and
other possibilities for D¯≤:
“dominant
function”
later. ii7 V7
I
I
ii7 V7
I
9.4.3 Tonic-PreDominant-Dominant-Tonic Progression
This sequence of harmonic functions can be realized in four possible ways:
• I – ii – V – I
• I – IV – V – I
• I – IV – vii◦ – I
• I – ii – vii◦ – I
Here are examples with I – ii – V – I .
CHAPTER 9. HARMONIC PROGRESSION AND HARMONIC FUNCTION72
14
194
14
194
196
196
198
&c
?c
‰
œ‰
œ œ
œ œœ ‰ œœœœœœ‰ œœœœœœ
œ
œ
≈ œJ .œ œ œ ≈ œJ œ. œ œ
≈ œJ . œ
≈ œJ . œ
˙
˙
˙
˙
C
D m7/C
‰
œ œ œ ‰ œ œ œ œ ii‰7/7thœ œ œ œ œ œ ‰ œ œ œ œ œ œ
œ
c
& ≈ œ .œ tonic
œ œ ≈ œ œ. œ œ
œ . pre-dominant
œ
≈
≈ œJ . œ
J
J
G 7/B
C
J
‰ ˙ œ œ ‰ ˙ œ œ ‰ ˙ œ œ ‰˙
œ œœ
œœœœœ
?
& c œ .œ œ œ œ œ œ .œ œ œ œ œ
œ
œ
≈ J
≈ J
≈ œJ . œ
≈ œJ . œ
C: I
ii7/7th
˙
˙
˙
˙
?
tonic
pre-dominant
C
D m7/C
C: I
‰
œ‰
œ œ
œœœœœ
& œ .œ œ œdominant
œG m
œ
≈ J
≈ œJ . Gœ m œ
Œ
b C œ œ œ œ œ˙œ œ œ œ
b
˙
&
œœ
œœ œœ
œœ
?
G 7/B
V7/3rd
‰
œ tonic
œ‰ œœ œœ
œ
œ
œ œ
Ͽ
œ
≈œ œJ . G m œ
≈ œJA . 7/G œ
œ
Œ
˙œ œ œ œ œ œ œœ˙œœ œ œœ œ œœ œœ
C
I
œ œ œœ œœ œ œ œœ œœ œ œ YT:
œœ œœvqM4tCZ7RV8
œ œ œœ œœ œ œ œœ œœ œœ œœ œœ œœ œ œ œœ œœ œ œ œœ œœ œ œ
Figure 9.4.9 J.S. Bach, Well-Tempered Clavier, Book I, Prelude 1 in C major
7/3rd
I
BWV V
846
198
œ Œ tonic
Œ Ó
Ó
ø Œ Ó
Gm
Aœ7/G
œ
g:
i
i
i
iiø7/7th
œ
œ
Œ
œ
œ
œ
œ
b C œœ œ œœœ œœ œ
œ œ œ œ œœ œ Œ œœ œœ
b
&
œœ
œœ œœ
œœ œœ
œœ œœ œ œ œœ œœ œœ œœ œ œ œœ œœ œ œ
ø
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
#
7
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œœ
A /G
D 7/F
D7
Gm
? bb C Œ
œ Œ Ó
dominant
Gm
Gm
b œ œ œœœ œ œ œ œœ œ Œ œœ œœ # œ œ œ œ œ œ œ œ œ Œ
b
?
& b b Cœ Œœ œœ œœ œ œŒ œœ œœÓ œ œ œ œ Œœ œÓœ œ œ œ œœŒ œœ Ó# œ œ œœ œœ œ Œœ œœÓœœ œ œ
œœ œœ
œœœ œœ
œœ
œœ œœœ œœ
203
g:
203
207
207
i
? b b A œøø77/G Œ Ó
ii /7th
b
& b œœ œ œœœA bœœœ œœ œ œœœ œœœ
b b b œ 3œ ˙ . œ œ
b
&
4 ˙.
? bb œ Œ Ó
Z
? b b biiø743/7th œœœ œœœ
b (pre-dom.)
œ
°
A
A¯≤: I b
bb b b 3 ˙ .
&
4 ˙.
i
i
iiø7/7th
Œ Ó
œ Œ Ó
G im Œ Œ
œ
# œ œ Œ œ DV77
Œ
œ
#
œ
œ
œ
œ
œ
œ œœ œ œ
œ
œ
œ
œœ Dœœb œ œ œœ œœ œ œ Eœœb œœ œœ œœ # œœ œœ œœ Aœœb œœ œœ œœ œœ œœ œœ
˙.
œ œ œ œ œ Œ
˙.
œ œ œ œ œ
Œ Ó
œ Œ Ó
œ Œ Œ
#œ
œœ V7 œœ œœ
œœ
V7/3rd œ
i œ
œ
œ dominant
œ tonic
œ
œ
* °
*°
*°
*
b
DIV
Eb
AIb
V
.
˙YT: O0PChj-uQPo œ œ œ œ œ Œ
˙.
œ œ œ œ
Figure 9.4.10 W.A. Mozart, Symphony No. 40 in G minor, K. 550, I.œ (textural
reduction)
Z œœ œœ
œœ œœ
œœ œœ
œœ œœ
? b b b 43
œ
œ
b
œ
œ
œIV
A¯≤: Iœ
V
I
* °
*°
*°
°
*
#
DV77/F/3rd
tonic
pre-dom.
? ## œ
œ
œ
V7
œ
œ
œ
I
œ
œ
CHAPTER 9. HARMONIC
PROGRESSION AND HARMONIC
(dominant)
tonic FUNCTION73
116
116
Db
Db
bb 4
&bbb 4 œ
œ œœ w
Œ
œ œ œ œ
E b m7 A b 7
Œ
w
Db
œ œ œ œ
œ œœ
œ
œœ œœ œœ œ œœ œœ œœ œ
œ
œ œœ œœ œœ œ œ œœ Œ Ó
Startspreading
- the news
bb 4
&bbb 4 Œ Ó
? bb 4
bbb 4
E b m7 A b 7
∑
I'm lea - ving to
œ Œ
œ
Œ œŒ
D¯≤: I
œ
day,
Œ
I
tonic
œœ
I want to
be
œ Œœ Œ
œŒ œ Œ œ
ii7
ii7 V7
V7
pre- dom.
dom.
I
pre- dom. tonic
dom.
YT: 5-pyc_z7WbY
Figure 9.4.11 John Kander and Fred Ebb, “Theme from New York, New
York” (1977)
A
jj j
? ### 4
4 œ. #œ œ œ œ œ Œ Ó
295
j œ
œ . œ œJ œJ œ Œ Ó
Bm
A: I
? ###
299
ii
tonic
pre-dom.
j jœ j Œ Ó
œ œ œ
#
œ
œ.
jj j Œ Ó
œ. ‹œ œ œ œ œ
E
A
V
? # # # 44 A
w
303
I
dominant
tonic
w
w
D
w
E
E
YT: 7PCkvCPvDXk
A: I
IV
V
V
I
Figure 9.4.12 Meghan Trainor and Kevin Kadish, “All About That Bass”
(bass line and chord symbols only) (2014)
˙˙˙ are examples
˙˙
Here
˙˙˙ with I˙˙˙– IV – V – I
˙
&
progression.
308
309
C: I
vi
IV
V
versus
˙˙˙
˙˙
˙
I
vi
C
Am
˙
C: I
311
G¯≤
? b b b 44
bb w
D¯≤: IV
315
˙˙
˙
vi
ii/3rd
V
F
G
˙
IV
A¯≤
D¯≤
B¯≤m
V
I
vi
w
˙˙
˙
realizing the Ton-PreDom-Dom-Ton
? 44 ˙
w
˙
V
w
? 4 œ œ œ œ œ œ œ œ bœ œ œ œ œ œ œ œ
b 4
œœœœœœœœ œœœœœœœœ
F
F: I
FUNCTION:
319
œ
A
tonic
E¯≤
B¯≤
F
¯≤VII
IV
I
ton. prol.
pre-dom.
tonic
? bb œ Œ Ó
Œ Ó
#œ
œ Œ
Ó
Œ Œ
œ
7/3rd
CHAPTER
HARMONIC V
PROGRESSION
AND
iiø79./7th
V7 HARMONIC FUNCTION74
i
(pre-dom.)
Ab
dominant
Db
b
& b b b 43 ˙˙ ..
207
Eb
˙.
˙.
Z œœ œœ
œ œ
? b b b 43
b A œ œ œ œ œ
? # # # 44 œ # œj œj œ œj Œ Ó
ϡ
.
* °œ
*
295
A¯≤I: I
A:
pre-dom.
œ œ œ
œ œ œ
tonic
œ œ Œ
œ œ
œœ œœ
œœ œœ
œ
Bm
œ j œ
œ . œ œJ *œJ °œ Œ Ó *
°
iiV
I
dominant
pre-dom. tonic
j jœ j Œ Ó
j œj œ œj Œ Ó
œ œ œ
#
œ
œ.
œ. ‹œ
œ YT: pceSX1hceOI
? ###
299
IV
tonic tonic
Ab
E
A
V
I
Figure 9.4.13 Frédéric Chopin, Waltz in A-flat major, Op. 34 No. 1
dominant
? # # # 44 A
w
303
18
˙˙˙
&
? # # # 44
C: I
D
IV
tonic
w
E
E
V
A
œ
V
pre-dom.
I
dominant
tonic
˙˙˙
˙˙˙A
˙˙
˙˙˙
˙˙
˙˙˙
˙˙˙
Bm ˙
˙
j
j
j
j œ YT: CXnEgbDcITo
œ œ œ Œ Ó
. œ œJ œ œJ œ Œ Ó
#
œ
œ
œ
.
vi David
IV Crane,VMarta
versus
I
vi
ii/3rdAlleeV Willis,
Figure 9.4.14
Kauffman,
Michael
Skloff,
308
295
309
A:Danny
I
ii (bass line and chords only)
Phil Solem,
Wilde, “I’ll Be There For You”
C
Am
F
G
(1995)
E
A
Progressions using vii◦ ( I – IV – vii◦ – I and I – ii – vii◦ – I ) are less common
because of the instability of diminished chords.
C: I
vi
IV
V
V
I
9.4.4 The Tonic-Tonic
Prolongation-PreDominant-Dominant
G¯≤
A¯≤
D¯≤
B¯≤m
A
D
E
E
A
Progression
? 44 ˙
˙j œj œ ˙œj ˙Œ Ó
j
j
jœ œ œ
Œ Ó
#
œ
œ.
œ
œ. ‹œ
œ
? ###
299
311
303
315
308
w
w
A: I
tonic
? b b b 44
w
b# b 4 w
w
?
#
w
w – Vw , althoughœ in
w
#
This progression
4 w is most commonly realized with I – vi – IV
D¯≤: IV
V
I
vi
classical music
one will often encounter
I – vi – ii/3rd
– V (mentioned
above in
A:onI vi – ii – V – I ). IV
V
the section
F
E
¯≤
B¯≤thirds.
Notice the bass line starts with descending
V
F
I
? b 44 œ œ œ œ œ œ œ œ b œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ
˙˙
˙˙
˙˙
˙˙ œ œ˙œ œ œ œ˙˙œ œ
˙˙
˙
˙
˙
˙
˙
˙ I ˙˙
& F: I
˙
˙ ¯≤VII˙
IV
C: I
FUNCTION:
vitonic IV
V prol.
versus
ton.
I
vi
pre-dom.
ii/3rd
tonicV
309
319
&
? b b 22 b œ . j
b
œ œ œ
Figure 9.4.15 Compare I – vi – IV – V to I – vi – ii/3rd – V (the bass lines are
the same) D¯≤sus2 A¯≤
E¯≤
A¯≤ E¯≤
D¯≤sus2 A¯≤
E¯≤
A¯≤ E¯≤
Here is a musical example with I – vi – ii/3rd – V .
315
&
319
&
E¯≤: ¯≤VII IV
I
œ œ ˙
IV I
b œ . œj œ
œ
¯≤VII IV
I
œ œ ˙
IV I
CHAPTER 9. HARMONIC PROGRESSION AND HARMONIC FUNCTION75 15
b
&bb
211
? bb
? ###
? ###
œ. ‹œ
œ
A
˙˙˙
&
?
?
323
327
E¯≤: I
vi
ii7/3rd
V
tonic
˙˙
˙
223
vi
I
˙˙˙
tonic
B¯≤
ton. prol.
pre-dom.
F m7/A b
Bb
dominant
œBm
œ œ œ njœ œ œ œ b œ œ
œ . œ œJ œ œJ œ œ œŒn œ œÓœ œ b œ œ œ œ n œ œ œ œ
Cm
AŒ
ii
œœ j œœj œœ j Œ
œ œ œœ
œw. # œ œ œ wœ
ii7/3rd
vi
I
œœœ
Œ
ton. prol.
F
œœœ œœœ Œ œœœ œœœ œœœ
Ó w
V
pre-dom.
Cm
dominant
Gm
w
w
ww
www
w
ww
YT: SSeveT_9ZxEw
œ
w
w
w
Figure 9.4.16 Ludwig van Beethoven, Pathétique Sonata, Op. 13, I
V
V
I
?IVb c
b
w
w
w
9.4.4.1 I–vi–IV–V
w
˙
D
A: I
319
Bb
b
&w b c
? # # # 44
w
?
F m7/A b
˙ œ œ œ œ œ œnœ œ œ œ bœ œ
œ
œœnœœœœ bœœœ
C
œnœ œ œbœ
p
C œ & œœ œœ œœ Œ œœ œœ œœ Œ œœ œœ œœ Œ œ œ œ
œ
w
w œ œ œ
w
44 215# œj œj œ œjb Œ˙˙ Óœ œ
œ.
& b bœœ
ÿ cresc.
A: I
E
Œ œœ œœ œœ
?
j œj œ œj b b b wŒ Ó
A
219
311
Cm
Eb
V
C: I
b
Eb
˙˙
˙
E
˙˙
E
˙˙
˙
˙˙
˙
A
˙˙
˙
B¯≤: I earlier, the progression
V
vi
As mentioned
I – vi –iiIV – V was so prevalent
in the
1950s that it is known as the “’50s
progression”
and
the
“’50s
doo-wop
unusual
unusual
F ˜7
Asus2
E9
G
D
Em7
F ˜7
progression.”Bm
IV
V
versus
I
vi
ii
/3rd
V
Listen
309 for this bass line in the following examples.
#
wC
& # c www
ww
? 44 ˙
# ww
? # # c www
C: I
www Am ww
w
w
w
w
w
Fw
w
˙ w ˙
#w
w
vi w IV
w
b: i
V7
VII
IV9
VI
Figure 9.4.17 I – vi – IV – V bass line in C major
w
Gw
w
˙w
Vw
III
ww
w
ww
iv7
w
ww
# ww
V7
unusual
unusual
• Hoagy Carmichaelunusual
and Frank Loesser,
“Heart
and Soul” (in C major)
YT: pNjpTOB4ksY
• Curtis Williams, Jesse Belvin, Gaynel Hodge, “Earth Angel” (in A-flat
major) (1954)
YT: VJcGi4-n_Yw
18
j œj œ œj Œ Ó
? # # # 44
#
œ
œ.
œ
j
œ . œ œJ œ œJ œ Œ Ó
A
Bm
CHAPTER 9. HARMONIC PROGRESSION AND HARMONIC FUNCTION76
295
• Dolly
“I Will Always Love You” ii(in A major) (1974)
A: Parton,
I
? ###
299
A
j œj œ œj Œ Ó
j œj œ œj Œ Ó
#
œ
œ.
œ
œ. ‹œ
œ YT: 3JWTaaS7LdU
E
• Johnny
V Ramone, Dee Dee Ramone, Joey
I Ramone, “Rock ‘n’ Roll High
School” (in C major)
A
D
E
E
A
? # # # 44
w
303
w
w
w
YT: vSkQEoZngyc
œ
A: I
IV
V
V
I
In the above examples, the chords have have half-note harmonic rhythm. In
the following example, the chords have whole-note harmonic rhythm (4 beats
per chord).
˙˙
&˙
308
˙˙
˙
˙˙˙
˙˙
˙
˙˙˙
˙˙
˙
˙˙
˙
˙˙˙
• John Stephens and Toby Gad, “All of Me” (in A-flat major) (2013)
C: I
vi
IV
V
versus
I
vi
ii/3rd V
309
? 44 ˙
C
Am
YT: 450p7goxZqg
˙
F
˙
G
˙
The I – vi – IV – V progression can also be rotated to IV – V – I – vi , as in the
C: I
vi
IV
V
following example.
311
G¯≤
? b b b 44
bb w
D¯≤: IV
? bb b
bb
A¯≤
D¯≤
B¯≤m
V
I
vi
w
w
w
315
YT: PIh2xe4jnpk
Figure 9.4.18 Nasri Atwey, Adam Messinger, Mark Pellizzer, Ben Spivak,
Alex Tanas, “Rude” (bass line and chords only) (2014)
? bb b
bb
323
You will see more examples of Tonic-Tonic Prolongation-PreDominantDominant progressions, including the use of the iii chord, in the Practice
Exercises and the Homework.
Remember, there are two exceptions in Harmonic Function: IV has tonic
prolongation function when it progresses to I , and I/5th has dominant func327 when it progresses to V .
tion
? bb b
bb
9.5 Exceptions Created by Harmonic Sequences
Exceptions to the harmonic flowchart often can be explained by harmonic
sequences.
FUNCTION:
œ ŒPre-Dom.
Œ œœ œœ Prol.
œœ œœ œœDom.Œ œTon.œ œ Œ œ œ œ
œ
?Ton.b w Ton.
œIV œ œ
œœ œœ œœ w œœ œœ œœ
w
bb
iii
w
V
ROMAN
I
NUMERALS:CHAPTERI 9.
I
vi
ii
HARMONIC
vi PROGRESSION
ii7AND
/3rd HARMONIC
V FUNCTION77
b
VII
b
bm
E b VII
CVII
F m7/A b
Bb
B¯≤
F
Cm
Gm
b 4 œ ˙ œ œ œ œ œ œnœ œ œ œ bœ œ œœ œœœ
b
nœ
& b b b 4C w
ww
www
&
ww
w
p
E
D
A
?
4
??#bb#bb#b# 4C44 œœ œ&œœœœœœœ œœœ œ œ Œwn œ œœœ œ œœœœ œœœœ œ Œ œœ œœ œœ
w
wwœ œ œ œ œ œ œ œ
wœ
219
211
(dashed lines represent possible movement within a functional area)
327
BE
¯≤:¯≤E:: III
223
331
ˆ
339
7/3rd
ii
iiIV
ton.
prol.
pre-dom.
unusual
unusual
F m7/A b
nwŒœ œœœœ œ œœ œœœœ œ
w
D
¯≤viV
VII
Bb
˙ œ œ œ œ œ œ nœ œ œ œ bœ œ
bb
G ∑
A
A
Gœ∑œ n œ œGœ œ b∑œFœ˜m
˙G
∑
∑
œ œ n œF∑˜œmœ œ
&
b
#
? # # 44œ
YT: Q4TK82N1nEk
w
w
ÿ n wKeith Forsey,
n w Giorgio
nw
nw
w
wWhat
Figure 9.5.1 cresc.
Moroder, Irene Cara, “Flashdance...
A Feeling”
A:Œ(1983)
¯≤œVIIœ œ ¯≤VIIŒ œ I œ œI
Œ ¯≤VIIœ∑œ œœ¯≤VII
Œvi cadence
?
œœ œœvi∑ œœ
œ
∑œ œ dom.
∑
∑
∑
œ
œ
œ
œ
deceptive
FUNCTION:
tonic
?Thebb bb sequence
œ
dom.
w
œ
œ
œ
œ
œ
œ
is between
w the first two bars
b
w and the last wtwoœbarsœ ofœthe
example.
FUNCTION:
215
Eb
viV¯≤VII
bwœ œ œ œ n œ œ œ b œ
ww
tonic
Cm
dom.
vi
ii /3rd
V
? b b 44 I
w
wF
Cm
w up a P5 Gm
bb 4 wB¯≤ up a P5
& 4 w
ww
www
www
ww
w
sequenced up a M2
? b b 44
Figure
9.5.2 Exceptions in w
“Flashdance... What A Feeling”wcreated by sew
quence
w
7
219
? bb
343
223
? bb
353
There
in theii verse of “HotelviCalifornia,” in
B¯≤are
: I unusual chord resolutions
V
the example below.
unusual
unusual
#
& # 44 www
Bm
? # # 44 www
b: i
F ˜7
ww
w
Asus2
V7
VII
# ww
www
w
w
unusual
ww
w
ww
ww
D
w
ww
Em7
IV9
VI
III
iv7
E9
# www
G
w
w
ww
ww
unusual
ww
w
F ˜7
ww
w
# ww
V7
unusual
YT: YW4dzWE1SUs
Figure 9.5.3 Don Felder, Don Henley, Glenn Frey, “Hotel California” (1977)
The example below shows how these exceptions come about through harmonic sequences.
15
sequenced up a M2
CHAPTER 9. HARMONIC PROGRESSION AND HARMONIC FUNCTION78
343
? ## 4
4 w
up a P5
w
18
w
up a P5
down a M2
? ##
w
w
w up a P5 w
w
pre-dom. dom.
down a M2
jœ œ œ
j œj œ œj Œ Ó
? # # # 44
Ó
œ
.
#
œ
œ
œ Œencounter
œ.
Look for harmonic
sequencesœas a possible explanation
J when
J you
351
295
A
Bm
Figure 9.5.4 Exceptions in “Hotel California” created through sequences
A: I progressions.
unusual chord
299
ii
E
A
j j
#
jPopular
?
#
j
j
j œ œ œ VIIŒ Chord
Ó
Œ Ó
9.6 #The Subtonic
in
œ œ œ œ Music
#
œ
œ
.
œ. ‹œ
œ
we will discuss mode mixture and the Mixolydian mode later, the
? b bAlthough
V
I
ubiquity of the subtonic chord (2 VII ) in rock and popular music makes it
bimportant to Adiscuss here. D
E
E
A
323
?The
# # # 2 VII
44
w
˙˙˙
&
˙˙
˙
w
w
w
œ
chord can precede tonic, dominant, and pre-dominant chords,
which means it can substitute for any function except tonic.
303
A: I
FUNCTION:
308
Ton.
ROMAN
NUMERALS:
C: I
vi
309
311
I
˙˙˙
IV
V
Ton. Prol.
˙˙˙
iii
vi
bVII
V
versus
V
˙˙˙
˙
IV ˙˙
Pre-Dom.
ii
bVII
I
vi
I
Dom.
Ton.
ii/3rd
bVII
V
˙
V˙˙
˙˙˙
I
? 44 ˙movement within a functional area)
(dashed lines represent possible
˙
˙
˙
C
Am
F
G
C: I Music vi
IV
V chord
Figure 9.6.1 Harmonic Flowchart for Popular
with Subtonic
VII
in Major
G¯≤
A¯≤
D¯≤
B¯≤m
Notice also that movement from IV – I (from the plagal cadence) is common
in the following examples from popular music.
Here are examples ending with 2 VII – IV – I , where IV progresses to I (a
D¯≤: IVand is precededVby 2 VII .
I
vi
plagal cadence)
? bb
327
IV
b ? b b b b 44
b
w
w
w
w
F
E¯≤
B¯≤
F
? b b ? b 44 œ œ œ œ œ œ œ œ b œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ
b
œœœœœœœœ
315
335
¯≤VII
F: I
? bb
339
319
FUNCTION:
tonic
ton. prol.
IV
I
pre-dom.
tonic
b
YT: A_MjCqQoLLA
? bb C b œ . j
b œ . œj œline and chords
Figureb 9.6.2 Lennon-McCartney,
Jude” (bass
œ œ œ œ œ“Hey
˙
œ œ œ ˙only)
(1968)
the following questions: When a phrase ends on the IV chord,
? b bdoesConsider
it have dominant function (i.e, is it a half cadence)? Does IV have
b
dominant
function in popular music when it progresses to I ? If so, does 2 VII
347
have pre-dominant function in the above progression?
? bb
355
b
19
? b 44 œ œ œ œ œ œ œ œ b œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ
œœœœœœœœ
F: I 9. HARMONIC¯≤PROGRESSION
VII
IV
I FUNCTION79
CHAPTER
AND HARMONIC
FUNCTION:
?319b b
323
tonic
ton. prol.
pre-dom.
tonic
Notice that 2 VII begins the phrase in the following example, and proceeds
19
to a IV – I conclusion.
b
D¯≤sus2 A¯≤
E¯≤: ¯≤VII IV
Ton.
Ton. Prol.
FUNCTION:
? bb
323
E¯≤
A¯≤ E¯≤
? bb C b œ . j
b
œ œ œ
E¯≤
b œ . œj œ
œ
I
IV I
¯≤VII IV
Dom.
Ton.
Pre-Dom.
iii
ROMAN
NUMERALS:
œ œ ˙
D¯≤sus2 A¯≤
IV
I
A¯≤ E¯≤
œ œ ˙
IV I
19
V
ii YT: z8rQ575DWD8 I
bVII
Figure 9.6.3 U2, “Desire” (bass line and chords) (1988)
b
I
vi
bVII
bVII
2 VII preceding and following the IV chord.
The following
example
(dashed
lines represent
possiblehas
movement
within a functional area)
Does the 2 VII chord have tonic prolongation as labeled, or is it “pre predominant” in function?
Ton.
Dom.
Ton.
FUNCTION:
Ton. Prol. Pre-Dom.
327
E
D
A
D
iii
IV
V
ROMAN
I
I
vi
ii
NUMERALS:
bVII
bVII
bVII
E: I
¯≤VII
IV
¯≤VII
? # # # # 44 œ œ œ œ œ œ œ œ n œ œ œ œ œ œ œ œ
œ œ œ œ œ œ œ œ nœ œ œ œ œ œ œ œ
? ####
331
327
? ####
339
? ####
347
331
? ####
? ###
ton. prol.
tonic
pre-dom.
FUNCTION:
(dashed lines represent possible movement within a functional area)
dom.
E
D
A
D
#
?
#
4
œ
œ
œ
œ
œ
œ
œ
œ
# 4 Keith Forsey andn œ Steve
œ œ œ œSchiff,
œ œ œ “Don’t
œ œ œ œMe)”
œœ
Figure
# 9.6.4
œ œ œ œYou
œ œ œ(Forget
œ n œ œAbout
(bass line and chords) (1985)
YT: CdqoNKCCt7A
VII cadencing to
IV the I chord in
¯≤VIIthe first four
Here is E:
an I example with 2¯≤VII
ton. in
prol.
tonic
pre-dom.
dom. four
FUNCTION:
bars
then progressing
to the vi chord
a deceptive
cadence in the second
bars.
? # # # 44
nw
G
A: ¯≤VII
FUNCTION:
G
nw
¯≤VII
dom.
A
w
I
A
w
I
tonic
G
nw
¯≤VII
G
nw
¯≤VII
dom.
F ˜m
F ˜m
vi
vi
w
w
deceptive cadence
355
339
? ####
? ###
363
347
? ###
355
YT: GaH25Sghoqc
Figure 9.6.5 Walter Becker and Donald Fagen, “Reelin’ in the Years” (bass
line and chords)
CHAPTER 9. HARMONIC PROGRESSION AND HARMONIC FUNCTION80
16
9.7 The Best-Seller Progression
#
& # 44 ˙
˙˙
231
D
A
Bm
G
˙˙
˙
˙˙
˙
˙˙˙
V
vi
IV
? # # 44 ˙
˙
˙
D: I
˙
#
∑ progression
∑
∑occurs∑in many∑ popular
∑ songs,
∑ has ∑a Wikipedia
∑
&The# I – V∑ – vi – IV
233
Figure
9.7.1 The I – V – vi – IV “Best-Seller” Progression
page, and has been mentioned in a New Yorker article about bestselling novels
(see the third paragraph from the end of the article). The music group Axis of
Awesome made a compilation of several songs with the I – V – vi – IV progression that makes for an entertaining summary (warning: there is some language
13
after the 5-minute mark).
Here is a written-out example that includes the I – V – vi – IV progression.
? # # ∑
122
122
∑
∑
∑
##
& # 44 ∑≈ œ œ œ œ ∑œ œ œ œ
A
243
E
∑
∑
# # # ∑ ∑
&
#
∑
& #
? # # # ∑ ∑
? ##
∑
∑
∑
∑
∑
∑
∑
F˜m
∑ œ œ œ ∑ œ œ . ˙ ∑
#
? ## ## 44 ∑ œ ∑ œ
&
œ ∑
œ
œœ œ œœ œ œœ œœ œ œ
? ### 4
4 ˙
249
˙
##
˙
∑
∑
∑
& A: I
V
124
# # # ∑ ∑ ∑ ∑ ∑ ∑ ∑
&
? ##
∑
∑ YT: hLQl3WQQoQ0
∑
Ne-ver mind I'll find
∑
some-one like
∑
∑
∑
∑
∑
D
œ∑ œ
you
∑
∑
∑
∑
∑
∑
I wish
œ ∑ œ œ ∑ œ
œ œ œ œ œ œ œœ œœœ œ
˙
˙
vi
∑
∑
∑
˙
IV
∑ ∑
∑
∑ ∑
∑
∑
∑
∑
∑
124
Figure
9.7.2 Adele Adkins and Dan Wilson, “Someone Like You” (2011)
∑
∑
The I – V – vi – IV progression can be rotated to become vi – IV – I – V and
255
IV – I – V – vi .
##
& #
137
137
&
###
? ###
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑ ∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
20
352
13
? # # 9. HARMONIC PROGRESSION AND HARMONIC FUNCTION81
CHAPTER
# # # 4 ≈ start
& 4 œ œ œI œ œ œ œ œ
A
122
# # # 4IV
& 4
122
F˜m start
E
œ œ œ œ œ . vi˙
Ne-ver mind I'll find
œ
some-one like
œ œ
you
œ
V
vi
œ
œ
I wish
œ œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ œœœ œ
œœ œœ œ œ œ
? # # # 44
˙
˙
œ
D
V
œ
˙
˙
˙
IV
I
˙
Figure 9.7.3
A: IExample of I – V –Vvi – IV rotation tovivi – IV – I – V IV
360Here is an example with the vi – IV – I – V progression.
? ##
bb 4
&bb 4 œ œ œ œ œ œ œ
124
Fm
? ##
D¯≤
bb 4
& b b 4 œ.
œœ ..
16
Hel - lo
from
? b b b 44
b
œ.
the
oth - er
j
œœ ˙˙
œ ˙
j
œ ˙
E¯≤
œœ ..
œ.
j
œœœ ˙˙˙
œ.
377
124
j
œ ˙
A¯≤
side
œ.
j
œ ˙
I
V
#
& # 44 ˙
˙˙
˙˙
˙˙
˙˙
˙
˙
˙
126
∑ ∑YQHsXMglC9A
∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
? b#b#b b44 ∑ ˙ ∑ ∑ ∑ ∑ YT:
&
˙ Greg Kursten,˙ “Hello” (2015)˙
Figure 9.7.4 Adele Adkins and
231
D
A¯≤: vi
A
IV
Bm
G
bb
& b b ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
– IV
can also bevithought of as IV
being in minor:
I – I – V progression
V
126The viD:
i – VI – III – VII
233
bbbb
&
? bb b
b
Fm
œœœ
∑ ∑
? bb b œ
b
A¯≤: vi
D¯≤
œœ
œ∑ ∑
œ
IV
A¯≤
E¯≤
bb œ
œœ
œ∑ ∑ œœœ ∑ ∑ b∑b ∑œœ ∑
œ
I
Fm
œ
bbbb œ
V
f: i
D¯≤
A¯≤
œœ
∑œ ∑
œœ
œ∑ ∑
œ
œ
VI
III
E¯≤
œœœ
∑ ∑
œ
VII
Figure 9.7.5 “Best-Seller” Progression with Roman Numerals in Major and
Relative Minor
235
Whether you hear this progression in major or minor depends on whether
you hear the first chord as the tonic or if you hear the third and fourth chord
as tonic and dominant.
Here is an example with the IV – I – V – vi progression.
b
& b b b ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
? b b b ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
b
b
& b bb
249
∑
∑
∑
∑
∑
∑
B¯≤: I/5th
V7
I
dom.
ton.
CHAPTER 9. HARMONIC PROGRESSION AND HARMONIC FUNCTION82
bb 4
&bbb 4 Œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ
G¯≤
157
bb 4
& b b b 4 ww
w
157
D¯≤
Now that it's rain - ing more than ev - er Know that we still have each oth -
ww
w
? b b b 44
bb w
w
D¯≤: IV
I
159
b
& b bbb œ œ œ œ œ œ œ œ œ œ œ œ
œ œ œ œ œ œ œœ
A¯≤
159
&
bbbb
B¯≤m
er You can stand un - der my um - br - el - la You can stand un - der my um - br - el -
b w
ww
ww
w
V
vi
? bb
bbb w
20
? ##
352
w
start
start
YT: CvBfHwUxHIk
vi
I
Figure 9.7.6 Christopher Stewart, Terius Nash, Kuk Harrell, Shawn Carter,
“Umbrella” (2007)
V
IV
IV
V
9.8 The i–VII–VI–VII Progression
I
Thevii – VII – VI – VII ( Am – G – F – G ) progression
is similar to the descending
1̂ –27̂ –26̂ –5̂ bass line of the “Andalusian progression” ( Am – G – F – E ) in flamenco music, with the exception of the last bass note or chord.
Here are examples of the i – VII – VI – VII progression.
360
? 44
Am
œ œ Œ
a: i
?
G
œ œ
VII
Œ
F
œ.
VI
G
œ œ œ œ œ.
œ œ
VII
362
YT: iXQUu5Dti4g
Figure 9.8.1 Jimmy Page and Robert Plant, “Stairway to Heaven” (chords
and bass line only) (1970)
?4
4 œ œ Œ
Am
360
vi
G
F
Œ
œ œ
œ.
G
I
œ œ œ œ œ.
œ œ
CHAPTER 9. HARMONIC PROGRESSION AND HARMONIC FUNCTION83
a: i
VII
VI
VII
362
16
231
Cm
a: i
c: i
362
? bb
366
b
Am B¯≤
G
A¯≤
F
B¯≤
G
VII
VI
VI
VII
VII
4
? b b 44 œ œ œ ?
4œ œœœ œœ œŒœ œ œ œœ œœœ Œœ œ œ œœœ. œ œ œœ œœ œ œœ œ œœ œœœ. œ œ œ
œ
œ
b
360
VII
B¯≤
A¯≤
Cm
366
D: I
233
bb œ
œœ
& b b VII
Fm
? bb œ
bb
V
start
D¯≤
i
œœ
œ
œ
VI
A¯≤
œœ
œ
E¯≤
VII
œœœ
œ
œ
start
vi
IV
VI
Fm
D¯≤
œ
œ
b b b bVIIœœœ
bbbb
A¯≤
œœ
œ
E¯≤
œœVII œœ
œ
œ
i
œ
œ
374
Figure
9.8.3 The i – VII – VI – VII progression rotating to VI – VII – i – VII
A¯≤: vi
IV
I
V
f: i
VI
III
VII
?In bsome
b b cases, the fourth chord is eliminated. In that case, VI – VII – i – VII
becomes VI – VII – i – i , as in the following examples.
235
B¯≤
G
? b b 44 œAœ œ œ œ œ œ œ œ œBm
œœœœœœ œœœœœœœœ œœœœœœœœ
b
#
& # 44 ˙
c: i ˙
VII ˙
VI ˙
VII
˙˙
˙˙
˙˙
˙˙ YT: rYEDA3JcQqw
Figure 9.8.2 Adele Adkins and Paul Epworth, “Rolling In The Deep” (chords
and bass line only) (2010)
? #b # 44 ˙
?
The
can also be˙rotated to become
b b i – VII – VI – VII progression
˙
˙ VI – VII – i – VII .
D
4 œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ
b
& 4
B¯≤
C
Dm
B¯≤
C
Dm
? b 44 ˙
˙
˙
˙
w
w
˙
˙
˙
˙
w
w
d: VI
VII
i
VI
VII
i
& b ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
239
YT: 4RYlgoQrshw
? b ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
Figure 9.8.4 Christopher Bridges, Calvin Broadus, Johnny Mollings, Lenny
Mollings, William Roberts II, “All I Do Is Win” (chords and bass line) (2010)
?4b œ44 ˙œ Œ ˙
Œ
œ œw
˙ VII w
a: i ˙
œ˙ œ ˙œ œ œww.
˙
˙
œ.
œ œ
VI
VII
d: VI
VII
iPROGRESSIONVI
VII
i FUNCTION84
CHAPTER
9. HARMONIC
AND HARMONIC
Cm
B¯≤
A¯≤
B¯≤
? b b 44F œ œ œ œ œ œ œ œG œ œ œ œ œ œ œ œAm
œœœœ
b w
w œ œ œ œ œ œ œ œ wœ œ œ œ
w
c:w i
VII
VII
w VI
w
4
w
&4
362
239
? b
bb
366
œ œ œ œ œ œ œ œ œœœœœœœœ œœœœœœœœ
? 44 œœ œ œ œ œœ œ œ œ œ
start
start
i a: VI
VII
VII
VI
i
VII
VII
VII
YT: F6AggxvVFRY
12
Figure
9.8.5 Philip Glass, Metamorphosis Two (1989)
VI i – VII – VI – VII
i be thought
The
www can# also
# wwww progression
# # # # w of asb being
www inb ba wwmajor
# wwww
12
b b b _____
key:
vi – V – IV –&V .# _____
w
w
w
w
w
w_____
_____
_____
_____
_____
407
407
Am
ww F
ww G
G1.# b: _____
w 2. Eb¯≤: _____
Ex. e: III /5th
9.9 Practice
Exercises
b b b 1. A: ii7
b
& _____
b _____
bb
Day One Day One:
& 1. a: iv7 b b b 2. D¯≤: iii7
_____
419
_____
M7
419
1.
425
425
431
431
432
432
433
433
435
434
434
441
447
_____
_____
_____
w
www 6.bBb ¯≤G: ww_____
˙˙˙
˙˙˙ # wwww˙˙ 5.b d:F˙˙_____
˙˙˙ww
&˙˙ # w ˙˙ b b ww ˙˙
w
&
˙ _____˙
˙
˙
˙
_____
_____
_____
_____
_____
www 5.b d: _____
ww 2. E¯≤:#_____ww 3. e:# _____
# w 4. E:b _____
ww 6. B#¯≤: _____
?1. b:b _____
w
ww
n
b
w
# ww # www b w b b n w
bb w
ww
_____
_____
_____
_____
_____
_____
a: i
VII
VI
VII
C:
vi
V
IV
V
www
w # ww #9. f#˜: _____
ww 12.#G: _____
? b 7.b f:n_____
ww
ww # wwww 10.b bg: _____
w b b11.b c:n w_____
b b www 8. #D: _____
w
ww
Figure 9.8.6 The same
progression
relative major
maj7/D
G_____
_____ viewed
_____from minor
_____
_____ and _____
413
# 7. f:more
# # #12.
_____# common
10. g: _____ b 11.to
c: _____
b 9. f˜: _____# #progressions
There are several
explore
fu# # G:in_____
# # 8. D: _____bharmonic
b
b
&
7
maj
G
_____
/D
_____
_____
_____
ture chapters
dealing with topics like secondary _____
chords, mode
the
_____ mixture,
413
#augmented
# # sixth
# # # M7
b ø7and# jazz ø7harmony.
b
Neapolitan chord,
7
7 chords,
&Ex. e: IIIM7/5th # 1. A: ii b 2. g: ii #3. D: vii b b 4. c: V #5. B:# IV /3rd
401
374
_____
_____
401
2.
# # wwww
Am #4. #E:# _____
G
3. e: _____
# #2.# g: iiø7
_____
##
_____
3. D: viiø7
# # #3. f˜: viio7 # #
_____
_____
4. D: vi7
bbb
#
_____
_____
4. c: V7
5. B: IVM7/3rd
b b 5.b c: iv7/3rd # 6. G: IM7
_____
_____
Write the circle
of fifths _____
progression
in the following
keys
root
_____
_____
_____
_____ with_____
o7
7
7 Label
7
7
position
triads.
Roman
numerals
below
and
lead-sheet
symbols
1.
a:
iv
2. D¯≤: iii
3.
4. D: vi
5.
? b
# f˜: vii
# c: iv /3rd b 6. G: IM7
b
b
above. b b b _____ b b _____ # _____ b _____
_____
_____
(a) In
7. f: V7
?F bmajor:
8. A¯≤: ii7
#9.#b: viio7/5th b10.b B¯≤: viiø7 11.# e: iiø7/3rd b12. F: IVM7
b bb
bbb
?b
7. f: V7
8. A¯≤: ii7
9. b: viio7/5th 10. B¯≤: viiø7 11. e: iiø7/3rd 12. F: IVM7
? b _____
I
I
_____
_____
_____
_____
_____
_____
_____
7
8
1
2
3
4
5
6
# I
I
_____
_____
_____
_____
_____
_____
_____
_____
(b) In
&B #minor:
7
8
1
2
3
4
5
6
# I
I
_____
_____
_____
_____
_____
_____
_____
& # _____
7
8
1
2
3
4
5
6
? b b _____
i
i
_____
_____
_____
_____
_____
_____
_____
7
8
1
2
3
4
5
6
13
I
I
?
_____
_____
_____
_____
_____
_____
_____
_____
b
Review. Write
intervals above the given note.
b 1 the following
7
8
2
3
4
5
6
#
?
#
b
w
w
I
& & # _____
w _____ _____ _____# w _____ _____
_____
# w_____
w8I
7
1
2
3
4
5
6
5. º5↑
6. m7↑
3. P5↑
1. º7↑# #
2. M3↑
4. M7↑
I
I
_____
_____
_____
_____
_____
_____
_____
_____
#
&
7
8
1
2
3
4
5
6
&
&
bw
1. m3↑
w
i
_____
1
w _____
2. m6↑
w
2
w
_____
3
3. P5↑
bw
? w
_____
_____
4
5
4. º7↑
? #w
w
_____
6
5. M3↑
w
_____
7
b w_____
i
8
6. M6↑
w
&
457
bw
F˜º7
w
w
F˜7/C˜
3. P5↑
?
w
bw
?
4. º7↑ Dm/F
5. M3↑
&
Am
6. M6↑
& 9. HARMONIC PROGRESSION?
CHAPTER
AND HARMONIC FUNCTION85
447
3.
453 461
&
G
B˜º
¯≤m/B
?
?
FF˜˜7m/C˜
5. g:
b: _____
_____
5.
ADº/F
¯≤maj7
&
2.2.cA:
˜: _____
_____
?
FF˜˜º
/A7˜
w
8. F: _____
3.3.Ec:¯≤:_____
_____
Am/G
C˜m
4. E:
G: _____
_____
4.
?
Dmaj7
Dm/F
&
6.6.D:
B:_____
_____
?
f ˜_____
: _____
7.7.d:
Fm
Am
8.8.AF:
¯≤: _____
_____
Review. Correct the rhythmic notation of the following example.
G˜º/B
Incorrect
ã&44 œ œ œ œ œ
465
Day Two:
5.
? 44 œ
A¯≤maj7
Correct
&& b w
ww
_____
?b w
F: _____
1
7.
œ œ&
2. c˜: _____
Bo/D
C/E
Incorrect
F˜/A˜
Dm/F
Am/G
3. E¯≤: _____
C/G
G
4. G: _____
C
Correct
Half Cadence =
6. D: _____
= œ 7. f ˜: _____
œ
œ
œ Cadence
œ Deceptive
Plagal Cadence =
Authentic
= I/5th
viio/3rd
I/3rd Cadence
ii/3rd
V
˙
œ œ œ œ)
Fm
8. A¯≤: _____
I
passing
Analyze the following
progressions with lead-sheet symbols above and
pre-dom.
FUNCTION:
tonic
dom.
tonic
Roman numerals
below.
469
245
œ œ.
≈
5. b: _____
C: I
6.
B
7
F˜m
(4
œ œœœ œ ?
œ ˙˙˙œ
&
4œ œœœœ œ œ œœœœ œ ?œ œœœœ œ œ œœœœ œ ) (œ œœœ œ œ Dmaj
6
œ
œ
œ
œ
œ
œ
œ
œ
For
each
cadence,
label
the
chord(s)
involved.
.
&
ã&8
C
253
B
D
1. f:a:_____
_____
1.
1. a: _____
471
# w7. d: _____ w
( œ œ œ œ œ œ œ œ?œ œ œ œ œ œ œ œ ) ( œ œ œ œ œ œ œ œ ?
œ œ œ œ œ œ œ œ)
461
243
bw
6. B: _____
Review.
lead-sheet
symbol and
key, write
the key signature,
7. º7↑Given the
8. M3↑
10. m7↑
11. º5↑
12. P5↑
9. +6↑
triad or seventh chord, and Roman numeral.
&
4.
2. m6↑
w 5. g: _____ w
&
465
457
469
1. m3↑
_____
ww
w
w
_____
2
_____
ww
w
w
_____
3
####
_____
ww
w
_____
ww
# # # # ww
w
E: _____
1
_____
4
_____
_____
ww
ww
w
w
w
w
_____
2
_____
3
_____
ww
ww
_____
4
# # ww the wRomanwwnumerals,
ww write
(a)
chords
b b the
ww triads
ww or seventh
ww
ww
ww
& Given
w
w
w
w
w
w
w
_____
_____
_____ do
For the _____
progression,
the following:
_____
_____
_____
_____
(b) Analyze the harmonies with lead-sheet symbols above the staff
w harmony
w using
(c)
the harmonic function ofbeach
? #Analyze
w the wabbre#viations
w “ton.”
b
w forwtonic function,
w
“dom.” for dominant function,
“pre-dom.”
for pre-dominant
“ton. _____
prol.” for
tonic
b:
_____
_____
_____ function,
B¯≤: _____ and_____
_____
_____
1
2 function
3
4
1
2
3
4
prolongation
#
bb w
w
b
ww _____ ww_____ ww
w
_____
_____ that
_____
_____
_____ the
(d) Specify
cadence
ends the_____
progression
&
#
&? ##
261
14
473
ww
w
44
w
D:
ww
w
www
w
_____
I
G: _____
_____
_____
1
2
FUNCTION:
ww
w
_____
w
iii
_____
_____
3
w
vi7
w
bbb w
ii7/3rd
_____
ww
w
_____
V
w
E¯≤: _____
_____
_____
_____
_____
_____
_____
4
1
2
3
_____
˙˙˙ ˙˙
˙
_____
˙ ˙
I
_____
_____
4
Cadence: _______
479
? b b 44
g:
FUNCTION:
_____
_____
_____
_____
_____
i
VI
iv
iiø7/3rd
V7
_____
_____
_____
_____
www
_____
_____
i
_____
17
CHAPTER 9. HARMONIC PROGRESSION AND HARMONIC FUNCTION86
Click here to download the first homework assignment for this chapter.
Click here to download the second homework assignment for this chapter.
Chapter 10
Non-Chord Tones
10.1 Introduction to Non-Chord Tones
Non-chord tones are notes that do not belong to the chord. Sometimes
referred to as “embellishing tones” and “non-harmonic tones,” non-chord tones
are classified by how they are approached and left (either by same tone, step,
or leap).
There are nine types of non-chord tones.
Table 10.1.1
Non-Chord Tone
Passing Tone
Neighbor Tone
Appoggiatura
Escape Tone
Double Neighbor
Anticipation
Pedal Point
Suspension
Retardation
Approached by
step
step
leap
step
see text
step
same note
same note
same note
Left by
step in same direction
step in opposite direction
step
leap in opposite direction
see text
same note
same note
step down
step up
The following qualifiers can be applied to non-chord tones:
• Accented—occuring on the beat
• Unaccented—occuring on the weak part of the beat (on the offbeat)
• Chromatic—not belonging to the key
• Metrical—equal to the duration of the beat
• Sub-metrical—smaller than the beat
• Super-metrical—larger than the beat
10.2 Passing Tones
Passing tones are notes that pass between chord tones.
87
CHAPTER 10. NON-CHORD TONES
88
E¯≤
b 4
&bb 4 Œ
Cm
(E¯≤-G-B¯≤)
œ
Girl
Œ
pt
œ (œ ) œ
Œ
you're the one
œ
I
app
œ
( )
want
œ
to
(C-E¯≤-G)
pt
œ œ
( )
want
me
b b∑b b b
&
(C-E¯≤-G)
4
E¯≤
b 4
&bb 4 Œ
œ
? bb b 4 Œ
& b b4
YT: rClUOdS5Zyw
Cm
(E¯≤-G-B¯≤)
app
pt
pt Martin,
Figure 10.2.1 Jason Desrouleaux, Ian Kirkpatrick, Samuel Denison
9(˜5)=A¯≤-C-E-G¯≤-B¯≤ D¯≤6=D¯≤-F-A¯≤-B¯≤
D¯≤=D¯≤-F-A¯≤
A¯≤
E¯≤ Mitch Allan, “Want to Want Me” (2015)
Cm
Lindy Robbins,
( )
( )
((C-E¯≤-G)
)
(E¯≤-G-B¯≤)
app the passing tone is
In the first bar of the “Want toptWant Me” example,
pt
Girl
you're the one
I
want to
want me
unaccented. In the third bar, it is accented (on the beat). The non-chord tone
( )
( )
( )
in bar 2 is an appoggiatura.
4
There can
be
two
consecutive
diatonic
passing
tones
in
a
descending
sigh
is
just you're athe one sigh
Girl
I want to
want
me scale
segment from the root and fifth of a chord.
œ Œ œ œ œ Œ œ œ œ œ œ
œ
œ
˙
˙
œ
Œ
Œ
œ
œ œ œ
œ œ œ œ œ
? b b ∑
bbb
7
4
D¯≤
A¯≤9(˜5)
D¯≤6
? ? b ∑b
(D¯≤-F-A¯≤)
(A¯≤-C-E-G¯≤-B¯≤)
(D¯≤-F-A¯≤-B¯≤)b b b b ∑ b b b
b
œ (œpt) (œpt) œ
˙
˙
A¯≤9(˜5)
D¯≤6
? b b b D¯≤
b b (D¯≤-F-A¯≤)
(A¯≤-C-E-G¯≤-B¯≤)
(D¯≤-F-A¯≤-B¯≤)
8
œ
œpt œpt) œa ˙sigh
? b b bb ∑sigh∑ ∑ ( is∑) ∑ ∑(just
∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ˙∑ ∑ ∑ ∑ ∑ ∑
b
7
sigh
is
just
a
sigh
? b b ∑b
bb
YT: d22CiKMPpaY
5
5
5
? b b ∑b
bb
8
? b b b ∑ ∑ ∑ B¯≤∑ 7 ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑E¯≤∑7 ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
bb
(B¯≤-D-F-A¯≤)
(E¯≤-G-B¯≤-D¯≤)
pt
pt
pt
pt
bb 4
& 4 j œ ( œœ ) ( # n œœ ) œœ œœ ..
j œœ ( b( œœ )) (( # n œœ )) œœ œœ ..
œ
pt
pt
œ œ (pt ) ( pt )
Figure 10.2.2 Herman Hupfeld, “As Time Goes By” (1931)
7
Here is an example with chromatic passing tones.
8
b
∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
& b ∑ ∑ ∑ ∑ ∑ ∑ ∑ YT:
_40V2lcxM7k
11
Figure 10.2.3 Thelonious Monk, “Blue Monk” (1954)
In the next section we discuss the neighbor tone.
10.3 Neighbor Tones
Neighbor tones move away from a note by step then return to the note.
b 4
Œ
&bb 4 Œ œ Œ
(œ ) œ
œ (œ ) œ
CHAPTER 10. NON-CHORDœ TONES
(E¯≤-G-B¯≤)
18
Girl
(C-E¯≤-G)
app
pt
you're the one
I
want
pt
œ
( )
to
want
œ
89
me
G
? b b ∑
bbb
# 3 . ( œ ) œ .. ( # ntœ ) œ .. ( ntœ ) œ .. (ntœ ) ˙
œ
œ
œ
œ
˙
œ
#
œ
œ
œ
& 4 D¯≤œ . ( )
( )
(
)
A¯≤9((˜5))
D¯≤6
nt
pt
nt
nt (D¯≤-F-A¯≤-B¯≤)
(D¯≤-F-A¯≤)
(A¯≤-C-E-G¯≤-B¯≤)
p
œ (œpt) (œpt) œ
˙
˙œ
??b b# b 43 Œ
œ
œ
bb
œ
œ
(G-B-D)
Allegretto
269
5
4
pt
sigh
is
#
& ∑
just
∑
272
∑
a
∑
sigh
∑
∑
∑
YT: frrGAqzuOlA
∑
∑
∑? b b b∑b
7
Figure 10.3.1 Ludwig van Beethoven, Minuet in G, WoO 10, No. 2
In the next section
B¯≤7 we discuss the appoggiatura.E¯≤7
(B¯≤-D-F-A¯≤)
(E¯≤-G-B¯≤-D¯≤)
? # ∑
∑ pt∑ pt ∑
∑
∑
∑ pt ∑pt ∑
∑
bb 4Appoggiatura
10.4
& 4 j œ ( œœ ) #( n œœ ) œœ œœ ..
j œœ ( b( œœ )) #(( n œœ )) œœ œœ ..
œ left by ptstep.ptIt is usually ac)(
)
The appoggiatura
by leap and
œ œ is(ptapproached
pt
cented
282
# (on the beat), which makes it a particularly expressive non-chord tone.
∑Cm
∑ B¯≤ ∑
∑
∑
∑ B¯≤ ∑
&
A¯≤
8
11
b
&?b #b 44 ∑˙
(C-E¯≤-G)
Near,
289
&
#
∑
(B¯≤-D-F)
∑ œ .
far,
∑
(A¯≤-C-E¯≤)
app
leap
∑ j (∑œ )
œ
where - ev
∑
step
-
∑œ
er
∑
∑
YT: WNIPqafd4As
pt ant
(
(B¯≤-D-F)
œ ) ∑( œ ) œ ∑
you
are
∑
? b b œŒÓ
∑ b
13
live
Figure 10.4.1 James Horner and Will Jennings, “My Heart Will Go On”
(1997)
?The# example
∑ above∑ also has∑an anticipation,
∑
∑ is discussed
∑ in a∑ later
which
section in this chapter.
2
14
E
?&# ### # 44∑ w
296
(E-G˜-B)
∑
Œ œ∑ ( œ œ ) ∑œ
app
A
(A-C˜-E)
w ∑
Bsus4 B
(B-E-F˜) (B-D˜-F˜)
∑˙
˙ ∑
? # ∑
∑
∑
∑
∑
∑
∑
? # # # # ∑ ∑ ∑ ∑ ∑YT: IxuThNgl3YA
∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
18
Figure 10.4.2 Bruce Springsteen, “Born to Run” (1975)
Notice that both the appoggiaturas in the following example resolve up.
Both the leap to and step away from any appoggiatura can be from any direction.
b
?# 3 Œ
4
œ
œ
œ
œ
œ
CHAPTER 10. NON-CHORD TONES
A¯≤
j
bb b 6 œ
& 8 œ
272
b
& b b ∑
E¯≤/G
j app
j
j
œ
œ
œ Œ
(nœ )
(nœ )
œ
œ
œ
(nœ )
(nœ )
app
app
‰ œ œ œ œ œ ‰ œ œ œ œ œ
œ œ‰ œ‰ œŒ . œ œ œ œ‰ œ‰ œŒ . œ œ
œ
œ
J
J
(A¯≤-C-E¯≤)
app
? b b 68 ‰
b
∑
∑
∑
j
œ Œ
œ
∑
(E¯≤-G-B¯≤)
∑
∑
∑
∑
∑
? b b ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
In the
b next section we discuss the escape tone.
∑
∑
∑
∑
275
∑
∑
YT: Fcomfvmq28Q
∑
Figure 10.4.3 W.A. Mozart, Symphony No. 40, K. 550, II
10.5 Escape
Tone
E
2
90
(E-G˜-B)
(A-C˜-E)
(B-E-F˜) (B-D˜-F˜)
app
An escape
b#b b 4tone
∑ is approached
∑ by( œstep
∑œ ) andœ left ∑by leap in the
∑ ˙opposite˙ ∑direc&
?
#
tion. An
Œ œ is the end of wthe “Star-Spangled Banner.”
# # easy
4 wexample to remember
A
288
14
Bsus4
B
The word “of” in “home of the brave” is an escape tone.
18
? b b B¯≤/F∑
b (B¯≤-D-F)
b 3 œ.
&b 4
∑
home
b
& b ∑
20
∑
F
∑(F-A-C-E¯≤)
∑
œ
œ
J
esc
( )
of
∑
∑
∑
∑
(B¯≤-D-F)
˙
the
∑
∑
B¯≤
7
brave.
∑
YT: LGvW6jHUHiY
∑
∑
∑
∑
∑
Figure 10.5.1 Francis Scott Key and John Smith, “Star-Spangled Banner”
(1814)
Here is another example, with escape tones used in a melodic sequence.
? b b 68 ‰
b
œ œ‰ œ‰ œŒ . œ œ
œ
J
CHAPTER 10. NON-CHORD
TONES
C
G/F
(C-E-G)
(G-B-D-F) (C-E-G)
œ
& 43
f
3
?&# #4# # Π44
275
2
14
œ . ( œ )œ . (esc
œ) œ
esc
E
œœ œœ
w
(E-G˜-B)
œ œ
F
(F-A-C)
app
app
(
# œ) œ
œ œ
? œapp œ
Œ
œœŒ
( œ œ)
œ
œ
G7
C
(G-B-D-F)
(C-E-G)
91
œ
‰ ( œ) ‰ œ œ ‰ œ Œ Œ
œ
œ
A
Œ
w
(A-C˜-E)
F7
B¯≤/F
œœ
Bsus4 B
(B-E-F˜) (B-D˜-F˜)
˙
Œ˙ Œ
B¯≤
& b ∑ 3 ∑œ . ∑ ∑ ∑ (∑œ) ∑ ∑œ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
˙
&b 4
J
279
18
C/E
œ œ œ œ œ
œ ‰ ‰ Œ.
œ
J
(B¯≤-D-F)
(F-A-C-E¯≤)
escYT: A-Qfd7gpGfU
(B¯≤-D-F)
Figure 10.5.2 Joseph Haydn, Piano Sonata in C Major, Hob. XVI:35, III
(1780)
of
the
brave.
?Here∑ ishome
∑an example
∑ ∑ of∑an escape
∑ ∑ tone
∑ in∑popular
∑ ∑music.
∑ ∑ ∑ ∑ ∑
2
C
Em7
E
20
Fmaj7
Bsus4 B
(A-C(F-A-C-E)
˜-E)
(B-E-F˜) (B-D˜-F˜)
esc
? 4# # # # 44 œ.wœ. œ œ œ œ œ Œ œœ. ( œ œœ) œ. œœ. œ( œw.) w
≈ R
&4 Œ
˙ w ˙
b b ∑43 œ . ∑
&
&
∑
(C-E-G) (E-G˜-B)
pt pt
14
A
(E-G-B-D)
app
( ) ( )
F7
B¯≤/F
18
B¯≤
œ
œ ∑
∑ JYT: ∑ap87QgZKTNw
(B¯≤-D-F)
esc
24
(F-A-C-E¯≤)
(B¯≤-D-F)
∑˙
( )
∑
Figure 10.5.3 Paul McCartney and Linda McCartney, “Silly Love Songs”
home
of
the
brave.
(1976)
Em7
C
20
(E-G-B-D)
10.6(C-E-G)
Double
pt
.œ œ. œ(ptœNeighbor
. œ. œ(esc
œ .)
œ
œ
œ
.
œ
(
)
)
œ
œ
4
&4 Œ
≈ R
Fmaj7
(F-A-C-E)
w
w
The double neighbor (sometimes called a “neighbor group”) occurs when
both the upper and lower neighbor occur before the return to the starting
tone.
C
24
dn
œ
4 œ ( œ œ ) œ œ (# œ dn œ ) œ œ (# œ œ ) œ
&4
(C-E-G)
dn
Figure 10.6.1 C major arpeggio embellished with double neighbors
25
&
∑
∑
∑
∑
∑
∑
∑
j
?b
bb 6 œ
& b 8 œ
A¯≤
E¯≤/G
j app
j
j
œ
œ
92
œ
Œ
( n œ)
( n œ)
œ
œ
( n œ)
œ) implied)œ
( n(Dm
C
G
C
G
C
Dm
app
app
‰ œœ. jœ œ œœ œ œ œ .œ œ œ œ‰(# œ œœ) œ œœ (œ œœ)œ œ #œœ œ) œœ .
j
œ
œ
œ
œ
.
?
6
c
œ
œ œ œœ œ œ J
œ œ œ (œ œ
& b b b 8 œ‰
œ ‰ œ‰ Œ .
œ ‰ ‰ Œ.
p
œ
dn
œ dn
dn
˙˙
œ J œœ ˙˙
œ œœ œœ J
œ
œ
272
j
œ Œ
œ
(A¯≤-C-E¯≤)
app
(E¯≤-G-B¯≤)
CHAPTER 10. NON-CHORD TONES
319
?c œ
C
C: (C-E-G)
I
275
G/F
C/E
(G-B-D-F)
V
I (C-E-G) V
œ œ
Ó
∑
G7
C
(G-B-D-F) (C-E-G)
I (F-A-C)(ii implied)
F
œ
ii
esc
œ ( œ )œ œ
(# œ)
œ) œ
3 œ œ . ( œ )œ . ( esc
‰
‰ œ‰ œ Œ Œ
&4
YT: ep6rzB1Kx3U
f
œ
œœ
œ
œœin C Major, Op.
Figure
10.6.2 Friedrich Kuhlau,?Sonatina
55, No.
1, I (1823)
œ
3
Œ œ œœ œœ Œ œ
Œ
Œ Œ
&The4 double
neighbor
is
sometimes
confused
with
escape
tones
and
appogœ
app
app
giaturas. Be sure to keep track of chord tones when analyzing non-chord tones.
Look at the next example and ask yourself how you would analyze the harmony
and non-chord tones on beat 4 of the first measure.
D
279
E¯≤
(D-F˜-A)
(E¯≤-G-B¯≤)
nt
nt
nt
b 4 # œ(#app
œ
œ
) œ ( œ ) œ ( œ ) œ ( œ ) œ ( n œ) œ œ œ œ œ
b
& 4
œ (œ œ ) œ œ (œ œ ) œ
dn
dn
œ
œœ
? b b 44 œ
# œœ
Œ
Œ
Œ
dn
?
YT: PmO3Wlono6w
Figure 10.6.3 W.A. Mozart, Piano Sonata K. 333, I (1784)
In the next section we discuss the anticipation.
10.7 Anticipation
An anticipation is a non-chord tone that anticipates the arrival of the next
chord and is often found at cadences, as in the next example.
œ.
œ ˙
(E-G˜-B)
app
A¯≤: vi
IV ( œ œ )
#
œ
?
#
4
ΠTONES
CHAPTER
# # 4 10.w NON-CHORD
œ
2
œ.
(A-C˜-E)
E
14
B¯≤/FA
126
18
I
œ ˙
Bsus4
B
(B-E-F˜) (B-D˜-F˜)
˙
V
7 E/B B7
AmajB¯≤
˙
93
E
nt(B¯≤-D-F) ant
(F-A-C-E¯≤)
# # # # (B¯≤-D-F)
œ
œ
3
(œ) (œ) esc œ
œ
œ
œ
‰
& b 3 œ4.
(œ)
œ J œ (œ)˙ œ œ (œ) ˙ .
&b 4
3 J
pt pt
E
20
w
B7/A E/G˜
F7
F˜m/A
# # # #home
3
& C 4 œœœ œœœ Œ
(C-E-G)
pt pt
?4# #Œ# # 43œ. œ. œ œ œ œŒœ
œ
&4
126
A
che
so
( ) ( )
E: IV ii/3rd
-
spi - ri
the
la
li - - - ber
brave.
-
œœ7 œœœ ‰ œj œœ (œ) œœ 7 œ œ
Emœ
( )
œ ntFmaj ant
(E-G-B-D)
(F-A-C-E)
œœ.) œ œœ
œœ. œ œ œ.Œ œ. œ(esc
w œ
≈ R
of
IVM7 I/5th V7
V7/7th I/3rd
tà
˙.
˙.
w˙˙ ..
I
C
dn
œ ) œ œ (# œ œ ) œ œ
4 œ ( œ œ ) œ œ (#YT:
œ dnE6lV3nKg-nc
&4
Figure 10.7.1 George Frideric Handel, Rinaldo, “Lascia ch’io pianga” (1711)
(C-E-G)
dn
24
Here is an example of an anticipation in popular music.
25
G
A
Dm
F
(G-B-D)
pt pt
(A-C˜-E)
(D-F-A)
(F-A-C)
& b 44 œj œ œ
( )
( )
ant
nt
ant
j j ntœ j ant
œ
œ œ œ œ œ œ Ó ‰(# œ ) œ ( n œ ) ˙ œ œ
ant
I know where you're com
&b
29
( )
( )
∑
-
ing from
( ) ( )
Call me
∑
YT: StKVS0eI85I
on the
line
Call me
∑
Figure 10.7.2 Debbie Harry and Giorgio Moroder, “Call Me” (1980)
Sometimes syncopation will lead to an anticipation of a note in a chord in
the following measure, as occurs at the ends of bars 1, 2, and 3 of the “Call
Me” example.
10.8 Pedal Point
A pedal point is a note that is held through changing harmonies, starting as
a chord tone before becoming a non-chord tone. Pedal points are often in the
bass voice (the term “pedal” relates to the foot pedals on an organ).
CHAPTER 10. NON-CHORD TONES
281
94 19
C7
F/C
Dm7/C
(C-E-G-B¯≤)
(F-A-C)
(D-F-A-C)
& 44 ‰
‰
‰
œœ œ
œ œœ œ œ œœ
œ
b
œ
œ
œ œœœœ œ
œ
œ
œ
œ
œ
œ œ
≈ j
≈ j
≈ j
? 44 œ . œ
œ. œ
œ. œ
˙
˙
˙
˙
˙
C pedal (in bass) starts as consonant note (in the chord)
283
G7
(G-B-D-F)
C
(C-E-G)
œ œ œ œ œ œ œ
œ œ
œ œ œ ( œ ) œ www
& ‰
pt.
≈ ped.
j
? (œ .) (œ )
(˙ )
˙
(˙ )
w
w
( )
ped. pt.
pedal point (in bass) is now a non-chord tone
∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
& ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑YT:∑ W4271Rm9TSU
285
Figure 10.8.1 Bach, J.S., Well-Tempered Clavier, Book I, Prelude 1 in C
major BWV 846 (1722)
14
130
130
?Here
∑ is∑ an∑ example
∑ ∑ ∑ from
∑ ∑ the∑ Romantic
∑ ∑ ∑ ∑era.∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
b
& b 68
Gm
D7
F˜o7
Gm
(G-B¯-D)
(D-F˜-A-C)
(F˜-A-C-E¯)
(G-B¯-D)
b
& b 68 ‰
p
ben legato.
œœ
j
œ
œœ ..
œ˙ .)
V7
(i)
(
œ
ped. pt.
B¯m7
E¯
‰ #œ
œ
ped. pt.
( )
g: i
œ
œ
œ
œ
œ
œœ
œœ
J
j
œœ
(bass note is still sounding)
viio7
i
Fm7
inc. nt.
YT: jYgW5PhsQOE
bbb 6 œ
œ
(œ )
b
œ
œ . beide” (1844)
&
8
J No. œ2,. “Sie liebten sich
Figure 10.8.2 Clara Schumann,
Op.
13,
J
da -
132
œ #(œœ ).
œ
? b b 68
œ˙ . œ
132
3-2 sus.
œ
bb b b 6 œœœ
&
8
-
- re - Por -
œ œ
œ œ
J
-
- ta
œ
( œ)
J
( )
œ
inc. nt.
Ros -
œœ ..
œœ ..
-
-
- sa
œœ
œœ ..
œœ ..
œœ
281
283
283
(C-E-G-B¯≤)
(F-A-C)
(D-F-A-C)
≈
≈ j
≈ j
? 44 œj. œ
‰œ . œ
‰œ. œœ ˙
& 4 ˙‰ 10. NON-CHORD
œ
œ
œ
œ
˙
˙
˙
CHAPTER
TONES
95
œ bœ œ œ œ œ œ œ
œœœ œœœœœœœœœœ
(in bass) starts as consonant
(in the chord)
≈ jC pedal
≈ note
The Clara
Schumann ≈example
above also
j
jhas a suspension (“3-2 sus.”);
?
4
œ
œ section.œ . œ
suspensions
inœ the
. next
4G7 œare. discussed
C˙
When
a
pedal
point
is
in
the
bass,
it
is
not
necessary
to
specify
˙
˙
˙
˙ the inversion
(G-B-D-F)
(C-E-G)
of the chord because the bass pedal point obscures the inversion.
œ œ starts
œ asœconsonant
pedal
(in bass)
(in the
chord)
You‰ mightC also
pointœ in note
voice,
as well as a “douœ œencounter
œa pedal
&
œ
œ œa higher
œ ( œ ) œact aswww pedal points.
ble pedal point,” where two notes (often a fifth
apart)
7
G
ped. pt.
(G-B-D-F)
C
(C-E-G)
≈ j
10.9
? Suspension
œ
& ˙‰ (œ œ.) œ (œ )
œ œ ( ˙œ ) œ œ
ww
œ
œ
œ
w
œ
œ
˙
) downbeats. A suspenSuspensions
are accented non-chord
( ) tones occurring( on
( )
sion is approached by the same note and resolves down by step. A suspension
ped.
pt.pt.
ped.
is made up of a preparation, suspension, and resolution. Sometimes the prepa(in bass) is now a non-chord tone
ration is tied pedal
to thepoint
suspension.
?
≈ j
(œ .)
˙
G
( )
(
œ)
(G-B-D)
ped.
pt.
285
285
(C-E-G)
Preparation
& 44 G˙˙˙
?4
& 44
˙
(˙ )
w
w
( )
C
Suspension Resolution
œ˙ )
˙C
Prep.
Sus.
˙˙˙
œ
pedal point (in bass) is now a non-chord tone
(no tie)
(
(G-B-D)
(C-E-G)
˙
(œ )
˙˙
˙˙
˙˙
Preparation
˙˙
˙˙
Suspension Resolution
C: V
œ
I
Prep.
œ˙ )
˙
Res.
Sus.
Res.
(
œ
˙
(œ )
˙˙
(no tie)
C: V
œ
I
˙
˙
˙
?4 ˙
4∑ ∑ ∑ ∑are∑classified
∑ ∑ ∑by∑numbers
∑ ∑ ∑(9-8,∑ 7-6,
∑ ∑4-3,∑ 2-3,
∑ ∑and∑ sometimes
∑ ∑ ∑
&Suspensions
287
Figure
10.9.1 Introductory Suspension example with and without tie
6-5) that
distance of the
suspended noteI and its resolution
C: V
C: Vspecify the interval
I
to the bass note
287
G∑ ∑ ∑C ∑ G/B
C ∑ ∑
? ∑G ∑ C∑ ∑ ∑ Dm/F
∑ ∑ C/E∑ ∑ C∑ ∑ sus.
∑ ∑ ∑ F∑ ∑sus.
sus.
& ˙˙˙
?˙
C: V
(œ ) œ
˙˙
sus.
7 - 6
9 - 8
˙
I
œ
œœ
(
œ) œ
œœ
ii/3rd I/3rd
œœ
œ
œ
I
œœ œ
œ
4 - 3
( )
œ
V
œœ
œ
œœ
œ
œ
( )
I
œ œ
2 - 3
sus.
V/3rd
6 - 5
˙˙
˙
( )
IV
I
˙
œ˙ œ
˙
˙
Figure 10.9.2 Examples of the 9-8, 7-6, 4-3, 2-3, and 6-5 suspensions
In the example above, the notes in the 4-3 suspension are an 11th and 10th
higher than the bass. Reduce all intervals larger than an octave to the numbers
7-6, 4-3, and 6-5.
Here is an example with a 4-3 suspension.
292
? # 44
(
) œ (œ ) œ
G
D/F˜
D
œ
pt
#
pt
2-3
œ
œ
sus.
(œ ) œ
& 44 œœ10. NON-CHORD
CHAPTER
TONES
œ
œ
œ
G: I
V/3rd
294
296
296
D
œ
œ
I
V
˙
)
pt
œœ ( œ ) ˙˙
V
96
pt
˙
(œ
) œ
œ
œ
œ
œ
œ
œ
œ
(
)
œ
œ
œ
œ
œ
( )
? # 44
(
) œ ( œ ) sus.
pt ˙
nt
pt
4œ - 3
bb b œ4 W
& bb 2
ww 2 - 3 pt (Wœ ) n œ ( œ ) pt œ œ ( œ ) œ ( œ )
∑
w sus.
nW
W
G: I
V/3rd V
I
V
π
E¯≤m7
F
? b b 4 ∑
bbb 2
Wsus.
w
pt
nt
pt
4 - 3
W
bb b 4 W
w
( œ ) n œ (œ ) œ
œ (œ ) œ (œ )
& bb 2
ww
W
∑
w
nW
W 7
F˜m
G/B
Em
A
D
Em/G
π
sus.
sus. 9 - 8
7 - 6 nt
? b b b 42 ∑
7 - 6 nt
pt
YT: b8G9vRqq3RI
b
b
(
œ
œ
œ
œ
œ
œ
œ
œ
(
)
œw(œ)œAdagio
œ œ forœWStrings
œ (œ )œ(1936)
# 3 œ Samuel
œ œ œ œ ( œ˙ )) œœ ((œœ ))œœ
˙
Figure# 10.9.3
Barber,
œ
œ
˙
& 2 œ
œ œW
w
˙
Here is an example with 7-6Œand 9-8 suspensions.
nt Œ
˙
F˜m
G/B
Em
A7
D
Em/G
? # # 32 œ œ œ ˙sus. Œ œ œ œ ˙
œ
œ
Œ œ sus.˙97 -- 86 ntŒ
7 - 6 nt
pt
) œ
œ œ œ (IVœ˙ )/3rdœ (œ)œ iiœ œ œ Vœ7 (œ )œ œI œœ œœ œœ ((iiœœ/3rd
)œ
# # D:
œ
) œ (œ
iii
3
œ
œ
(œ )
œ
˙
œ
˙
& 2
œ
œ ˙
Œ
nt Œ
˙
300
? # # 32 ∑ œ œ ∑œ ˙ ∑ Œ œ∑ œ œ ∑ ˙ ∑ Œ œ ∑ œ œ ∑ ˙ ∑ Œ
&
pt
294
(
G
? ##
D: iii
∑
E¯≤m7
∑
IV/3rd
∑
F
ii
∑
∑
∑
∑
V7
pt
∑
I
∑
∑
∑
∑
ii/3rd
∑
# # ∑
∑
∑ YT: ∑HawWrnUGH_0
∑
∑
∑
∑
∑
&
Figure 10.9.4 George Frideric Handel, Suite No. 2 in D Major, HWV 349:
300
II. Alla Hornpipe (1717)
? ##
∑
∑
∑
∑
∑
The 2-3 suspension is the “bass suspension” and is measured against an
upper voice. Again, you may encounter the literal intervals 10-9 but should
label the suspension as 2-3.
G: I
V/3rd
V
I
E¯≤m7
294
20
292
b
& b b b b G42
# 4 œ
& 4 œ
? bb 4
bbb 2
F˜m
296
300
F
sus.
4 - 3
CHAPTER 10. NON-CHORD TONES
W
w
∑ pt ww D/F˜
π ( œ ) œ œ
œ
∑ œ
pt
w
œ
œ
? # 44 œ ( ) œ w( œœ ) œ
œ
G/B
V
nt 97
œ ) n œ (œ ) œ œ ( œ ) œ ( œ )
W
D
W
nW G
œ
œ
œœ ( œ ) ˙˙
œ
œ
pt
W
pt
œœ Wœ œœ (( œœ )) œœ œ ˙˙
( )
pt
pt
(
D
ptD
A7
2 - 3Em pt
sus.
sus.
7 - 6 nt
V/3rd V
Em/G
sus. 9 - 8
# # 3 œœ œ œœ ( œ˙ ) œ (œ)œ œœ œ œ œ (œ )œ œ œœ œœ œœ (( œœ˙ )) œœ ((œœ ))œœ
˙
& 2 œ
œ œ
Œ
˙
nt Œ
294
˙
#
YT: VKNcvMcGlvI
∑ ∑ Bach,
∑ J.S.,
∑˙ Chorale
∑ ∑ 238,
∑ “Liebster
∑ ∑ Jesu,
∑ ∑wir ∑sind ∑hier,”∑ BWV
∑
& 10.9.5
Figure
œ
œ
˙
œ
œ
˙
? ## 3 œ
Œ œ
Œ œ œ œ
Œ
373
2
When a chord is inverted, you will sometimes encounter non-standard sus/3rd3-2. ii
? # numbers
pension
∑D: iii∑ like
∑ 5-4∑IVor
∑ ∑ ∑ ∑ V∑7 ∑ I ∑ ∑ ∑ ii/3rd∑ ∑
G: I
Ipt
G7/F
C/G
sus.
5
-
& ˙˙˙
œ˙
˙
( )
? ˙
œ
sus.
3
-
˙˙
˙
˙
(
˙
V7/7th
C: I/5th
G7/F
F
4
V 7 - 6 nt
œ˙ )
˙
2
œ
˙
V7/7th
C: IV
Figure 10.9.6 Non-standard suspension numbers because of inverted chords
You will sometimes encounter decorations of suspensions where other notes
occur before the resolution, as in the following example.
324
D7/C
& b 43 # œœ (œ) ˙˙
pt
pt
? b 43 n œœ . (œ) # ˙(b œ ) œ œ
J
app
&b
A7
Gm/B¯≤
sus.
œ œ (œ ) œ
(œ )
(œ )
œ
œ
œ (# œ ) # œœ
œœ
ret.
( )
res.
œ
œ
œ
œ
app
nt
œœ
327
YT: fTwkVsECg9w
Figure 10.9.7 Bach, J.S., French Suite No. 1 in D Minor, BWV 812, Sarabande (1722)
?Theb “ret.” in the tenor part in the second measure is a retardation, which
&b
348
23
21
B¯≤7
Cm/B¯≤ B¯≤7
Cm/B¯≤
CHAPTER 10. NON-CHORD TONES
302
Ÿapp
œ
œ (œ) œ (œ ) œ
. œ ( ) section.
is &
covered
b b c inœ the®œnext
J
pt
9-8
B¯≤ Aø7 B¯≤ Aø7
/B¯≤
/B¯≤
F7
/B¯≤
B¯≤
Ÿ œ pt
œ . ret.
j
®œ. œ ( ) œ (œ ) œ œ́ ≈ œ . œ œ́ ≈
œ (œœœ) œœ ‰
œ
R
R
(œ )
( )
98
app
j
≈
œ œœ
bb c
?
œœ œ meaning
œ
œ œœ ‰
œ bœ œ
œ œ ( # œ ) œ non-chord
œ œ œœtone,
A&
retardation
œ œœ œœ œ œœ it occurs on a
œ˙ œ is usuallyœ anœ˙accented
app
10.10 Retardation
4
9
-
3 sus.
(8)
downbeat. A retardation is approached by the same note and resolves up by
step.
G/B
304
Am/C
# 3 œ ( œ) œ ( # œ ) œ œ
œ œ.
& 4 ≈
app
app
app
G
nt
œ (œœ) œ ( œ) œ ((œœ)) œ
9 - 8 sus.
ret.
4 - 3 sus.
œ œ œ œ œ œ œ œ œ œ œ (œ˙ ) œ
œ
? # 43 œ œ œ œ
G: I/3rd
D7
G/D
ii/3rd
I/5th
V7
Œ
..
Œ
..
I
#
Figure
Piano Sonata in C major, K.
∑
∑ 545, II (1788)
& 10.10.1 W.A. Mozart,
YT: hSqwR_dsecg
307
Classical composers like Mozart often used retardations and suspensions at
cadences in slow movements.
?#
∑
10.11 Incomplete Neighbor
∑
Because composers are notorious for “breaking the rules,” you will encounter
examples in the real world that either defy explanation or have multiple valid
explanations. One “utility” non-chord tone is the incomplete neighbor.
b b 8 œ˙ . œ
(
( )
ped. pt.
CHAPTER
g: 10.
i NON-CHORD
V7TONES
i
B¯≤m7
E¯≤
132
b
œ
& b b b 68
da -
132
œœ
bb b b 6 œœ
&
8
-
œ œ
J
- re - Por -
œ œ
œ œ
J
œ
J
inc. nt.
( )
-
- ta
œ
( œ)
J
( )
œ˙ .)
ped. pt.
(bass note is still sounding)
viio7
i
99
Fm7
œ.
Ros -
œœ ..
œœ ..
-
-
œ.
- sa
œœ ..
œœ ..
œ
œœ œœœ
? b b b 68 œ œ œ œ œ œ œ œ œ œ œ œ œ
œœ
≈
b
œ
œ
A¯≤: V
inc. nt.
ii7
vi7
b
∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
& b b b ∑ ∑ ∑ ∑ ∑ ∑ ∑YT:∑ Sf-tjXevlyQ
134
Figure 10.11.1 Giacomo Puccini, Gianni Schicchi, “O mio babbino caro”
134
(1918)
b b ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
&Youb bmay∑ also
find incomplete double neighbor figures, especially in late
Romantic music and jazz. Keep an open mind when analyzing music.
? b b b Adding
10.12
∑ ∑ ∑ ∑ ∑ ∑ Tones
∑ ∑ ∑ to
∑ ∑a ∑Chord
∑ ∑ ∑ Pro∑ ∑
b ∑ ∑ ∑ ∑ Non-Chord
gression
Here are ideas for how to add non-chord tones (or “embellishments”) to the
melody or inner voice part of a chord progression:
1. Repeated note: add upper or lower neighbor
2. Step down:
(a) Add a suspension by delaying the resolution of the note
(b) Add an escape tone by moving by step in the opposite direction of
the original stepwise movement, then leap
(c) Add a double neighbor
(d) Add a chromatic passing tone
(e) Add an anticipation
3. Step up:
(a) Add retardation by delaying resolution of the note
(b) Add a double neighbor
(c) Add a chromatic passing tone
(d) Add an anticipation
(e) Add an appoggiatura by leaping one step beyond the note of resolution, placing the appogiatura on the beat, displacing the note of
resolution to occur after the beat
app
304
G/B
Am/C
G/D
Am/C TONES
G/D
CHAPTERG/B
10. NON-CHORD
# 3 œœ (œ) œ (# œ ) œ œ
&
# 43 of≈ 3rd:(œ) œ (# œ ) œ œ œ œ .
4. Leap
œ œ.
& 4 ≈ app app
D7
app
D7
nt
app
nt
G
G
100
œœ9 - œ8 sus. Œ ..
œœ œ Œ ..
(a) Fill inapp
the 3rd with a passing tone
4 - 3 sus.
ret.
app
œ
œ
œ
(b) Add an appoggiatura
by
leaping
one
step
beyond
( 4the
) - note
œ3 sus.of resoœ œ œ œonœtheœ beat,
œ displacing
œ œplacing
œ œtheœ appogiatura
˙
? # 43 lution,
œ
œ œ œ œ œ œ (œ˙ ) œ the Œnote ..of
œ œ œto occurœ after
œ
? # 43 resolution
œ
the
œ beat œ
Π..
œ
œ œ
304
œ (œœ) œ ( œ) œ
œ (œœ) œ ( œ) œ
9 - 8 sus.
( )
( )
(ret.
)
( )
G: Iof
/3rd4th or larger:
ii/3rddo not embellish
I/5th
V7 now)
I
5. Leaps
(for
G: I/3rd
ii/3rd
I/5th
V7
I
Here is a basic framework with all possibilities labeled.
#
&#
&
44
44
G
G
˙˙
˙˙
˙
? # 4 ˙˙
? # 44 ˙
4
307
307
step down
step
step down
down
step down
repeated note
repeated note
leap of 4th
leap of 4th
D
D
˙˙
˙˙
˙
˙
˙
step down
step down
step down
leap of 3rd
leap
stepofup3rd
step up
G: I
V
G:
I
V
Here is one possible solution:
G
D
esc.
G
D
#
&#
&
309
309
?#
?#
4
44
4
œ˙
œ˙
œ
44 ˙œ
44 ˙
G: I
G: I
œ
(œ )
(esc.
)
œ
( œ)
nt
( nt)
˙(œ ) œ
˙(œ4-3) sus œ
œ
œ˙
˙
4-3 sus
˙˙
˙˙
˙˙
˙˙
C
C
repeated note
repeated note
repeated note
step up
step up
leap of 3rd
leap of 3rd
vi
vi
Em
4-3 sus
Em
˙˙
˙˙
˙
˙
˙
IV
IV
C
nt C
œ˙4-3 sus œ (œnt) ˙˙
(œ )
œ (œ ) ˙˙
˙
( )
pt
œ (œ )
œ (œ )
pt
V
V
Em
Em
˙œ
˙œ
vi
vi
œ
œ (œ ) (œ˙)
œ (œ ) ˙
pt
app
(app
)
pt
œ
œ
IV
IV
Notice that, when non-chord tones are added to different voices on the same
beat, consonant intervals (3rds, 5ths, 6ths, or 8ves) are made. If consonant
intervals can’t be made, the voices are staggered rhythmically (as occurs on
beats 3 and 4 in measure one of the example above).
10.13 Practice Exercises
1.
Fill in the blanks in the following table.
Non-Chord Tone Type Approached by
same tone
step
leap
2.
Left by
step up
leap in opposite direction
step in same direction
Analyze the harmonies with lead-sheet symbols above the staff and Roman
numerals below. Add the following non-chord tones: two suspensions, one
passing tone, and one appoggiatura. Do not add non-chord tones to the
bass.
CHAPTER 10. NON-CHORD TONES
101
22
b
& b 44 ˙˙
Lead-sheet: _____
_____
? b b 44 ˙
˙
311
Rom. num.:
b
& b 44
313
3.
139
139
˙
˙
˙˙
˙
˙
_____
_____
_____
? b b 44
315
317
˙˙
_____
_____
_____
_____
_____
_____ above the_____
Lead-sheet:the
Analyze
harmonies with
lead-sheet symbols
staff and Roman
numerals4 below, then analyze the non-chord tones.
&b 4 ˙
˙
˙
˙
˙ In the Name
˙ Dozier, Eddie˙ Holland, “Stop!
(a) Brian˙Holland, Lamont
of Love” (1965)
16
˙
? b 44 ˙ _____
˙_____
4 Œ œ ‰ œj œ ( œ .) j
&_____
4
œ ˙
_____
Rom. num.:
44
&b &
4 4 Œ œœ ‰ œœj œœ
œ œ œ
Stop!
in the
_____
name
(
Œ œ) œ
œ
_____ (
of love
be - fore you
j
œ .) œ ˙
œœ .. œœ ˙˙
˙
Fmaj7 _____
Œ (œ ) œ
œœ œœ œœœ
j
œ. œ ˙
_____
( )
break
(
my heart
j
œœ ..) œœ ˙˙
œ. œ ˙
œœ
? ?
4
œœ
œœ
œœ œœ
b 4 44 œ œ œ œ œ œ œ œ œ œ œ œ œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
( )
C C: _____G
319
C
_____G
C
(Dm implied)
_____
____ _____
Dm
I
(ii implied)
ii
œ
j∑œ œ œ œ ∑ œ . j œ∑œ œ œ œ∑. œ œ ∑(# œ œ ) œ ∑œ(œ œ )œ œ∑(# œ œ ) c ∑œ .
4
œ
.
&4& œ
œ
J
p
YT:
dn
dn
dn
143
˙˙
œœ œœ
œœ œœ ˙˙
œœ tuei1XUAGRo
∑ Dichterliebe,
∑
∑ Op.
∑ c ∑œ
? 44Robert
&œ ∑Schumann,
Ó ∑48, 1. ∑“Im ∑wunderschönen
(b)
143
Monat Mai” (1840)
?
C: I
∑
V
∑
I
∑
V
∑
∑
∑
∑
∑
151
∑
∑
∑
∑
151
&
∑
∑
∑
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∑
∑
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15
CHAPTER 10. NON-CHORD TONES
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134
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Chapter 11
Melodic Analysis
We will divide analysis of melodies into motives (which can be broken into
fragments) and phrases (which can be broken into subphrases) in order to
understand the construction of melodies. We will discuss periods and sentences
in another chapter.
11.1 Motive
A motive (or motif) is the smallest identifiable melodic idea in music. However, we will find times when it will be necessary to discuss a smaller fragment
21
(called a “germ” by some authors) from a motive.
In the following example from the first movement of Beethoven’s Symphony
No. 1, we find four motives within the first four measures of the primary theme.
mot. 1
mot. 2
& C œœœœ ˙.
ƒ
376
& 44 œ
382
œ. œ ˙.
S
œ. œ.
œ
œ
œ . œ œ. œ. œ. œ. œ. œ. œ. œ. œ. . .
mot. 3
mot. 2
mot. 3
mot. 4
mot. 1 (rhy. ch.)
‰ # œj œ œ YT:œ tFafjC-180E
‰ œj ‰ # œj œ œ œ
mot. 1
Figure 11.1.1 Ludwig van Beethoven, Symphony
rhythmic No. 1, Op. 21, I, Motives
in Primary Theme (1800)
change
(same)
384
386
Later in the movement we find Beethoven extracting motives from this
four-measure phrase
sequences.
mot.in
1 order to develop them through
mot.
1 (inv.)
Here is development of motive 1.
& œ œ œ œ œ œ œ
& œ œ œ œ œ œ œ
œ œ œ œ œ œ œ
&
387
388
œ œ œ œ œ œ œ
& 44
#œ
œ bœ
mot. 1
œ
103
7
illustration of
mirror inversion
œ bœ
œ #œ
mot. 1 (ret.)
CHAPTER 11. MELODIC ANALYSIS
330
330
24
24
334
334
337
337
340
104
˙˙ # ˙˙
ww
# ww
ww
b
˙˙ ˙˙
w
w
& w
w
w
w
p
œ œ œœ
œ Œ Œ œœœ
? Ó Œ œ bœ œ œ œ Œ Ó
Ó Œ
œ
cresc.
p
cresc.
ww b ˙ # wwn ˙
˙˙ ˙˙˙ # #˙˙˙˙˙
w
ww b ˙˙˙
ww˙˙
˙˙ ˙ ˙˙˙
& b˙˙˙˙ww b ˙˙˙
& w
˙
˙
cresc.
p
œ œ œœ œ
? Ó Œ œ b œœœbœ œœ œŒ b Óœ
Ó Œœ œ
Œ Œ œœ œœ œœ œ
?
œ
œ
Œ
Œ
Œ
Œ
œ
Œ
Œ
cresc. œ
p
œ
cresc.
˙˙
# ˙˙
b ˙˙
n ˙˙
˙˙
√˙˙˙
b
˙
˙˙ œ
˙˙
˙
b ˙˙ ˙ ˙˙
#
˙
& ˙˙
˙
œœ
˙˙
˙˙
bcresc.
˙˙
& ˙˙˙
œ
˙
˙
œ
˙
b
œ
œ
œ bœ
ƒ
œ
?
œ
b
œ
Œ
Œ
œ œ œ Œ Œœ œ œœ œœœ œœ œ œ Œ Œ œ œœ œ
? œœ Œ Œ
œœœ œ
ƒ
√
œœ
˙˙
# ˙˙
˙˙
˙
b
œœ
˙
˙
˙
340
& ˙˙
˙˙
˙
˙
ƒ
YT: tFafjC-180E
&
œ
b
œ
œ
œ œ No. œ1, œI, development
œ
? œ 11.1.2
œ œ œ œ ofœ motive
Figure
Symphony
ΠBeethoven,
Œ
œ œ œ1
Here is development of motive 2
ƒ
?
Œ bœ. œ bœ
Ó
∑
Œ bœ. œ bœ Œ
Œ Ó
&
p
b˙.
Ó
Œ bœ. œ bœ
bœ. œ bœ
?
Œ Ó
œ bœ
Œ bœ.
Œ
344
&
YT: tFafjC-180E
Figure 11.1.3 Beethoven, Symphony No. 1, I, development of motive 2
?
Here is development of motives 2 and 3 together.
CHAPTER 11. MELODIC ANALYSIS
˙.
& ˙˙ ..
f .
#˙
? #˙.
344
348
344
348
352
356
. . . . . . . .
œ.#œ œ œ œ #œ œ œ œ œ
Œ
∑
p
Œ
∑
. . . . . . . .
. . . . . . . .
œ . # œ œœ œœ œ # œ œœ œœ œ œ
œŒ . # œ
œ # œ∑
œœ
Œp
∑
∑
pŒ
Œ
. . . .∑ . . . .
œ.#œ œ œ œ #œ œ œ œ œ
105
œ
œ
# œœ
pœ.
Œ Ó
b ˙˙
œœ
˙
œ
œœ b ˙˙
œ #˙
25
∑
œœ
œ
.
Œ œ Œ #œ Œ œ Œ
˙.
œ Œ Ó
∑
b
˙
b
˙
œœœ ˙Œ Ó œœ œœ ˙ ∑ œœ
& ˙˙ ..
#
œœ b˙
œœ œœ b# ˙
˙
œœœ
œ
˙
œ
œ
˙
& f ˙˙ ...
#œ ˙
œ œ #˙
œ.
pœ..
#˙.
.Œ
? #f˙ .
p Œ œ Œ #œ Œ
œ
œ
? ˙.
Œ œ Œ #œ Œ œ Œ
#˙.
˙.
œ Œ Ó
b˙
b ˙ ∑ œ
˙
œ
œ
œ
.
œœ œœ # ˙˙
œœ
& ˙˙ ..
352
# œœ ˙˙
Œ
∑
YT:
∑
∑ tFafjC-180Ep. ∑
∑ .
&
p
Figuref 11.1.4 Beethoven, Symphony No. 1, œI, development of motives 2 and
3 ? ˙.
Œ
∑
Œ œ Œ #œ Œ œ Œ
excerpt leads directly into the next, which features develop.
?The# ˙previous
∑ 4.
∑
∑
∑
ment of motive
.
˙.
. . œ. œ w
bœ
b
œ
∑
œ
œ
œ
& b ˙˙
356
˙˙
b ˙˙
˙˙
b ˙˙
˙˙
b œœ œ œ b œœ
∑ @˙
∑@˙
∑@ @ @ ∑ @
& @˙ ∑ @˙ ∑ @˙ ∑ @˙
. . . .
.
.
p
.
. . œ œ œ œ bœ nœ
? œ b œ œ œ œœ Œ Ó
œ b œ ∑
œ b œ b œ ∑ œ
? ∑b œ œ œ∑
∑
∑
∑
∑
.
œ. .
.
˙.
. . œ. œ w
bœ
b
œ
Œ
Ó
b
œ
œ
œ œ bœ
363
b
˙
˙
b
œ
& b ˙˙˙ ∑ ˙˙˙ ∑ b ˙˙˙ ∑ ˙˙˙
˙
˙
œ
∑ ˙
∑˙
∑ @œ @œ ∑@œ
& @
@
@
@
@
@
@ .
. . . .
.
. . œ œ œ œ bœ nœ
. œ. œ
.
œ
b
œ
? œ ∑ œ œ∑ œ Œ∑ Ó
œ b œ ∑
∑
∑œ b œ b œ ∑ œ
b
œ
œ.
∑
YT: tFafjC-180E
In the next section, we will look at some of the various ways one can alter a
melody
Figure 11.1.5 Beethoven, Symphony No. 1, I, development of motive 4
25
CHAPTER 11. MELODIC ANALYSIS
106
11.2 Melodic Alteration
While there are more than a dozen ways to alter a melody, we will focus on
seven methods of basic melodic alteration at this point of the text.
11.2.1 Inversion
26
Inversion as applied to music means an idea is exactly upside-down or “mirrored” across a horizontal plane, like mountains reflected in a lake.
First, listen to the following example.
360
& c ≈
?c Ó
m
œœœœœœœœœ œ œ œ
m
œ
œ œ
œ
œœœœœœœ
≈ œ œ
≈ œ œ œ œ œ œ œ œ œ Œ
œœœœœ
21
œœœœœœœœœœœœœœœœ œœœœœœœœœœœ
&
œ #œ œ œ œ
362
œ
œ œ œ œ œ œ œ
# œ œ œ œœ œ œ œ. œ.
&?C œ œ œœ œ ˙ .
œ
œ . œ ˙ . œ . œ œ. œ. œ. œ. œ. œ. œ. œ. œ. . .
ƒ
S
mot. 1
376
mot. 2
mot. 2 mot. 3
mot. 3
mot. 4
mot. 1 (rhy. ch.)
∑ ‰ ∑ j ‰ ∑ j ∑
&44 œ∑ ‰ ∑# œj œ ∑ œ YT:œ E8EvUmq0Zao
œ
œ œ œ ∑
&
#
œ
Figure 11.2.1 Bach, Invention No. 1 in C Major, BWV 772 (1723)
382
mot. 1
364
?
∑
∑
∑
∑
rhythmic
∑
∑
∑
∑
The first seven notes in measure 1 are change
inverted in measure 3, shown in the
following example.
(same)
384
386
mot. 1
&372
œ ∑œ œ ∑œ œ œ∑ œ
&
?
387
∑
∑
œ œ œ œ œ œ œ
mot. 1 (inv.)
∑
& œ œ œ œ œ œ œ
∑ œ ∑
∑
∑
œ œ œ œ œ œ
&
∑
∑
of
∑illustration
inversion∑
∑
∑
∑
∑
∑
∑
& ∑
Melodic inversion can be real (where every interval is exactly the same qual& or tonal (where the intervals abide by the scale or key). For the majority
ity)
of this text, we will encounter tonal inversion until we discuss techniques of
? and∑21st-century
20th∑ music in∑ the final∑chapters of∑ this text.∑
∑
379
Figure 11.2.2 Melodic inversion in Invention No. 1 in C Major by J.S. Bach
388
413
&
& 44 Œ
&
w
≈ R
CHAPTER 11. MELODIC ANALYSIS
A
CG
24 25
w
Dm
107
F
(D-F-A)
(F-A-C)
dn
œ
œ
)
œ
œ
4 j( œ œ ) œ œjœ (œ# jœœ œjœ ) œ œœ œ Ó(# œ ‰ # œnt œ n œ ant ˙ œ œ
& b4 44œ change
Intervallic
œ exact than inversion. With intervallic change, the
œ œis less
(C-E-G)
(G-B-D)
(A-C˜-E)
11.2.2 Intervallic
Change
ant
dn
ptdn pt
nt
ant ant
œ
rhythm is generally intact and the motive relates to a previous iteration, but
( )
I know where you're com - ing
some of the
intervals are different.
G
29
25
mot. 1
(G-B-D) m3
ant
pt pt
( ) ( )
( )
( )
( )
from
Call me
33
)
on the line
Call me
Dm
(A-C˜-E)
( ) ( )
( )
( )
( )
(
)
(
)
andonI the
forline
- get to do
Call me
Call me
mot. 1 (int. ch.)
P4
mot. 1
m3
YT: v9V98ECtsfY
b b 4 ∑j
j ∑ œ œ ˙ . ∑
b
∑
œ
œ
œ
Ó ∑of‰You”
V
Figure 11.2.3
4 œ Rayœ Noble, “The˙ .Very∑ Thought
œ œ(1934)
œ
33
360
(
mot. 1 (int. ch.)
F
P4
(D-F-A)
(F-A-C)
A
- y you're
thought
I The
knowver
where
com of- you
ing from
26
)
b b b4 44 j œj œ œ œ œj œ œj˙œ.ntœj œ œantÓœant Ó ‰ ‰œ#jœntœ œœn œ antœ ˙œ ˙œ. œ
V
b
& 4 œ œ œ œ
( )
29
(
The nextTheexample
twoofintervals
changed, one of
ver - y has
thought
you
andwhich
I for -includes
get to do a change
in contour.
mot. 1 (int. ch.)
m
œ mœ œ
M2
↑ œ
œ
œ
œ
œ
m3↓
c
≈
œ
œ
œ
&# # # # œ œ œ œœœ œœ œ œœ œ
œ nœœ œ œ œ œœ n œ
Œ
‰
Œ
Ó
Œ
‰J
Œ Ó
V
J
œœœœœ
œ
so don't for - get œ itœ
? c Ó I'm not in love
œ
œ
œ
≈ œ œ œ œ
≈
œ Œ
mot. 1
362
&
STugQ0X1NoI
œ œ œ œ œ œ œ œ œ œ œ œYT:
œœœœ œœœœœœœœœœœ
œ #œ œ œ œ
Figure 11.2.4 Eric Stewart and Graham Gouldman, “I’m Not In Love” (1975)
œ œ
œ œ
œ œ œ #œ
œ Diminution
11.2.3
œand
? œ Augmentation
œ œ œ
œ
Augmentation usually refers to an exact doubling of the duration of every
rhythmic value in a motive or phrase.
364
œ œ œœœœœ œ œœœ
mot. 1 inv.
mot. 1
& ≈ œ œ œ œ œ œ œ
?
∑
mot. 1 inv.
œœœœœ œœœœœœœœœœœ œ œ
œ #œ œ
œ œ œ œ œ œ œ œ
frag. a aug.
frag. a
mot. 1 inv.
mot. 1 inv.
frag. a aug.
œ
œ
œ #œ œ œ œ
frag. a aug. & ext.
∑ ∑ ∑ ∑ YT:
∑ E8EvUmq0Zao
∑ ∑ ∑ ∑ ∑ ∑ ∑
&
Figure 11.2.5 Augmentation of fragment “a” in Invention No. 1 by J.S. Bach
367
We will discuss extension and fragmentation of motives later in this chapter.
Diminution is the opposite of augmentation and usually refers to the
exact halving of the duration of every rhythmic value in a motive or phrase.
? ∑
379
&
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
CHAPTER 11. MELODIC ANALYSIS
108
Score
However, diminution can also refer to the use of shorter rhythmic values, as in
the following example.
mot. 1
U
w.
? 6 w.
4
ƒ
?6
4
?6
4
bU
w.
bw.
U
w.
U
w.
w.
(Trumpets & Trombones)
∑
∑
∑
∑
∑
w.
w.
w.
Ó ˙ b ˙ ˙˙ w .
˙ b˙
w.
ƒ (Tubas)
∑
∑
mot. 1 (dim.)
2
∑
∑
∑
˙. œ Œ Œ
˙. œ
2
∑
mot. 1 (dim.)
Ó. bœ œ œ œ
ƒ 4
∑
(Timpani)
8
8
8
?
∑
?
?
?
?
15
?
15
∑
∑
∑
∑
∑
∑
YT: aDFGmiXnLjU
∑
mot. 1
&
∑ C œ œ œ œ ∑˙ .
ƒ
∑
mot. 2
11.2.4 Rhythmic Change
∑
∑
∑
∑
21
Figure 11.2.6 Diminution of the first four notes in “Uranus” from The Planets,
Op. 32, by Gustav Holst (1916)
∑
376
15
∑
∑
œ. œ ˙.
S
∑
∑
∑
. .
∑œ œ œ œ ∑ œ œ œ. œ∑ œ
œ . œ . . œ. œ. . . œ. œ. . .
mot. 2 mot. 3
mot. 3
mot. 4
Similar to the inexact nature of intervallic change, label a motive as having
rhythmic change when some but not all rhythmic values of the motive are
varied.
382
∑
∑
∑
& 44 œ
384
∑
∑ & ∑
mot. 1
‰ ∑# œj œ ∑œ œ
∑
∑
∑
∑
mot. 1 (rhy. ch.)
∑ ‰ j ∑‰ j ∑
∑
œ
#œ œ œ œ
∑
∑
rhythmic
change
YT: vCadcBR95oU
∑
∑(same)
∑
∑
∑
∑
Figure 11.2.7 Hurby Azor and Ray Davies, “Push It” (1987)
Imagine the effect if there had been no rhythmic change and the first measure was merely repeated.
In the next example, from Beethoven’s “Pathétique” sonata, motive 1 has
dotted rhythms during the introduction of the piece.
392
&
399
&
406
&
413
?
364
œ œ œ œ œ œ œ œ
frag. a aug.
frag. a
∑
frag. a aug.
œ œ œœœœœ œ œœœ
œ
CHAPTERmot.
11.1 MELODIC
ANALYSIS
mot.
1 inv.
mot. 1 inv.
& ≈ œ œ œ œ œ œ œ
367
&
b b bfrag.c a
mot. 1
œ
œ #œ œ œ œ
frag. a aug. & ext.
mot. 1 inv.
mot. 1 inv.109
œ œ œ œ œ œ œ œ œ œ œ œmot.
œ œ1œ œ œ œ œ œ
#œ
j ‰frag. a aug.
œœœ œ œ n œœœ œ
œ
Í
œ ≈ . Kr œ
J œ
j
a .aug.
& ext. ‰
œ
œ
œ
œ
œœœ frag.
œ
.. œ œ . œ œ œœ œ
œ. #œœ œ œ. œ œœ œ
œ œ . œœ n œœ .. œœ n œœœœ
∑
21
Í
.
œ
œ
œ . œ œ œ ≈ . œ
? b b c œœœ œœœ ... œœ œœ .. œœ # œ
b œœ œœ .
J RÔ
mot. 1
œ œ ..
mot. 1
mot. 2
mot. 4j
mot. 2 mot. 3 mot. 3
b b b mot.
c 1
j
‰
‰
œ
œ
.
&
œ
œ
œ
œ
.
369
œœ .. œœ n œœœ œœ
œœ œœ .. œœ œœ .. œœ œœ œœœœ. œ.
.
œ
œ
œ
n
n
C
& b b œ œ œ∑œ ˙ . ∑ ∑ ˙ . ∑ ∑ œ œ ∑ œ œ∑ ∑œ œ ∑œ. ∑
& b Í
œ. œ
œ . œ . K. œ.Íœœ. . .œ .œ. œœ. . .
ƒ
S
YT:
SrcOcKYQX3c
œ . œ œ œ ≈ . œ
? b b c œœœ œœœ ... œœ œœ .. œœ # œ œJ ≈ . r
b
œ
œ
œ
J (1799)
RÔ
Figure 11.2.8œ Beethoven,
13, I, Introduction
... 1 Pathétique Sonata, Op.mot.
œœmot.
1 (rhy. ch.)
œ
?In bthe
b b development
∑ ∑ section,
∑ Beethoven
∑ ∑ changes
∑ j the∑rhythm∑ of motive
∑ 1 then
∑
j
j
4
abbreviates
it
in
the
following
measure
when
it
is
sequenced
up
a
step.
‰ #œ œ œ œ
‰ œ ‰ #œ œ œ œ
&4 œ
?
367
376
382
frag. a aug.
œ
´ œ´ ˙ # œ
#
œ
œ
œ
œ
& C Œ œmot.Œ 1 Œ œ # œ œ ˙ # œ
œ œ
p ÿ
f
&? œœ œœ œ œœ œœ œ œœœ œœ œœ œ œœ œœ
œC
œ
œ
rhythmic
mot. 1 (rhy.change
ch.)
369
384
386
387
# ϫ
Πmot. 1Π(inv.)
#œ
œ
œ
œœ œ œœ
bœ
ϫ ϫ ϫ
œ œ œ
œ œ
œœ œœ
œ
œ
illustration of
& œ œ œ œ œ œ œ
mirror inversion
YT:
œ œSrcOcKYQX3c
œ œ œ œ œ
Figure 11.2.9 Beethoven, &
Pathétique Sonata, Op. 13, I, development section
# œ œ means
œ
b œ the
b œ œ or#embelœ notes in a motive
Ornamentation
7 can be œornamented
lished
& 44 with passing tones, neighbor tones, and the other non-chords tones we
mot. 1
11.2.5 Ornamentation
388
mot. 1 (rhy. ch.)
(abbrev.)
(same)
mot. 1 (ret.)
studied in the previous chapter.
Here is an example of the ornamentation of a 4-note motive.
397
##
& # # # 44
400
&
####
#
mot. 1
œ. Œ
œ
.
œ
œ
mot. 1 (orn.)
œ. Œ
œ
œ
‹
œ
œ. œ. œ œ œ nt
nt
YT: s6fPN5aQVDI
Figure 11.2.10 Stevie Wonder, “Sir Duke” (1976)
mot. 1 (orn. & ext.)
n œ . œ.
n
œ
œ
œ
œ
œ
.
n œ. œ. . . nt
j
‰ #Cœj œœœ œ œ
‰ œ ‰ # œj œ œ œ
œ. œ.
&
œ
œœ ˙.
œ ˙ . œ . œ œ. œ. œ œ. œ. œ. œ œ. œ. œ. .
rhythmic
œ
.
. 110.
CHAPTER 11. MELODIC ANALYSIS
change
ƒ
S
(same)
4
&4 œ
11.2.6
Extension
mot. 1
382
mot. 1 (rhy. ch.)
œ œ œ œ œ œj œ j
j
‰ œ ‰ #œ œ œ œ
&
œ cœ œ œ œ‰ #œœ œ œ œ
œ œ &
384
mot. 1
mot. 1 (inv.)
Extension of a motive needs little explanation: additional material is added to
the end of a motive upon its repetition or reoccurrence at a later point in a
piece.
Refer to the “Sir Duke” example directly above and to therhythmic
final measure of
change
the J.S. Bach Invention in C Major example in the section on augmentation.
386
&
(same)
œ œ œ œ œ œ
œ
illustration of
11.2.7 Retrograde
inversion mot. 1 (inv.)
1
œ œ mot.
œ
œ
œ
œ
œ
384
While rare in tonal music, it is worth mentioning retrograde,
œ which
œ isœ an œ œ œ
exact reversing of the&
order of notes, as can be seen in the following example
387
&
œ œ œ œ œ œ œ
from popular music.
#œ
386
388
387
& 44
œ bœ
mot. 1
œ
7
œ #œ
mot. 1 (ret.)
& œ œ œ œ œ œ œ
œ œ œ œ œ œ œ
&
397
&
œ bœ
œ
illustration of
mirror inversion
YT: ECVbVwEzY2E
#œ
œ bœ
œ bœ
Figure 11.2.11 Melodic Retrograde
mot. 1 in “Toxic” by Cathy Dennis, Christian
Karlsson, Pontus Winnberg, Henrik Jonback (2003)
388
&c
œ
7
We will not consider transposition of a motive (also known as a sequence)
to be a motivic alteration worth labeling since it is so common.
œ #œ
mot. 1 (ret.)
11.3 Fragment
####
1 smallest identifiable
mot. 1 melodic
(orn.) idea in a
While 397
the motive is usually definedmot.
as the
composition, “compound” motives can be broken into fragments (sometimes
called “germs”).
In J.S. Bach’s Invention 1 in C Major I, the opening 7-note compound
motive can be divided into two overlapping four-note fragments
that
nt can each
nt
be developed independently.
&
400
# c
œ. Œ
œ
.
œ
œ
mot. 1
œ. Œ
œ
œ
‹
œ
œ. œ. œ œ œ
n œ . œ.
n
œ
œ
œ
œ
œ
.
n œ. œ. . . nt
mot. 2
& c ≈ œ œ œ œ œ œ œ œ œ œ œ
frag. a
mot. 1 (orn. & ext.)
frag. b
Figure 11.3.1 Fragmentation of motive 1 in C Major Invention
Here again is the example of development (in augmentation) of fragment
“a.”
œ œ œ œ œ œ œ œ
?
œ
œ #œ œ œ œ
CHAPTER 11. MELODIC ANALYSIS
364
œ œ œœœœœ œ œœœ
mot. 1 inv.
mot. 1
& ≈ œ œ œ œ œ œ œ
?
frag. a aug.
∑
111
mot. 1 inv.
œœœœœ œœœœœœœœœœœ œ œ
œ #œ œ
œ œ œ œ œ œ œ œ
frag. a
mot. 1 inv.
mot. 1 inv.
œ
frag. a aug.
œ
œ
œ #œ œ œ œ
frag. a aug. & ext.
∑ ∑ ∑ ∑ YT:
∑ E8EvUmq0Zao
∑ ∑ ∑ ∑ ∑
&
Figure 11.3.2 Development of fragment “a” in Invention 1
367
∑
∑
In the following example Bach develops an inversion of fragment “b” leading
into a cadence in G major.
374
? ∑
&c œœ
& ∑
?c œ
? ∑
379
&
∑
?
∑
377
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
m
œ
œ
j
œ
œ
œ
œ #œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ ‰
∑ a aug. &∑ext.
∑
∑
∑
∑
frag.
œ œ
≈ œ œ
œœ
œ œ œ œ #œ
œ.
œ
œ
∑
∑
∑
∑
∑
∑
frag. a inv. frag. b inv. frag. b inv. frag. b inv.
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
YT: E8EvUmq0Zao
Figure 11.3.3 Development of fragment “b” in Invention 1
11.4 Phrase
Musical form is full of sections, and the phrase is the smallest category of
section. Unlike a motive, a phrase gives the sense of completing a formal unit.
385
In classical music, phrases always end with cadences; if you have encountered a cadence, you have just witnessed the completion of a phrase. In popular
music, a phrase might be completed by a melody reaching four measures in
length or by completing a line of lyric instead of by a cadence.
To generalize (or perhaps over-generalize), most of the phrases you encounter will be four measures in length and will end with one of the four
cadence types (authentic cadence, half cadence, deceptive cadence, and, less
commonly, the plagal cadence). While four- and eight-measure phrases are the
most common, you will also encounter phrases that are five, six, and seven
392
measures
in length. Less commonly, you will encounter three-measure phrases.
Here are examples of four-measure phrases. Notice that these phrases have
a sense of completion even though they do not end with cadences.
&
∑
∑
∑
∑
∑
∑
∑
?
∑
∑
∑
∑
∑
∑
∑
&
∑
?
∑
27
3
112
CHAPTER 11. MELODIC ANALYSIS
phrase “a”
pickup
notes
C
F
C
F
œ . œ.
V 44 J ≈ œJ œ œ œ . œ œ œ . œ œ œ œ œ œ . œ w
37
I've got sun - shine
on a phrase
cloud “a”
- y day
pickup
C: I
notes C
37
42
IV
F
37
42
53
CI
IV
F
Fm
pickup
I'm
notes
man
IV
-
it's all
in
Ime
IV
phrase “a”
bbbbb 4 ∑˙
V
& b 4
46
C
∑
∑ œ . ∑
∑
∑
œ œ œ œj
œ œ œ œ œ ˙.
œ . phrase “a”
ev - 'ry wo
-
man
it's all
F
in
C
me
∑∑
3
F
b œ . œ.
∑ Ó Œ ‰ œ∑ œ
V 44b b J ≈ œJ∑ œ œ œ∑. œ œ œ . œ∑œ œ œ œ œ .∑œ w
b I've got sun-shine ∑
a cloud - y day
when it's
YT:
∑ onvNAq7Cv34l4
∑
∑
∑
∑
& b b C:∑ I
IV
I
IV
Figure
11.4.2 Nickolas Ashford and Valerie Simpson, “I’m Every Woman”
59
phrase “a”
(1978)b
b
∑
∑
∑
∑
∑
∑
b
VHere is an
Fm example of a five-measure phrase. Notice that the final chord
j discussed
(a minor
be
mode mixture)
b b b 44iv ˙chord,œwhich
œ . œ inœ the
∑
&
œ œwilldeceptive
œ chapter
˙ .on has
œ œ . cadence,
œ œphrase
is partb of a half cadence or
yet the
a feeling of
∑ ev - 'ryconsidering
∑wo - manits∑ relation
∑ me ∑ before and∑ after
& b b I'mespecially
completion,
it's all to
in the phrases
65
it. b
∑
∑
∑
∑
∑
V b b E¯≤: ii∑
E¯≤: ii
53
46
when it's
phrase “a”
œ . œ.
Ó Œ ‰œ œ
V 44b J ≈ œJ œ œ œ . œ œ œ . œ œ œ œ œ œ . œ w
œ. œ œ œ œ ˙.
∑
V b bI've˙ got sunœ -shineœ œ œj YT: onnz80onuEhHE
a cloud - y œday
when it's
œ . and Ronald White, “My Girl”(1964)
Figure 11.4.1 Smokey Robinson
I'm C: Iev - 'ry wo
42
Ó Œ ‰ œ œ3
phrase “a”
46
bb b4 ‰ œ∑
b
∑
∑
∑
∑
∑
&
b
& 4
71
œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ
b
V b b You must not know 'bout me You ∑must not know - 'bout me I can have an B¯≤
59
F
B¯≤: I
b (phrase∑ “a” continued)
∑
& b bCm
65
48
&b
51
∑
∑
∑
b œ œ œ‰œ œ œ œ‰
œ œ œ œ œ œœ. œ.
œ œ bœ œ œ œ
œ œ œ œ œœ œ
b
& b bii
b
& b ∑
71
∑
V
E¯≤m
oth - er you by to - mor - row So don't
∑
∑
∑
ev - er for a sec - ond get to think - ing
iv
∑
∑
you're ir - re - place - a - ble
∑
YT: 2EwViQxSJJQ
∑
∑
Figure 11.4.3 Shaffer Smith, Mikkel Eriksen, Tor Erik Hermansen, Espen
Lind, Beyoncé Knowles, “Irreplaceable” (2006)
&b
b
∑
∑
∑
∑
∑
∑
&b
b
∑
∑
∑
∑
∑
∑
59
65
œ
j
& c œ œ œ #œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ ‰
? c œ œ œ œ œ #œ œ œ œ.
≈ œ œ
œœ
frag. a inv. frag. b inv. frag. b inv. frag. b inv.
œ
Here is an example of a six-measure phrase that ends with
m aœ V7 - i cadence
œ
in G minor.
œ œ œ œ œ œ œ œ œ œ œ œ œj ‰
& c œ œ œ # œ œ œ œ œ œ œ œ phrase
“a”
frag. a aug.ANALYSIS
& ext.
CHAPTER 11. MELODIC
374
7 Gm/D
D/F˜ G7/Ffrag.
C/E E
a ¯≤aug.
& ext. D7
377
377
C˜o7
? cb 3œ œœ ˙ œ œœœ œœœ œœœ ##œœœ œn ˙œ . Œœ œ œ .˙œ œ œœ œ œ œœ # œœ œ œœ ≈œ œœ œ
œ œ œ œ ˙.
œ œ œ œ œœ Œ
œ œ
& b 4 œ nœ œ # œ
œ
p
#œ nœ nœ bœ
œ œ.
œ.
Gm/D
G7/F
E¯≤7
D7
phrase
# œ “a”
œ
o7
œ
∑
∑
œ Œ
œ
œœ
œ Œ
Gm
∑
œ Œ
œ
∑
phrase “a”
œ œœ œ
A˜o7/G G
œ.
# 3
œœ œ œ œ. œ
œ# œ œ . œ
4 ˙
œ Œ
œ Œ
bb
∑
∑
& p
œ
œ
œ
œ
œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ # œ# œ œ œ œ œ œ œ œ œ œ œ
œ œ œ
œ œ œ
œ œ œ
?# 3 œ œ œ œ œ
4
G
D7/A G
C/G
&
391
? bb
∑
∑
not a cadence
(phrase “a” continued)
D7/A
388
Gm
œœ œ œ
œ œ
œ œ œ Dœ7 # œ œ
D/F˜
C/E
Gm/D
C˜
Gm/D
Œ Œ
Œ Œ
œœ œœ œ œ # œ œ œ Œ œ ˙œ œ œœ# œ œ œ œ
˙
b 3 œ
œ œ œ œ œ n ˙˙ ..
œ œœ œ œœ œœ œœ
& b 4 œ nœ œ # œ
384
b #pœ∑ n œ ∑
b
∑œ. PbwJhFGUiFc
∑
n œ b œ œ œ. YT:
&
# œ ∑œ œ œœ œœ∑ œœ
? b 3
# œœ œœ
b 11.4.4
4
Figure
W.A. Mozart, Symphony No. 40, œK. 550, IIIœ (1788)
Œ Œ œ Œ Œ
? b 3
b 4
is an example of an 8-measure phrase.
?Here
bb
∑
∑
∑
∑
384
D7
113 27
&
# œ.
œœ œ œ œ
G
Em G/B
œ. œ œ
Œ
C
C/E
G/D D
œ
œ˙
œ œœ œœ œ œ
# œ n œ œ œ œ œ .œ œ œ œ # œ n œ œ
œ œ œœœ œ œœœ œ œ œœœ œ œ
œ œ œ œœ œ œ
?# œ
˙
œ
˙
œ Œ
œ œ
œ œ
I/5th V
half cadence
YT: 1vDxlnJVvW8
Figure 11.4.5 W.A. Mozart, Piano Sonata in C Major, K. 545, II
Examples of seven-measure phrases are rare and often involve elisions,
which will be covered in a later chapter when we discuss how phrases are
combined to create small forms like periods and phrase groups.
œ
You must not know 'bout me
You
œ
must not know - 'bout me
B¯≤: I
CHAPTER 11. MELODIC ANALYSIS
I can have an -
V
114
(phrase “a” continued)
E¯≤m
11.5b Cm
Subphrase
œ
œ œ‰œ œ œ œ‰
œ œ œ œ œ œœ. œ.
&b
œ œ bœ œ œ œ
œ œ œ œ œœ œ
48
51
Subphrases are smaller than phrases but larger than motives. Most of the
oth - er we
you byencounter
to - mor - row So will
don't beev -two
er for measures
a sec -ond get tolong.
think - Subphrases
ing
you're ir - reare
-placecalled
- a - ble
subphrases
ii
iv
“phrase segments” and “phrase members” in other texts.
We will label subphrases with letters (a, b, etc.). When a subphrase repeats
phrase “a”
but has slight alterations, we will put an
apostrophe after the letter (e.g., a’)
subphrase
“a”
subphrase “b”
and refer to it as “a prime.” If another alteration to subphrase
a occurs, we will
mot.
1
mot.
1
(int.
ch.)
label it as a” and refer to it as “a double prime.” If the subphrase is merely
transposed (in a sequence), we will label it as a, not a’ in our analysis.
We are including analysis of subphrases in this text because many compositions have melodic units that are two measures long. Analyzing subphrases
Stran - gersthe construction
wait - ing
up and down the bou - le - vard Their
helps us understand
of melodies.
E:
IV
I
In the following example, notice that subphrases a and a’ have the same
4 4
4
first six notes (G –F –B–C –E–E).
# ## 4
& # 4 œ . œj Ó
j
œ. œ Ó
Ó œ œ œ œ œ œœ œ œ
Phrase:
55
a
subphrase a
subphrase a'
3
3
3
3
3
3
#### 4 ΠΠ3
j
Œ
Œ
j
&
4 œ œ j œœ œ œ œ œ œ œ œ j œœ œ œ œ œ œ Œ
œ
œ
œ
Don't
stop
think - ing a-bout to - mor-row Don't
stop
it
-
'll soon
be here
YT: OvSbZEYlfnM
Figure 11.5.1 Christine McVie, “Don’t Stop” (1977)
Here is an example of a four-measure phrase with subphrases a and b.
Phrase:
a
subphrase a
4
œ œ
Fm
59
? bb 4 Œ
bb 4
E¯≤
D¯≤
œ . œ ˙D¯≤ Fmœ œ œ œ
œ
˙
J
œ œœ œ
œ œ œ
Œ
E¯≤
Par - ty rock is in the house to - night
f: i
? b b ∑
bb
63
subphrase b
VII
∑
∑
Ev - 'ry - bod - y just have a good time
VI
∑
i
∑
YT: KQ6zr6kCPj8
VII
∑
∑
∑
VI
∑
Figure 11.5.2 Stefan Gordy and Skyler Gordy, “Party Rock Anthem” (2011)
Notice that we are not looking at the motives within these subphrases. This
is because we are looking for melodic segments that are repeated. For some
compositions it is more informative to look at subphrases and less informative
to identify motives if motives are not extracted and developed.
There will be times when you will notice important melodic ideas happening
at three levels of analysis (motive, subphrase, and phrase), as in the following
example.
&b
of
the
b œ œhome
œ‰œ œ œ œ‰
œœ. œ.
œ œ œ œ œ brave.
œ œ bœ œ œ œ
œ œ œ œ œœ œ
7
C - er you by to - mor - row So don't Em
oth
ev - er for a sec -ond get
(C-E-G)
(E-G-B-D)
CHAPTER
11.
MELODIC
ANALYSIS
ii
iv
7
to think Fmaj
- ing
you're ir - re-place - a - ble
. œ. œ ptœ ptœ œ œ .
. œ. œ(esc
œ .)
œ
œ
œ
œ
4
w
w
Phrase: Œ
≈ Ra
&4
subphrase a
subphrase b
20
(F-A-C-E)
115
( ) ( )
# # # #C 4
j
& (C-E-G)
4 œ . œj Ó œ . œ Ó Ó œ œ œ œ œ œ œ œ œ
dn
œ
œ
dn œ
dn - gers
) œ
œ
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œ
Stran
wait
ing
up
and
down
the
bou
le - vard Their
(
œ
)
œ
4
œ
(# œ
& 4 œ (œ ) œ
51
mot. 1
24
mot. 1 (inv.)
E: IV
Phrase:
55
25
I
a
A
Dm
F
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subphrase
a
subphrase
a'
(G-B-D)
(A-C˜-E)
(D-F-A)
(F-A-C)
Figure 11.5.3
Cain,
“Don’t3 Stop3 Believin”’
antJonathan
3
3
3
antNeil
ant Schon,3 nt
pt Steve
pt Perry,
nt3
ant
G
## 4 Œ Œ
j j j
j
& 4 4œj œœ œœ œœj œ œ œ œœ œœ œœj œ œœ œœ ŒÓ œ ‰(Œ# œœ)jœ( nœœœ) œ ˙œ œ œœ œ œœ Œ
There is ambiguity between motive and subphrase. Reconsider the follow-
#
(1981)
& b# 4
( )
( )
( )
( )
( ) ( )
I Don't
know
where
you're
com
-on
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me
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ing example
from
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section
intervallic
E: I
29
mot. 1
m3
b
j
V b b 44 œ œ œ œ
The ver - y
IV
œ ˙.
thought of you
I
Ó
onit the- line
'll soon beCall
hereme
mot. 1IV
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P4
‰ œj œ œ œ œ ˙ .
and I for - get to do
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b b ∑
b
∑
∑
∑
∑
V
Figure 11.5.4 Ray Noble, “The Very Thought of You” (1934)
33
∑
When you listen to the music of “The Very Thought of You” you will hear
that each motive lasts for two measures. The difference is that motives are
typically short—two to seven notes—whereas subphrases will usually contain
six or more notes and occupy two measures (half of a four-measure phrase).
11.6 Practice Exercises
Day One:
1. For the following examples:
• Analyze motives using numbers (1, 2, etc.)
• Label lead-sheet symbols and Roman numerals when blanks are
provided
• Label non-chord tones for notes in parentheses
(Note: Even though there are 11 blanks for motives, there are only
six motives in this example due to motivic alteration.)
˙
____
____
____
____
CHAPTER 11. MELODIC ANALYSIS
116
Motives:
b 4
j
œ. œ. œ. œ œœ
& b 4 œ (œ) œ . œ œ œ (œ ) œ .(œ)œ œ œ œ(œ)œ (œ) (œ) (œ) (œ) (œ) œ . œ œ (œ)œ ˙
147
Ah
147
28
393
Ah
b 4
& b 4 œœ
œ
? b 4
b 4 œ
Lead-sheet:
j
œœ
œ
j
œ
__ __ __
œœ ..
œ.
œ.
B¯≤: __ __ __
Ooh
j
œœ .. œœ
œ. œ
j
œ
.
œ
__
˙˙
˙
˙
__
__ __
j
œœ
œ
j
œ
__ __
œœ ..
œ.
˙˙
˙
˙
œ.
__ __
j
œœ
œ
j
œ
__
__
œœ ..
œ.
˙˙
˙
˙
œ.
__
__
˙˙
˙
˙
#
& C œ (œ ) œ. (œ)œ # œ (œ) œ
œ )# œ œ.(n œ)n œ
. YT:œ (#RgKAFK5djSk
.
.
.
Figure 11.6.1 Charlie Puth, Cameron Thomaz,
Andrew Cedar,
Justin
œ
œ
œ
œ
œ
(
)
œ
œ
œ
(
)
( )œ
? # C“See You Again”
( )œ œ
Franks,
(2015)
œ œ œ œ. œ. œ. œ. œ. œ œ. œ œ œ œ œ œ œ
. example, alter the given
. motives
For the following
. . . Also,
J
. . as. specified.
Motives:
2.
28
provide e:lead-sheet
and Roman
__ symbols
__
__ numerals and analyze
__ non__
# ___
___
___
C œ (œ ) œ œ œ ___
&
œ
œ
œ
(
)
2
1
aug.
1
1
# œ. ( ) œ (# œ )# œ . (n œ)n 2œ aug.
Motives:
.
.
œ
œ œ œ œ. œ
& c œ (œ)œ(œ)œ œ (œ)( )œ œ
(œ )œ ( œ)
?# C
œ
œ˙ œ
w
œ
œ
œ
w
œ
œ
œ
? c www œ œ. . . .ww . œ. œ. œww.
. . ˙˙. .
393
chord tones.
Motives:
Lead sheet:
398
e:
C: ___
398
3.
__
__
__
___
Lead sheet: ___
___
For
402 the following example:
___
___
___
___
___
2 inv.
œ .
œ (œ)(œ) œ œ
œ˙˙ œ œ
.˙ . J
__ __
___
___
&• Write the lead-sheet symbols
œ (œ)(œ)œ
œ
c
&
œ
• Writeœ œthe
(œ) chords as whole
œ notes in œthe bass clefœ staff
œ( )
w
www including
?
• Analyze
˙˙ write
˙
?
∑
∑ tones,
∑
∑wwthe ones
∑ you
c ∑www non-chord
˙ ∑ ˙˙ ∑
2
1
Motives:
1 aug.
2 aug.
1
2 inv.
• Alter the given motives as specified to fit the harmony
C: ___
___
___
___
___
• Specify the cadence
410
&
___
Lead sheet:
402
___
b
˙
& b c∑ œ œ (œ∑)
?
1
Motives:
? b c
b
g: i
œ∑
iv
___
1 int. ch.
∑
œ
i
___
1 inv.
∑
œ
∑
1 inv.
∑
V7
Cadence: ____________
&b
Day Two: 406
b
? bb
CHAPTER 11. MELODIC ANALYSIS
4.
117
For the following example:
• Analyze the motives using numbers (1, 2, etc.), noting motivic
alterations when applicable
• Analyze subphrases using letters and primes (a, a’, b, etc.)
• Label lead-sheet symbols and Roman numerals when blanks are
provided
• Label non-chord tones for notes in parentheses
22
Lead-sheet:
___
___
___
___ ___ ___ ___ ___
Subphrases:
401
# 2 œJ (œ)œ(# œ)œ œ . œ œ . œ œ . œ œ œ œ
j
(œ) œ œ œ
& 4
J
J
( ) œ # œ . (œ) œ .
J
Í
Motives:
e:
410
&
#
i
iv
i
iio V
i
iv
V
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Figure 11.6.2 Robert Schumann, Album for the Young, Op. 68, No.
16, “First Loss”
Click here to download the first assignment for this chapter.
Click here to download the second assignment for this chapter.
Click here to download the Unit 2 Practice Test.
Chapter 12
Form in Popular Music
The overall form of a piece of popular music usually can be broken down into
smaller 4-, 8-, 12-, or 16-bar sections. The material in this chapter is informed
by John Covach’s essay “Form in Rock Music” from Engaging Music: Essays
in Music Analysis (ed. D. Stein).
12.1 Verse-Chorus Form
The Verse-Chorus form is arguably the most common musical form of
present day popular music and is probably familiar to most readers of this
text. In Verse-Chorus form, the chorus contains the “hook”—the memorable
refrain—while the verse typically contains less memorable melodic material. A
clear example can be found in the 1985 song “We Are the World.”
Table 12.1.1 Michael Jackson and Lionel Richie, “We Are The World”
(1985)
0:00–0:26
Introduction, 6 bars
0:26–0:53
0:53–1:18
1:18–1:49
Verse 1, 8 bars
Verse 2, 8 bars
Chorus, 9 bars
1:49–2:14
2:14–2:41
Verse 3, 8 bars
Chorus, 8 bars
2:41–3:08
Bridge, 8 bars
3:08–3:35
3:35–4:02
4:02–end
Chorus, 8 bars
Chorus, 8 bars ending with key change
Chorus, 7 times in F major with fade out
YT: 9AjkUyX0rVw
Common additions to the Verse-Chorus form, beside the bridge, are the
pre-chorus and post-chorus.
118
CHAPTER 12. FORM IN POPULAR MUSIC
119
Table 12.1.2 Kurt Cobain, Krist Novoselic, and Dave Grohl, “Smells
Like Teen Spirit” (1991)
0:00–0:25
0:25–0:42
0:42–0:58
0:58–1:23
1:23–1:31
Introduction, 12 bars
Verse 1, 8 bars
Pre-chorus, 8 bars
Chorus, 9 bars
Post-chorus, 4 bars
1:31–1:39
1:39–1:56
1:56–2:12
2:12–2:37
2:37–2:45
Interlude, 4 bars
Verse 2, 8 bars
Pre-chorus, 8 bars
Chorus, 12 bars
Post-chorus, 4 bars
2:45–3:02
Guitar solo, 8 bars
3:02–3:10
3:10–3:26
3:26–3:42
3:42–4:37
Interlude, 4 bars
Verse 3, 8 bars
Pre-chorus, 8 bars
Chorus, 21 bars
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It is worth noting that there may disagreement about labeling sections in
a form. One person may call a section a “pre-chorus,” another may call it a
“first chorus,” while another may call it “verse part b.” There is ambiguity in
naming sections and disagreement is to be expected.
There are “simple” and “contrasting” verse-chorus forms. A simple versechorus form has the same harmonic progression for the verse and chorus (e.g.,
“All About That Bass”). The chord progressions for the verse and chorus are
different in a contrasting verse-chorus form like “We Are the World.”
12.2 AABA Form
The AABA form is associated with the hits from Broadway musicals in the
1930s and remained one of the most popular forms of popular music until the
1950s, when Rock ‘n’ Roll became popular. Each section (A or B) is typically
8 measures long. The A sections contain the primary melody we associate with
the song while the B section provides contrast and is often called the “bridge”
or “middle eight.”
CHAPTER 12. FORM IN POPULAR MUSIC
120
Table 12.2.1 George Gershwin, “I Got Rhythm” (1930)
0:00–0:10
Introduction, 8 bars
0:10–0:18
0:18–0:26
0:26–0:35
0:35–0:45
A
A
B
A
0:45–0:53
0:53–1:02
A section, 8 bars (instrumental shout chorus)
Introduction, 8 bars (shout chorus continues)
1:02–1:10
1:10–1:19
1:19–1:27
1:27–1:35
A
A
B
A
1:35–1:54
Coda, 12 bars
section (A1), 8 bars
section (A2), 8 bars
section, 8 bars
section (A3), 10 bars
section (A1), 8 bars
section (A2), 8 bars
section, 8 bars
section (A3), 8 bars
YT: Q_jKTPsh54Y
It is common for one or more of the A sections to be instrumental, and it
is also common to eliminate an A section on the repeat of the entire AABA
form (AABAABA, for example).
Other well known songs with AABA form include “Over the Rainbow” from
The Wizard of Oz as well as many famous songs from the Great American
Songbook by George Gershwin (“Let’s Call the Whole Thing Off,” “Someone
to Watch Over Me”), Cole Porter (“Anything Goes,” “Love for Sale,” “I Get
A Kick Out of You”), Irving Berlin (“Blue Skies,” “Puttin’ on the Ritz”), and
Jerome Kern (“The Way You Look Tonight,” “Smoke Gets In Your Eyes”).
The AABA form continued to be dominant into the 1960s (including Beatles
songs like “Yesterday,” “Norwegian Wood,” and “Hey Jude,” to name a few).
The AABA form is less common in the present day but can be found in songs
like The Cure’s “Friday, I’m in Love” (1992) and Norah Jones’s “Don’t Know
Why” (1999).
A note on terminology: the entire 32-bar AABA form is sometimes called
a “refrain” or “chorus,” and some AABA songs are preceded by a “verse.”
This means a song like “Someone To Watch Over Me” begins with a verse
and is followed by a “refrain” (which could also be called a “chorus”). Other
synonymous terms you may encounter for “verse” in the context of AABA form
are “prelude” and “introduction.”
12.3 ABAC Form
Many popular songs from the 1930s–1950s were in the 32-bar ABAC form.
Well-known examples include “White Christmas,” “Someday My Prince Will
Come,” and “When I Fall In Love.”
“Star Dust” is an example of an ABAC form that is usually performed with
a verse preceding the refrain.
CHAPTER 12. FORM IN POPULAR MUSIC
121
Table 12.3.1 Hoagy Carmichael, “Star Dust” (1927)
0:00–0:13
0:13–1:13
Introduction, 4 bars
Verse, 16 bars (8 bars + 8 bars)
1:13–1:41
1:41–2:07
2:07–2:32
2:32–2:57
A
B
A
C
2:57–3:12
Coda, 4 bars
section, 8 bars
section, 8 bars
section, 8 bars
section, 8 bars
YT: hWkoFj14HkE
The ABAC form may also occur as ABAB’ where the B’ section begins the
same as the B section but ends differently.
12.4 The 12-Bar Blues
Associated with the Blues genre, which originated in the early 1900s, the 12-bar
blues was also popular during the Swing Era of the 1930s and 1940s, (examples
include “In The Mood” and “One O’Clock Jump”), as well as during the early
years of Rock ‘n’ Roll in the 1950s (“Johnny B. Goode,” “Hound Dog,” “Rock
around the Clock”). The basic 12-bar blues progression is shown below.
Table 12.4.1 Chuck Berry, “Johnny B. Goode” (1958)
Bars 1–4:
I
I
I
I
Bars 5–8:
IV
IV
I
I
Bars 9–12:
V
IV
I
I
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12.5 Harmonically Closed and Open Sections
A harmonically closed section ends on the tonic chord ( I ). A harmonically
open section typically ends on a non–tonic chord like V , but could also end
on IV .
In an AABA form, the A sections are usually harmonically closed, ending
on I , and the B section (or bridge) is usually harmonically open, ending on V .
In verse-chorus form, sections that leads into the chorus (verse, pre-chorus,
and bridge) are usually harmonically open, while choruses can be harmonically
closed or open.
If you compose a piece in AABA or verse-chorus form, placing harmonically
open and closed sections appropriately is important to the flow of the music.
For example, the verse and bridge on “We Are the World” are harmonically
open (ending on V ) while the chorus is harmonically closed (ending on the
tonic chord, I ).
CHAPTER 12. FORM IN POPULAR MUSIC
122
12.6 Practice Exercises
1.
For each song, fill in the beginning time for each section, label each section
type (verse, pre-chorus, chorus, post-chorus, interlude, introduction, A, B,
or C section, etc.), and the number of bars in each section of the form.
Table 12.6.1 Tom Bahler, “She’s Out of My Life” (1980)
(a)
Time:
Time:
Time:
Time:
Time:
:
:
:
:
:
Section
Section
Section
Section
Section
Type:
Type:
Type:
Type:
Type:
,
,
,
,
,
bars
bars
bars
bars
bars
,
,
,
,
,
,
,
,
,
,
bars
bars
bars
bars
bars
bars
bars
bars
bars
bars
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Table 12.6.2 Lennon-McCartney, “Penny Lane”
(b)
Time:
Time:
Time:
Time:
Time:
Time:
Time:
Time:
Time:
Time:
:
:
:
:
:
:
:
:
:
:
Section
Section
Section
Section
Section
Section
Section
Section
Section
Section
Type:
Type:
Type:
Type:
Type:
Type:
Type:
Type:
Type:
Type:
YT:
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Click here to download the homework assignment for this chapter.
Chapter 13
Phrases in Combination35
478
13.1 The Perfect
Authentic Cadence
& w
bw
We will now distinguish between two types of authentic ( V – I ) cadences: the
Perfect Authentic Cadence (PAC) and the Imperfect Authentic Cadence (IAC).
The Perfect Authentic Cadence must meet three requirements:
? w
w
1. V – I
2. Both chords in root position
3. Tonic scale degree (1̂ ) in the highest voice of the tonic chord
˙˙
&
479
1̂ in highest voice
˙˙
˙
˙
˙˙
?
C: V
I
both V & I are in root position
If at least one of these requirements is not met (one or both of the chords
are inverted, tonic is not in the highest voice, or vii◦ occurs in place of V ),
the cadence is an Imperfect Authentic Cadence (IAC).
13.2 The Sentence
∑ ∑ ∑ ∑ ∑ ∑ ∑ A sentence
∑ ∑ in∑ music∑ is ∑a phrase
∑ with
∑ a ∑specific∑ melodic
∑ ∑construction:
∑
a melodic
idea (motive 1 or subphrase a) is either repeated or sequenced then followed
by either related or unrelated material leading to a cadence.
In this first example, Mozart sequences motive 1 from measure 1 up a step
in measure 2. Measure 3 contains related material and measure 4 contains
cadential material.
123
∑
∑
∑
∑
∑
∑
∑
124 35
CHAPTER 13. PHRASES IN COMBINATION
36
489
related material
frag. b frag. b
### 6 œ . œ œ œ œ œ . œ œ œ œ
j œ œ œ œœ œ œ œj
& 8
J
J œ œ
J
J œ œ
p frag. a frag. b frag. a frag. b
j
j
j
j
j
j
œ œ œ œœ œœ œ œ œœ œœ œ œ œ œ œ
? # # # 68 œ . œ
J œ. œ œ
J œ œJ œ œJ œ œ œ .
J
mot. 1
A: I
479
mot. 1
I/3rd
V7/5th
V/3rd
vi7
& ˙˙
V/3rd1̂ in highest
I ii/3rdvoice
I/5th V
Half Cadence
˙˙
phrase a
493
480
497
485
˙
# # # œ . œ œ œ œ œ .YT:
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œ œ ?œ ˙˙ œj œ œ œ œœ œ œœ œj
œ
œ
&
J
œ
J K. 331, I J ˙ J
Figure 13.2.1 Sentence Structure in Mozart,
In thepnext example,
changes
C: j V of subphrase
j Beethoven
j
j
jthe intervals
j I a in meaœ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œœ rootsubphrases
sures 3–4 toœ fit the
dominant
harmony.
He
extracts
motive
2 from
both
V
&
I
are
in
position
œ lead
œ toœ a half
œ . œ œ 7–8
œ
œ
. œ œ œ 5–6.œJ Measures
? #a’# #in œmeasures
œ
a and
cadence.
J
œ œ.
J
J
J
b
& #b b#b
& #
? bb b
b
? ###
subphrase a
. œ . œ œphrase
œ
n œ œ. a'Œ
.
œ
C
œ
œ .
œ . œœ œ .œmot. 1œJ œ . œ œmot.œ32 œJ œ
p
œ
œœ
Cœ Œ œj œ ∑œj œ Œ œœœj œ œœœj œœœ
œ . œ œ œ œJ œ . f:œ œi œ œJ œ
related material
œ . œ œ n œ œ.
Œ
S 3
œœœ œœœ
? b b b Œ œœœ
b
bb
&bb
mot. 2
j
œ
i
.
. n œ. œ
œ
œ.
j
œ
œ
œ mot. 1œœ
Jœ
œ
n œœœj œŒ Ó
œ œ
œ7/3rd
V
J
J
œ . œ œ œ œ.(HC)
Œ
j
3
œœ mot.
œ œœœ œœœ2 ‰
œœ œœ œœ
Œ n œœ œœ œœ
œ jœ ‰
œ
subphrase a'
˙˙˙ œ œ œ œ
œ . œ œ œ œ.
j
œ
Œ ˙
S 3
œœ
n œœ œœ œœ ƒ œœœ
œ
Œ œ œ œ Œ Œ
mot. 2
viio/3rd
i/3rd iio/3rd
I/5th V
V7 I
(PAC)
nœ œ œ
œ œU
Œ
p œ
œU
Œ Œ
V
Half Cadence
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Figure 13.2.2 Sentence Structure in Beethoven, Op. 2, No. 1, I
In the next example, unrelated material follows subphrase a and its repetition.
& b œœ
Œ
œœ œœ œœ œœ
œœ
œœ
CHAPTER 13. PHRASES IN COMBINATION
I
V
510
..
œ ‰ 125
(PAC)
I
b œ œ . . œ œ . . œ. œ. œ. œ. n œ œ œ œ
œ œ
œ œ
&b c
Í
Í
Í
b
& b c œ œœœœœ œ œœœœœ œœ œ œ œ œœœ œœœ
œ
œ œ
œ œ
œ œ œ #œ
subphrase a
B ¯≤: V7/3rd
I/3rd
œ œ . . œ œ . .
bb œ œ œœ œœ œ œ œœ œœ
&
Í
Í
bb
&
œ œ œ œ œ œ œ œ
œ œ œ œ œ œ œ œ
. .
œ
œ
œ. œ. œ œœ nn œœ œ œœ œ
œ œ œ
Í
subphrase a
512
V7/3rd
514
b˙
b˙
˙
˙
œ œ œ œ œ œ œ œ #œ œ œ œ œ œ œ œ
I/3rd (not a strong cadence)
œ œ œ œ œ œ œ œ œ œ œ œ œ bœ œ œ
‰
‰
b ˙
&b ˙ ˙
˙
p
? b ‰ œ œ œ ‰ œ n œ œ ‰# œ n œ œ ‰ œ œ œ Œ
b
unrelated material
new phrase
œ
& bœ
ii/3rd
œ œ ˙˙
˙
˙˙
I/5th V7 I
(HC)
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Figure 13.2.3 Sentence Structure in Mozart, K. 333, I (1783)
13.3 The Period
In music, a period consists of at least two phrases with the final phrase ending
in a more conclusive cadence than the first phrase.
13.3.1 Conclusiveness of Cadence
Because period form involves “more conclusive” and “less conclusive” cadences,
it is important to distinguish between inconclusive and conclusive cadences.
Conclusive cadences end on the tonic chord, while inconclusive cadences do
not.
Inconclusive Cadences
Deceptive Cadence ( V – vi )
Half Cadence (ends on V )
Conclusive Cadences
Authentic Cadence ( V – I )
Plagal Cadence ( IV – I )
CHAPTER 13. PHRASES IN COMBINATION
36
489
126
In addition, the perfect authentic cadence (PAC) is more conclusive than
the imperfect authentic cadence (IAC). While the plagal cadence (PC) occurs
less frequently than the other three cadences listed in the table above, it will
sometimes occur in root position at the end of a phrase after an inverted
imperfect authentic cadence (IAC) has concluded a previous phrase, with the
related
material more conclusive
understanding that a root position PC could be
considered
mot. 1
mot. 1'
frag. b frag. b
than an inverted IAC.
Generally, a period will either contain a phrase ending in a half cadence
(HC) followed by a phrase ending in an authentic cadence (IAC or PAC), or
it will contain frag.
a phrase
endingfrag.
in aan IAC
following by a phrase ending in a
a
frag. b
frag. b
PAC.
### 6 œ . œ œ œ œ œ . œ œ œ œ
j œ œ œ œœ œ œ œj
œ
œ
& 8
J
J
J
J œ œ
p
j
j
j
j
j
j
œ œ œ œœ œœ œ œ œœ œœ œ œ œ œ œ
œ œ œ.
. œ œ Conclusive-More
? # # #Examples
6 œ . œ of the
J œ“Less
J œ œJ œ œJ Conclusive”
13.3.2
8
J
Cadential Formula
A: I
I/3rd
V/3rd V7/5th vi7
V/3rd
I ii/3rd I/5th V
In the first example, a HC concludes the first phrase and a PAC concludes the
Half Cadence
second phrase, making a period.
phrase a
493
535
497
539
a
# # # œ . œ œ œ œ . œ œphrase
j
œœ œ œ œj
œ
œ
œ
œ
œ
œ
œ
œ
&
J
J
J
J œ œ
j
p
j œ .j
jœj œ j œ œœ j n œœ j œ .
n
œ
œ
? b b b 42? œ# œ# œ œœ . œœ œœœœœ œœ œœœœ œœœœ. œœœœœœ œœœ œœ œ œœœ œ œœ œœœ œœ œœœœ œ œ œ œ œ œ
J
b
J
œ œ.
#
J
J
J
p
I/5th V
? b b b 42
œ
œ
œ
(HC)
œ
b
œ
œ phraseœ a' œ œ
œ
jV j
A¯≤: # # # œ œ œ œ œ
œ
œ
œ
œ
œ
œœ œœ œ ‰
.
.
œœ(HC)
&
J œ œ
J œ œJ
œ œ œœ
j
j
j
j
j
œ œ œ œœ œœ œ phrase
œ œœ b œœ œ œ œ
? ### œ . œ
J œ. œ œ
J œ œJ. œ. .œ . œ j œ 1̂ ‰
œ
œ
œ b œ b œœ œ nœ
œ œ b œJœ œœ œ7 œ. . œ.
œ
œ
œ
.
œ
œ
œ
œ
? bb b
œ œ
œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œVœ œI œ
b
(PAC)
501
3
###
? bb b &
œ
œ
b bœ
œ j
œ
YT:œvp_h649sZ9A
œ
œ
œ
Figure 13.3.1 Mozart, Piano Sonata K. 331, I
#
7
? ##
V
∑ diagram
∑ of the∑ above example.
∑
∑
∑I
∑
Here is a formal
(PAC)
a
a'
HC
PAC
Figure 13.3.2 Diagram of Mozart, K. 331, I, mm. 1-8
Notice that one or more phrases within a period can be a sentence, as in
39
CHAPTER 13. PHRASES IN COMBINATION
127
the example above, since sentences are phrases with specific melodic structure.
In the next example, the first phrase concludes with an IAC and the second
phrase concludes with a PAC.
501
phrase a
œœœœ œ
œ
œ
2
& b 4 œJ œ œ
& b 42 ‰ œœ
F:
Œ
I
œœœœ
œœ œœ œœ œœ
œ œ
œœœœœ œ œ
œœ3̂
œ
œ œ œ œ œ
œ œ œ œ
œœ
V
I
(IAC)
506
&b
œœœœœœœœ œ
& b œœ
Œ
phrase a'
1̂
œœœœ œœ œœ œœ
œœ œ
œœ œœ œœ œœ
I
&b
œœ
V
œœ
œ
I
(PAC)
‰ ..
‰ ..
510
?b
YT: hmu-6FJT5Bw
∑
∑
∑
∑
∑
∑
∑
∑
Figure 13.3.3 Joseph Haydn, Piano Sonata in F Major, Hob. XVI:9, III.
Scherzo
In the next example, the first phrase ends with an IAC and is followed by
a second phrase ending with a PAC.
37
CHAPTER 13. PHRASES IN COMBINATION
38
128
phrase a
3̂
œ # œ œ # œ œ œ n œ œ œj ≈ œ œ ≈
3
œ ≈ œ #œ
œ
&8
#
œ
œ
J œ
œœ J
π
œ
œ
#œ
? 38 ‰
∑
œœ ≈‰ œ œ ≈ ‰ œœ ≈‰
518
a: i
V
i
(IAC)
phrase a'
523
œ #œ œ œ nœ œ j ≈
œ
œ œJ
&
œ œ
?
∑
œ
i
œ œ ≈ ‰
œ
≈ œ œ œ
œ
1̂
œ #œ ≈ ‰
V
œ
œ œ ≈
i
(PAC)
phrase a = "antecedent"
527
GwcyH-aWUc8
# # # 6 œ . œ œ œ œ œYT:
j œ œ œ œœ œ œ œj
œ
œ
œ
.
œ
Figure
13.3.4
Beethoven,
Bagatelle
in
A
minor,
WoO
59, “Für Elise”œ œ
œ
œ
& 8
J
J
J
J
Another example with a less conclusive cadence followed by a more concluj on Me”j by Bill jWithers.
j
j
j
p
sive cadence isœ“Lean
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œœ
œ
œ
œ
œ
œ
œ
œ
œ
œ
.
? # # # 68 œ . œ œ
œ
œ
J
J
œ œ.
J
J
J
YT: fOZ-MySzAac
Figure 13.3.5 “Lean on Me” (1972) by Bill Withers
HC
(less conclusive)
j
## œ . œ œ œ œ œ . œ œ œ œ
œ
œ
œœ œœisj called
œ
œœcadence
œœ ‰ the
In &
a period, the phrase Jending with the Jless œconclusive
œ œ cadence
œ
“antecedent” and the phrase ending with the Jmore conclusive
is
j
jThese canj be thought
j of jas being in a “question and
called the “consequent.”
œ œ œ œ œ œ œ œ œ œ œ
answer” #relationship.
? # # œ . œ œ œ œJ œ . œ œ œ œJ œ œJ œ œ œ j ‰
J
œ œ
phrase a' = "consequent"
531
13.3.3 #Antecedents and Consequents
PAC
(more conclusive)
œ
i
V
CHAPTER 13. PHRASES IN COMBINATION
527
531
### 6 œ . œ œ œ œ .
& 8
J œ
j
j
p
œœ œ œœ œœ œœ œ
? ### 6 .
J œ.
8
### œ . œ œ œ
&
j
œœ œ œœ œœ
? ### .
œ
J
j
œœ
J
i
(PAC)
129
phrase a = "antecedent"
œœ œ
j
œ
œ œ œœ
œ œ œj œ œ œ œœ œ œœ œœj
J
J
J
j
j
j
œœ œ œ œ œ œœ
J œ œJ œ œJ
œ œ.
J
HC
(less conclusive)
j
œ œ œ œ œœ
J
œ
J
j
j
œœ œ œ œœ
J œ œJ
œ
J
phrase a' = "consequent"
œ. œ œ œ
j
œ œ œ œœ
œ. œ
œœ œœj œ ‰
œ œ œœ
œ
j ‰
œ œ
PAC
(more conclusive)
YT: vp_h649sZ9A
Figure 13.3.6 Antecedent and Consequent in Mozart, Piano Sonata K. 331, I
13.3.4 Parallel and Contrasting Periods
Periods are labeled as “parallel” or “contrasting” based on the melodic material. In a parallel period, the melodies in both phrases begin similarly. In a
contrasting period, the phrases begin differently.
The three preceding examples are parallel periods
The apostrophe mark (’) is called “prime” and is used to show a phrase is
similar to a previous phrase but ends with a different cadence. Therefore a’ is
called “a prime” and a” is called “a double prime.” If you are analyzing a piece
that requires triple and quadruple primes, it is clearer to use a1 , a2 , a3 , and
so on.
Below is an example of a contrasting period.
CHAPTER 13. PHRASES IN COMBINATION
130
39
phrase a
j
j a œ œ œ œ.
phrase
.
œ
n
œ
œ
n
œ
œ
œ
œ
? b b b 42 œ œ œ œ œœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ
b
j
j
œ n œœ œ .
p
.
œ
œ
n
œ
œ
œ
œ
œ
? b b b 4?
2 bœb bœb œ42 œ œœœ œ œ œœ œ œ œ œœ œ œ œ œ œ œ œœ œ œ œœ œœœ œ œ œ œ œ œ
œ
œ œ
b
œ
535
535
p
? b b b 42
b
œ
539
A¯≤:
œ
œ
œ
œ
phrase b œ œ
œ
V
(HC)
œ
œ
. . . V.
1̂
(HC)
œ œ œ œ œ bœ bœ
œ
œ
œ
œ
.
œ œ œ œnœœ œ œ œ
b œ œ œ œ œ œ. œ. œ.
? bb b œ œ œ œ œ œ
œ
œ
œ
œ
œœ œ œ
œ œ
b
phrase b
A¯≤:
. . ..
?œ b b b
1̂j
œ
œ
b
œ
b
œ
b
œ
œ
œ
œ
œ
œ
œ œ œ œnœœ œ œ œœ
b œ œ œœœœ œ œœ. œ. œ.
? b b b œ œ œ œb œœœ .œ œ œ
œ
œ
œ
œ
œœ œ œ
œ œ
b
V7
I
3
539
? bb b
œ
b 543b œ
? bb b
b
œ
3
(PAC)
œ
œ
œ
YT: SrcOcKYQX3c
œ
V7
j
œ
œ
I
(PAC)
Figure 13.3.7 Beethoven, Piano Sonata in C minor, Op. 13, (Pathétique), II
? b b b ∑
b
a∑
∑
∑
HC
∑
∑
∑
b
∑
∑
∑
PAC
? bb b
b
Figure
13.3.8 Formal diagram of the example above (2nd movement of Beethoven
553
Pathétique sonata)
13.3.5 Repeated Phrase
? bb b
b
∑
∑
∑
∑
∑
∑
If you encounter a section consisting of the same phrase occurring twice, call
it a “repeated phrase.”
39
40
CHAPTER 13. PHRASES IN COMBINATION
131
phrase a
543
? bb b
b
535
548
539
? bb b
b
? bb b
b
3
j 3
1̂
phrase a œ
# # # 2 œf . œ œœ œ œ œ
œ
œ
œ
& 4 œ . œ œ . œ œœ œœœ œœœ œœ œœ œ œ œ œœ œ œ œ œœ # œœ œ . œœœ ... œœ
f j
j
œ n œœ œ .
.
œ
œ
f
œ
œ
œn.œ
œ
œ
œ
?
24 #œ# #œ 42œ œ‰œœ œ œ Œœ œ œ‰œ œ . œœ œ œ œœ œœ œJœ œ œ œJ œœ œœ œœœ œ œœœ ..œ œ œ .œœœœ
p
f
E: V7 I
24
œ
œ (PAC)
œ
œ
œ
œ phraseœa œ œ
œ
3
3
j
1̂
A¯≤:# #
V
œœ œ œ œœ œ œ
œ
#
œ
œ
(HC)
œ
œ
œ
&
œ œ . œ œœœ œœ œœ œœ œ œ œ œ œ œœ # œœœœ œœ ..
œ.
phrase b
? # # # œœ œœ œœ œ . œ œ œœ œ œœJ œœ œœ. . .œ . œ . œ œ œ
1̂
œ
b
œ
b
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ œ œ œnœœ œ œ œ
b œ œE: Vœ7 œ œI œ. œ. œœ.
œ œ œ .œ œ œ
œ
œ œ œ œ œ œ œ œ œ (PAC)
? bb b ### œ
b &b œ
œ
552
3
œ
œ
œ
YT: Qy8NLd7d6VE
œ
œ
j
œ
? # # # ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ (PAC)
∑ ∑ ∑
Figure 13.3.9 Robert Schumann, Album for the Young,
Op. 68, No. 17,
V7
I
“Little Morning Wanderer”
a
566
&
a
###
PAC
PAC
Figure 13.3.10 Formal diagram of the example above (“Little Morning Wanderer”)
? ###
∑
∑
∑
∑
∑
∑
In following two sections, we will examine periods containing more than
two phrases.
13.4 The Asymmetrical Period
Asymmetrical periods consist of three or five phrases. In an asymmetrical
period, there will be an unequal number of antecedents and consequents, hence
the “asymmetry.” In the example below, there is one antecedent and two
consequents.
39
CHAPTER 13. PHRASES IN COMBINATION
132
phrase a
552
b
& b b c œœ œœ œœ .. œœ œ
œ œ
œ
ƒ
? b c œœ œ n œœ œœ
bb
œ œœ œœ œœ
nœ.
œœ b œœ œœ .. b œœ n œ n œ œ . œ b œœ œœ œœ # œœœ n œ n œœœ
œœ œœ b œœœ œœœ nn œœœ b n œœœœ œœ œ # œœ n œœ
œ b œ œ œœ œ
œ œœ n œœ œ œ œ
œ
œ bœ œ œ œ
œ œ œ
œ œ
V
(HC)
phrase b
556
b œ œ œ œ
& b b œœ œœ œ œ .# œ œœ œœœ
p œ
? b œ œ nœ bœ nœ
bb
nœ bœ nœ
œ
œ
# œœœ n œœœ ... n œœ n œœœ
œœ b œ œ .
œ b œœ œœ œ œœœ
b œœ b œœ œ . n œ œ
œœ
bœ
bœ
n œœœ
œ
œ
œœ # œœ n œœ .. n œ œ œœ b œ œ . œ
œ œœ œ . œ n œœ œ b œœ œœ œœœ b œœ b œœ œ . n œ œ
cresc.
nœ bœ œ nœ œ œ
œœ œœ n œœœ œœ
œ
nœ bœ œ nœ œ œ nœ
œ œ
nœ œ œ bœ œ œ
bœ
œ
U
bœ œ
bœ œ
nœ
nœ
œ œ nœ
œ œ nœ
œœ
œ
œ
ritenuto
œ
œ
phrase b
560
b œœ
& b b œœ œœ œœ œ . # œ œœœ
π
œ
? b b œ œ nn œœ bb œœ
b
œ
œœ
œ
œ
V7 i
(PAC)
ww
ww
U
w
w
V7 i
(PAC)
YT: UPptFNwQppA
Figure 13.4.1 Frédéric Chopin, Prelude Op. 28, No. 20, in C minor
13.5 The Double Period
The Double Period. A double period consists of at least 4 phrases and is
comprised of an antecedent group and a consequent group. The first two
phrases in a double period are the antecedent group and the final two phrases
are the consequent group, which ends with a cadence that “answers” the less
conclusive cadence (or “question”) that ended the antecedent group.
The melodic scheme of abab’ (four phrases) is commonly encountered in a
double period. A double period with this melodic scheme would be described as
a “parallel double period” because both the antecedent group and consequent
41
CHAPTER 13. PHRASES IN COMBINATION
133
group begin with the same melody.
42
42
42
42
565
565
565
565
b
& bb b bb bb 422 œœ
& b b b 42 œ
& b b b b 42
& b 4 ppœœ
?
2 pœ
? b bb b bb 42 pœœœœ
? bb b b b A442¯: œœ
? b b b b A42¯: œ
b
œ
T
T
T
T
œ.
œ.
œ.
œ.
œ
œ
œœœ
œœœ
œ
œ
œ
œ
œ
œ
b
& bb b bb bb
& bb b
& bbbb
& b
?
? bb bb b bb
? bbb b
? bbbb
b
œ œœœ .... œœ
œ œœ .. œ
œ œœcresc.
.. œ
œ œœcresc.
œ
œœœcresc.
cresc.
œœœ
œ
œ
œ ..
œœ ..
œœ ..
œœ ..
œœ
œœ
œœœ
œœ
œ
A¯:
A¯:
569
569
569
569
573
573
573
573
577
577
577
577
œ ..
œ ..
œ ..
œ ..
œ
œ
œ
œ
œ
T
bbb œ T
œ.
b
& bb
œœ . œœ
& bb b b b œœ T
& b b b b p T œœ .. œœ
b œ
&
? b b b pp œ œ œ œ œ œ œ œ
? bb bb œ œ œ œ œ œ œ œ
? bbb b p œ œ œ œ œ œ œ œ
? bbbb œ œ œ œ œ œ œ œ
b œ
œ
b
& bb b bb bb
& bb b
& bbbb
& b
?
? bb bb b bb
? bbb b
? bbbb
b
j
œj
œ
j
œj
œ
œ.
œ.
œ.
œ.
œ.
œ.
œœœ ..
œœœ ..
œ.
œ.
œ gg œœœ
œ gg œœ
œ gg œœ
œ ggÍœœ
g͜
ggÍ
œœœ
gggÍ
œœ
gg œœ
gg œœ
phrase a
phrase a
phrase a
j a
phrase
‰
‰
‰
‰
phrase b
phrase b
phrase b
œphrase
œ b
œœ œ œœ œœ œœœ
œœœ œ œ œ œœ
œœ œ œ œ œœ
œ
œœ
œ
œœ
œ
œœ
œ
œœ
œ
œœ
œ
œ
phrase a
phrase a T
a Tn
jphrase
n
phrase
œ
j
nœ œ a T
n
T
n œj
nœ œ n
œ.
œ ..
œ.
j
œ . œ œn œœ œœ
œ .œ œ œ œ œ œ œ
œ
œ œœ œœ œœ œœ œœ œœ œ
œœœ œ
œ
œ .. œ
œ ..
œ .. œœ œjj œœ .... œ
œ .. œ œj œ .. œ
œ .. œ œj
œ
œ
œ
œ
≈ œœ œœ œœ ≈ œ œœ œœ
≈œ œ ≈œ œ
≈œ œ ≈œ œœ
≈
≈œ œ
œœ
œ
œ
œœ
œ
œ
œœ
n œj
n œj
n œj
nœ
œ
œœœ
œœ
œœ
œ
œ
œ
œœ
œ.
œœ .
œœœ ..
œ
œœ .
œ.
œ.
œ.
œ
b œœ .. œœ
b œœ . œ
bœ
œ
œ
œ
œ œ œ œ b œœœ . œœ œœ œœ
œ
œœœœœœœœ
œœœœœœœœ
œ
œ
phrase b'
phrase b'
phrase b'
phrase
œ œ b'
œ.
œ.
nœ œ
n œœ œœœ
œ.
n œ œœ
Sœ .
nœ œ
S
S œ nœ œ œ œ
S≈ œœ .œœ œ n œ œ œ œ
≈ œœJœ .œ œ n œœ œ œ œœ
≈ Jœœ .œ œ n œ œ œ
≈ œJ . œ
J
j
œj
œ
j
œj
œ
T
Tnn œ .
Tn œ . b œ œœ œœ .
Tn œ . b œ
œœœ ..
œ
b
œ
œ . b œ œ œœœ .
œ
œ ...
œ œ œœ
œœ .
œ œ
œœœ ...
œ
œ œ
œ.
œ
œ œ
V
Vœ .
(HC)
j
n œj
n œj
n œj
nœ
‰
‰
‰
‰
(HC)
V
V
(HC)
(HC)
Ÿ
3
Ÿ
œ œŸnœ œ œœ œ œœ œœ œ œœ3 œ
œ œ œŸ œ œ 3
œ œ œ nnœœ œœ œ œ ‰‰œœ œ œ œ œœ
œ œ œ nœ œ œ œ ‰ œ œ œ œ
œ œj
‰
œ j
œ œœœœJj ‰‰
œ Jœœj
‰
œV œœJ
‰
V
(HC)
J
V
(HC)
V
(HC)
(HC)
œ
œœœ
œœ
œœ œœ n œ
œ nœ
œ œ nœ
œ œ nœ
Vœ
V
(HC)
(HC)
V
V
(HC)
(HC)
œ
œ
œ
œ
3
Œ
Œ
Œ
Œœ
œ
œ
œ
œ
œ
œ
œ
œ
œ bbœœ
œ bœ
œ bœ
j
b œœœ œœ œœ œœ œœ œ œ œ œj ‰‰
b œœ œ œœ
œj
œ
bpœœ œ œ œ œ œ œœ œœ œœ œJj ‰
Jœ ‰
bpœ
œ œ œœ
pœ n œ b œ œ œ œ œ œ œ œ œ œ œJjj
Jœ
pœœ n œ b œ œ œ œ œ œ œ
œ j‰‰
œœ n œ b œ œ œœ œ œ œœ œœœ .
œj ‰
œ n œ b œ œ œ œ œ œ œ.
œ‰
.
œ
œ 7 (PAC)
œ
.
V7
I
(PAC)
V
V7
antecedent group
consequent group
antecedent group
consequent group
V7
consequent
group
aantecedent group
b
a
aantecedent group
b
a
consequent
group
a
b HC
a
HC
HC
HC
HC
a
b HC
a
HC
HC
HC
YT: VlfL9LWtCls
HC
HC
HC
Figure 13.5.1 Beethoven, Piano Sonata Op. 10, No. 1, II
(PAC)
(PAC)
b'
b'
b' PAC
b' PAC
PAC
PAC
I
I
I
œœœ
œ
œ n œ œ œ œ œœ n œ b œ œ œœ œ œ œ œ
œ
? b b?
œ
œ
#
b b # #≈ ∑ ≈∑œ ∑ ≈ ∑œJ . œ∑ ∑ ∑ ∑ ∑ œ∑.
CHAPTER 13. PHRASES IN COMBINATION
antecedent group
699
###
a
œ
∑ ‰∑
(PAC)
V7
134
I
consequent group
b
a
b'
&
Figure 13.5.2 Formal diagram of a double period (Beethoven, Op. 10, No. 1,
II) ? # #
∑
∑
∑
∑
∑
∑
#
HC
HC
HC
PAC
A double period will typically have one of the following cadential schemes:
antecedent group
phrase 1
consequent group
phrase 2
phrase 3
phrase 4
Scheme 1:
HC
HC
HC
PAC
Scheme 2:
IAC
IAC
IAC
PAC
Scheme 3:
IAC
HC
IAC
PAC
Figure 13.5.3 Possible cadential schemes in a double period
Notice that the first two phrases of an antecedent group can consist of an
IAC followed by a HC (“Scheme 3” in the above example). This may seem
confusing if you are focused on analyzing phrases solely in groups of two instead
considering how many phrases are in a section before analyzing the cadential
scheme and the form.
13.5.1 Repeated Period
You may encounter a section consisting of four phrases that is not a double
period but instead is a repeated period.
∑
CHAPTER 13. PHRASES IN COMBINATION
135
phrase a
581
# ˙˙
&c ˙
# # œœœ # œœ
# œ
# # # ˙˙˙
& c # ˙˙
# # œœœ # œœ
# # # ˙˙˙
dolce e molto ligato.
E:
585
œœ # # œœœ
n #˙˙˙
#˙
˙
œ #œ
# œœ # œœ
n # # ˙˙˙˙
cresc.
?
# ˙˙
# ˙˙
˙.
# # ˙˙ œ
# ˙˙
w
# # ˙˙
S
&
V
(HC)
phrase a'
# ˙˙ # # œœ œ
œ # # œœ
? ˙
# # # ˙˙˙
p
? # ˙˙ # # # œœœ # œœ
#œ
# n œ˙œ # ˙˙ ..# œ
# ˙˙
˙
cresc.
# # # ˙˙˙
# ˙˙
nw
nw
&
œ #œ #œ œ
#œ
p
œ
Œ
œ
3
œ #œ nœ #œ œ #œ #œ ‹œ
3
3
3
Ó
V7
I
(PAC)
phrase a (with ornamentation)
3
3
3
# œ‹ œ œ œ œ œ œ# œ œ œ
œ
#
œ
œ
œ
#
œ
œ
œ #œ
& ˙
# œ˙# œ œ œ˙œ œ
3
589
3
3
3
dolce
& # ˙˙
# # œœœ
# œœ
?
3
# ## ˙˙˙
# ˙˙
3
œ #œ œ #œ œ #œ˙‹œ œ œ œ œ##œœ#œœ œœ œ œ
œ˙‹œ#œ œ œnœ #œ
œ#œ#œœ
3
3
cresc.
S
œœ # # œœœ
3
#n ˙˙˙
#œ
# ˙
? #œ#œ
& # ˙˙
# # œœœ œ
˙
3
3
3
3
3
#œ œ œ # œ œ œ
#œ #œ œ
# œ˙#œ œ œ˙œ œ œ # œ œ # œ œ œ œ œ œ œ # œJ
f
cresc.
œ
# ˙˙
###˙˙˙
nw
œ
nw
3
& #œ ‹œ œ œ œ œ œ #œ œ œ ?
˙
œ #œ
p
? # ˙˙
# # # œœœ # œœ
3
3
3
3
3
V
(HC)
phrase a' (with ornamentation)
593
3
3
3
3
3
3
3
3
V7
I
(PAC)
repeated parallel period
parallel period
parallel period
a
YT:a' lbblMw6k1cU a
HC Piano Sonata
PAC Op. 53, I HC
Figure 13.5.4 Beethoven,
a'
PAC
Examine the difference between these two formal diagrams, noting the cadence after the second phrase in each:
43
p
? # ˙˙
577
# # # œœœ
# œœ
###˙˙˙
# phrase
˙˙
b'
CHAPTER 13. PHRASES IN COMBINATION
bb
&bb
? bb b
b
j
œ
œ .. œ j œ .. œ
œ
œ.
cresc.
nw
nw
V
(HC)
œ
œ œ œ
n œ œœ b œœ
œ
repeated parallel period
p parallel period
S
parallel period
a'œ œ n œ œ œ œ aœ n œ b œ œ œ œ œ a'œ
œ œ œa
œ
œ
œ
œ
œ
≈
≈ œHC
≈ œ . PAC
œ
HC
J
j
œ
V7
f
œ
œ
136
I (PAC)
j
œ
œ‰
œ œ œœœ œ
J
j
œ
œ
‰
œPAC
.
Figure 13.5.5 Formal diagram of a repeated period (Beethoven,
Op. 53, I)
V7 (PAC)
I
antecedent group
a
consequent group
b
HC
a
HC
b'
HC
PAC
Figure 13.5.6 Formal diagram of a double period (Beethoven, Op. 10, No. 1,
II)
In the next section we will examine phrase combinations that are not periods.
13.6 Phrase Groups and Phrase Chains
Phrase groups and phrase chains are not periods. In phrase groups and phrase
chains, the final cadence is a half cadence. A phrase group consists of at least
two phrases whose melodies begin similarly and has the final phrase ending in
a half cadence. The terminology in this section draws from Douglass Green’s
Form in Tonal Music.
44
CHAPTER 13. PHRASES IN COMBINATION
.
# # 3 œ œ.
& 8
p
#
& # 38 œ œ
. .
597
601
.
.
# # œ œ. œ
&
f
? # # œ. œ. œ.
œ.
œœ
phrase a
œœœœœœ
œ.
œ œ œ œ œ œ œ.
œ.
œœ
137
œ.
œ.
œ3̂ œ œ œ
œ
V
phrase a'
œ œ œ œ
œ œ
œ.
œœ
I
(IAC)
œœ
œ œ œ œ œ œ œ œ œ œ œ œ
‰?
œ.
œ. œ
œ
V
(HC)
YT: oh6ByhUep0s
##
&
Figure 13.6.1 Franéois Couperin, 5 Pièces de Clavecin,
605
4. Le Petit-Rien
(Ordre XIV, 8)
? ##
∑
∑
∑
∑
∑
∑
∑
∑
A phrase chain also ends in a half cadence and consists of at least two
phrases with contrasting melodies.
45
CHAPTER 13. PHRASES IN COMBINATION
605
œ œ
œ
& b 42 ..
? b 42 ..
phrase a
œ
p
œ œ œ œ
138
œ #œ œ œ
# œ. œ.
œ
œ œ œ œ #œ œ œ œ
œ
œ œ œ œ
i
(IAC)
V/3rd
phrase b (is a sentence)
subphrase a
609
œ œ œ œ
&b
?
b
œ œ œ
œ œ œ œ
˙
œ œ œ
œ
œ œ œ œ
phrase b (continued)
œ
œ œ
œ
&b
f
œ œ œ
?b œ
œ œ œ œ
related material
613
œ œ œ œ
˙
crescendo
œ
subphrase a
œ œ œ œ
œ
œ
œœ
dim.
œ œ œ œ
&b
œ
#œ
œ
œ ‰ .
.
J
# œœ
J ‰ ..
V
(HC)
617
?b
YT: O93GspATPzs
Figure 13.6.2 Beethoven, Sonatina in F, Anh. 5 No. 2, II. Rondo
∑
∑
13.7 The Elision
∑
∑
∑
∑
∑
An elision is a special device for joining phrases together in an overlapping
manner. In an elision, the final bar of one phrase is simultaneously the first
bar of the next phrase.
CHAPTER 13. PHRASES IN COMBINATION
46
617
measure
number
in phrase:
#
& c ˙˙
?# c
measure
number
in phrase:
621
&
# ˙
˙
?#
measure
number
in phrase:
625
#
& ˙˙
S
?# œ
˙˙
1
p
1
&
2
œœ œœ œœ œœ
j
œœ
J
. .2 . .
œœ œœ œœ œœ œœ œœ œœ œœ
.. ..
˙
˙
˙
˙
˙˙
∑
j
œ
˙˙
˙˙
∑
j j
œœ œœ œ œ œ œ œj ‰ œœ ‰ œœ ‰ Œ
œ œ œJ J J
j
œ œ œ
j œ œœ
œ œ œ œ œœ ‰ œJ ‰ Œ
J
3
4
3
4/1
Ÿ
elision
. .
œœ œ œœ œœ œ œ œ œ ˙
œœœœœœ
œ œ œ ˙˙
œœ œ œ œ œ œ
p
S
œ œ œœ œ œ œœœœœ œ œ œ
œ œ œ œ
3
Ÿ
œœœœ
œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œ œ œ œ
cresc.
p
œ œ œ œ œ œ œ
œœœœœ œœ œ œ œ œ œ œ œ œ
2
1
628
j
œœ
J
139
2
#
3
4
1
2
3
4/1
2
3
œœœœ
œœœœ
4
œ œ
œ œ
4
YT: TpPuLwtDQrY
Figure 13.7.1 Mozart, Eine kleine Nachtmusik, K. 525, I.
?#
∑
∑
∑
∑
CHAPTER 13. PHRASES IN COMBINATION
140
13.8 Summary of Phrases in Combination
Table 13.8.1
Number of Phrases
2 phrases
3 phrases
Form
Parallel Period
Melodic Scheme
a a’
Contrasting Period
ab
Phrase Group
Phrase Chain
Repeated Phrase
Asymmetrical period
a
a
a
a
a
a
a
a
a
a
a
a
a
a
Phrase group
4 phrases
Phrase Chain
Double Period
Repeated period
a’
b
a
a b or
bb
a b or
bb
bc
b a b’ or
a’ a a" or
a’ a b
b a b or
b a c or
a’ a a’
Cadence Info
Less conclusive then
more conclusive
Less conclusive then
more conclusive
Ends with HC
Ends with HC
Same cadence twice
Ends with most
conclusive
Ends with HC
Ends with HC
HC–HC–HC–AC or
IAC–IAC–IAC–PAC or
IAC–HC–IAC–PAC
Less conclusive then
more conclusive
formula repeated
13.9 Practice Exercises
For the each excerpt below, do the following:
• Label chords with Roman numerals at the ends of phrases to determine
cadences
• Label cadences by type (PAC, IAC, HC, PC, DC)
• Examine the motivic structure to determine if a phrase is a sentence
• Create a diagram of the form using cadence abbreviations (HC, DC, PC,
IAC, and PAC) and letters to designate melody (a, a’, b, etc.). Use the
“prime” symbol (’) to show if a melody ends with a different cadence. In
this chapter, the prime symbol should not be used to represent embellishment of the melody or changes in the harmonization or register.
• Name the form of the excerpt (sentence, parallel period, contrasting period, asymmetrical period, parallel double period, repeated phrase, repeated period).
1.
Mozart, “Ein Mädchen oder Weibchen,”The Magic Flute.
CHAPTER 13. PHRASES IN COMBINATION
48
48
&
& bb
648
648
j
œœj
‰‰
4422
? b 422 ‰‰
?
b 4
F:
F:
œœ œœ
&
& bb œœœœœ ‰‰
JJ
?
? b œœjj ‰‰
b
653
653
œœ .. œœ œœ .. œœ œœ œœ œœ œœ œœ .. œœ œœ .. œœ œœ ‰‰
œœœ œœ
œœœ
œœœ
Œ
œœ ‰‰ œœ ‰‰
œ
Œ
œ ŒŒ
JJ JJ
œœ ‰‰ œœJ ‰‰
œœ
œœ ŒŒ
ŒŒ
JJ J
œœ œœ
œœœ
œJ ‰‰
J
j
‰‰ œœj ‰‰
œœ
œœ
œœ
JJ
œœJ
J
141
œœ
‰‰
____
____
____
____
œœ .. œœ œœ œ œ . œ œœ .. œ œ œ
œ œ . œ œ œ œ œœ . œœ œœ .. œœ
œœ
œœ ‰ œœ . ‰
œœ
ŒŒ
œœ ‰ œœ ‰
œ
JJ
JJ
jj ‰ jj ‰
Œ
Œ
œ
œ ‰ œœ ‰
œœ
j
œœ œœ œœj ‰‰
œœ Œ
œœ Œ
3
3
œœ œœ
œœœœ ‰‰
JJ
j
œœj ‰‰
j
œœj
____
____
ŒŒ
œœ
____
____
47
47
47
47
YT: CI0hJLioGF0
Figure 13.9.1
632
632
632
632
636
636
636
636
640
640
640
640
644
644
644
644
2.
Mozart,
Piano Sonata K. 333, jI.
bb
&
œœ œœ .. œjj œœ œœ
& bb bb cc œ . œœ œ œ
&
&
?
?
?
?
&
&
&
&
?
?
?
?
&
&
&
&
?
?
?
?
bb cc œœ ..
œœ ..
bb b cc œœ˙œœ ....
bb bb cc ˙˙œ .
˙˙
b
˙˙
B
B¯¯::
œœ œœœ œœ
œ
œœ ..
œœ ..
nn œœ œœ œœ
nn œœ œœ œ
œ
œ
œœ œœœ œœœ
œœ œ
œœ
œœ
œœ œœ œœ
œœ œœ œ
œ
œœ...
œœ.
bb bbb
bb b
bb bbb
bb b
bb bbb
bb b
j
## œœjj
# œj
#œ
œœœ ...
œœ ...
œœ ..
‰‰
‰‰ œœ
œœ
œœ
bb bbb œœ œœ
bbb œœ
bb bbb
&
&
bb
&
&b
?
?
?
?
B
B¯¯::
bb bbb
bb b
ÓÓ
ÓÓ
ÓÓ
ÓÓ
.
œœœ...
œ
œœ.
œœ..
.
œœ.
œœ..
.
œœ
œœ
ŒŒ
ŒŒ
œœ
œœ
œœ...
œœ.
œœ œœ œœ ..
œœ œœ ..
ŒŒ ˙˙˙
ŒŒ ˙˙
˙˙
œœ.
œœ..
.
jj
œœj
œj
œ
œœ ..
œœ ..
‰‰
‰‰ œœ
œœ
œœ œœ œœ
œœ œœ œ
œ
œ
œ
œœ œœ œœœ
œœ œ
œ œ.
œœ œœœ œœœ ...
œœ
˙˙
ŒŒ ˙˙˙˙
ŒŒ ˙
œ
œœ .. œœœ nnn œœœ œœœ œœœœ œœœ œœœœ œœœ œœœœ bbb œœœ œœœ
œ
œ bœ œ
œœ .. œ n œ
œœ œœ... œœ..
œœ œœ
œœ .
œ
‰‰ œœ œ œ. œœ. œœœ... œœ œœ
‰‰ œ
œ.
aa
aa
œ
œœj œœ œœ œJœJœ
JJ
œ
n
œœ
nn œœœœ
œœ
nœ
œœ
JJœœ
JJ
œœ
œœ
œœ
œœ
œœ
œœ
jj j jj
œœ œœœ œœœjj œœœ œœjjj œœœjj œœœ œœjjjj
œœ œ œ œ œœ œ œ œœ
ŒŒ œœ œ œœ
ŒŒ œœ œœ œ œœ
œ œ œœ
____
œœ œœœ
œœ œ
œœ
œœ
œœ
œœ
jœ
œœjjj œJœJœ
œœ JJ
œœœ
œœ
&
&
&
&
œœ
œœ
j
œœjjj
œœ
œœ
œœ
œœ
œœ
ŸŸ
ŸŸ
bb œœ ..
bb œœ ..
œœ
œœ
œœ œœœ œœœ
œœ œ œ
ŒŒ
ŒŒ
____
____ ____
____
____
____ ____
____
œ n œ œ ŒŒ
œœ œœœ nnn œœœ œœœ ### œœœ œœœ œœœ nnn œœœ œœœ ŒŒ
œœ œ n œ œ # œ œ
œœ œœœ œœ œœ œœ œœ œ œœ
ŒŒ
œœ œ œœ œœ œ œœ œœ œ
ŒŒ
œœ
œ œœ
œœ
____
____ ____
____
____ ____
____
œœ
œ œ
œ
œœ œœ œœ œœœ œœœ œœ œœ œœœ œœœ nnn œœœ bbb œœœ œœ œœ œœœ œœœ
œ
œ
œ n œ b œ œœ œœ œ œ
œœ œ
œœ œ
nn œœœ
nn œœ
œœ
œœ
œœœ
œœ
œœ
œœ
œœœ
œœ
œœœ
œœ
____
____
____
____
œœ œœœ œœ œœ œœ œœ œ œœ œ œ œœ œœ œœ œœœ œœ œœœ œœœ œœœ œœ œœ œœ œœ œœ œ œ ŸŸ œ
œœ œ œœ œœ œ œœ œœ œ œœ œœ œ œœ œœ œ œœ œ œ œ œœ œœ œœ œœ œ œœ œœ œŸœŸ.. œœ œœ
œ œœœœœ
œ œ œ œœ .. œ œœ
œœ
œœ
œœ œœ œœ œ œœ
œœ œœ
œœ
œœ œœ œ œœ œœ œœ
œœ
œœ
œ œ
œœ
œœ
IAC
IAC in
in B
B¯¯
IAC in B¯
œœ œœœ œœ
œœ œ œœ
œœ
œœ
____
____
____
____
œœ
œœ
____
____
____
____
œœ
œœ
ŒŒ
ŒŒ
ŒŒ
ŒŒ
œ
œœ œœœœ nnn œœœ œœœœ œœœ œœœœ œœœ œœœœ
œ
œœ n œ
____
____
____
____
CHAPTER 13. PHRASES IN COMBINATION
142
YT: PmO3Wlono6w
217
217
217
Figure 13.9.2
3.
250
250
250
338
388
.. œ œ . œœœ œœœ ...
.. œ œœ ..
ppœ dolce
grazioso
grazioso
p dolce
dolce
graziosoœ
œ
œ
œ
œ
œœœ
.. œœœœœ œœœœœ
.. œœ
œœ œœœ
œ
œ
œœ œœ ..
œ œ.
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Click here
? to download the first homework assignment for this chapter.
Click here to download the second homework assignment for this chapter.
Click here to download the Unit 3 Practice Test.
PDF versions of the textbook, homework exercises, and practice exercises
can be found at musictheory.pugetsound.edu
Chapter 14
Accompanimental Textures
In this chapter we will focus on common accompanimental textures. This
chapter does not make an attempt to catalog every known accompanimental
texture. Instead, it is meant to encourage you to listen to texture more closely
and increase your musical awareness.
14.1 Texture
We will consider texture in terms of vertical and horizontal elements. The
vertical nature of texture relates to the number of notes occurring simultaneously as harmonies. It could also relate to the number of voices or instruments
performing melodies simultaneously in a contrapuntal texture. The horizontal
element of texture relates to rhythmic activity: is the most common rhythmic
value in a passage a slow or fast one?
To illustrate, here is a texture with chords (vertical elements) containing
five voices with a melody (a sixth voice) above. Notice that the texture has
slow rhythmic values on the horizontal plane.
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Figure
14.1.1 Samuel Barber, Adagio for Strings (1936)
707
Our second example is an excerpt for four instruments—a string quartet.
While this a four-voice texture, it is full of rhythmic activity. The most common
rhythmic value is the sixteenth note, and the syncopated figures in measures
3–4 of the Violin I part and measures 5–6 of the Viola part add to the textural
complexity.
? # # # 68 ∑
∑
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∑
∑
143
∑
∑
∑
∑
∑
51
CHAPTER 14. ACCOMPANIMENTAL TEXTURES
Violin I
Violin II
Viola
Cello
5
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Vln. II
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b
&Inb bthe ∑following∑
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∑
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and-accompaniment textures in classical and popular music. In later chapters
we will explore more complex textures.
B bbb ∑
∑
∑
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14.2 Chorale Texture
∑
∑
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∑
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∑
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∑ (or nearly
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melody
A familiar example of chorale texture is the “Star-Spangled
Banner.”
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7
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172
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CHAPTER 14.œ ACCOMPANIMENTAL
145
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Chorale textures are also described as “homorhythmic” because all of the
parts move in the same rhythm.
12
& 44 œœ
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12
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Figure 14.2.3 Jeff Bhasker, Nate Ruess, Andrew Dost, Jack Antonoff, “Some
Nights” (2011)
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CHAPTER 14. ∑ACCOMPANIMENTAL
TEXTURES
146
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One way to express chords rhythmically is through arpeggios in one part
and a bass line in octaves in a lower part, as in the following example from
Beethoven’s Moonlight Sonata.
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(1802)
54
The next example has descending arpeggios.
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CHAPTER 14. ACCOMPANIMENTAL TEXTURES
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147
The following examples have arpeggios that ascend and descend through a
chord.
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Notice in the above example that there is also an organ playing block chords
to create a sense of legato in the texture.
The next two examples are from more recent popular music.
# œ (œ)œ œ
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CHAPTER 14. ACCOMPANIMENTAL TEXTURES
148
Í
Motives:
401
A
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Figure 14.3.7 Kevin Briggs, Kandi Burress, Tameka Cottle, Lisa Lopes, “No
Scrubs” (1999)
CHAPTER 14. ACCOMPANIMENTAL TEXTURES
10
149
14.3.2 Alberti Bass
Score
Alberti bass accompaniment patterns involve arpeggios that do not arpeggiate
Piano Sonata
K. 545, upward
I
Amadeus Mozart
chords
in a simple
or downward motion, but in aWolfgang
“low–high–middle–high”
( )
_____
_____
_____
_____
_____
_____
_____
pattern as you can see in the examples
below.
( )
145
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mot.7 1 (dim.)
Ó. bœ œ œ œ
ƒ 4
Cadence type: _______________
Figure 14.3.8 Mozart, Piano Sonata K. 545, I (1788)
(Timpani)
The
nextOp.
example
example
Piano
Sonata,
10, No. 1,uses
II the same Alberti pattern as in the Mozart Beethoven
above, but transposed
_____ register.
_____
_____to E minor
_____ and in a lower
_____
8
149
8
8
?#
12
12
&
#
?#
12
∑
∑
∑
∑
∑
∑
_____
j
Elec. Gtr.
j
b
.
?
& #b b b4 42 œœ ∑ (œœ .) œ œœ .œ œ ( n œœ) œ œœœ œ œ œ œ(œœœ) b œœ œ œ œœœ.. œ œ (œn œ )
4
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p
Keyboard
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#
.
œ
œ
4
œ
?
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œ.
‰ w
‰
& b b b b4 4 w œœ
.
w
w
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w
w
w
w
g w_____ _____ ggg ww_____
ggg _____
ggg ww _____
ww
Agg¯:w
_____
2
1
3
4
6
5
? # 44 œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ
œ œ_____
œ _____
_____
œ œ _____
œ œ _____
œ œ_____œ œ œ__________
œ œ œ œ
Elec. Bass
3
Ÿ
œ
œ
œ
..
bb
œ .. œ œ œ œ( )(œ )œ œœ œœ œ . œ œnœœ œ œ œ œ œ œ œ
& b b œœ .. œ œœ œ œœ ggg œ œ
œ œ œ
∑
∑
∑
∑ YT:
∑
∑
∑
∑ ‰ ∑
Í∑ L6zR7qJ9frA
don't include
cresc.
œœ œœ
œ œœ“Pipeline”
j these
œœ and
.
œ
œ
notes in
g
Figure 14.3.9
Brian
Carman
Bob
Spickard,
(1962)
œ
œ
œ
œ
œ
gg œ œ
œ
œœ your‰analysis
? bb b
œ
œ
œ
b
∑
∑
∑
∑
∑
∑
∑
∑ J ∑
∑
Elec. Gtr.
153
T
T
__________ _____
_____ _____
_____ _____
14.4 Block
Chord
Accompaniments
7
10
12
13
8
9
11
∑
∑
∑
∑
∑
∑
∑
This section contains the following subsections below:
• The “1 (2) &” rhythm
• The “Barbara Ann” Rhythm
• Repeated 8th-note Chords
• Repeated Quarter-note Chords
_____
14
Cadence type: _______________
∑
∑
∑
12
& b 8 14. ACCOMPANIMENTAL
CHAPTER
œ œ œ œ œ œ œ œ TEXTURES
œ œ œ œ œ œ œ œ 150
œ
œ
œ
œ
œ
œ
œ
œ
14.4.1 The “1 (2) &” Rhythm
? 12
In thisb section,
we will discuss some accompanimental rhythms that occur
8
frequently in popular music. The firstœsuch
rhythm has two chords per measure,
œ.
. on the upbeat
œ . after
. on beat œ1 .and the. second˙chord
with the first˙chord
beat
Fmaj7
752
Am
2.
E¯
b
& b b c œœœ ...
754
756
? bb c
b œ.
# c D
&
œœ ..
œ.
j
œœ ˙˙
œ ˙
Gm7
j
œœ ˙˙
œ ˙
A¯
B¯
œœ ..
œ.
j
j
Em
C
D
D
Em
œ
˙
.
œ
j œ ˙ j
j
œœ ˙˙
ww
œœ .. œœœ ˙˙˙
œœ .. œœœ ˙˙˙
œ ˙
w
œ.
œ.
j
j
YT: x6QZn9xiuOE
? # c œ . œj ˙
œ
.
œ
˙
œ
œ
. Ed Townsend, “Let’s Get˙ It On”w(1973)
Figure 14.4.1 Marvin
Gaye
and
w
œ. œ ˙
œ. œ ˙
œ. œ ˙
You will find a similar rhythm and bass line in the next example.
760
&
##
c
? ## c
D
œœ ..
œ.
œ.
D/F˜
G
j
œœ ˙˙
j
œœœ ˙˙˙
œœœ ..
.
j
œ ˙
#
& #
G/A
j
œ ˙
œ.
762
YT: fdz_cabS9BU
Figure 14.4.2 Ed Sheeran, “Thinking Out Loud” (2014)
? ##
∑
∑
∑
∑
∑
The “1 (2) &” rhythm is also found in “Don’t You (Forget About Me),” a
song associated with the film The Breakfast Club.
55
CHAPTER 14. ACCOMPANIMENTAL TEXTURES
#
& c
756
D5
œœ ..
? # c œ.
œœ .
.
760
##
C5
j
œœ .. œœ ˙˙
j
œœ .. œœ ˙˙
œ. œ ˙
D5
D5
j
œœ .. œœ ˙˙
j
œœ .. œœ ˙˙
œ. œ ˙
˙˙
˙˙
˙
D/F˜
D
E5
G
ww
ww
w
G/A
j YT: CdqoNKCCt7A
j
œ
œ
˙
œ
œ
˙˙˙ About Me)”
.
.
œœ .. You œœ(Forget
Figure 14.4.3
œœ .. Keith Forsey
œ and
˙ Steve Schiff, “Don’t
Score (1985)
?Below
# # care five more examples
of block chord accompaniment in the “1 (2)
j
j
&” rhythm.
œ ˙
œ.
œ ˙
œ.
Voice
&
c
j
œœ
j
œœ
œ
E5
151
bb 4
&bbb 4 œ
762
##
&b
œœ ˙
b 4 œœœ œœœ œœœ œœœ œœœ ˙˙˙
b
b
& b 4
Keyboard
Nev
-
? b# #b 4 œœ∑..
?
b b b 4 œ.
œœ ˙˙∑
œ ˙
J
Elec. Gtr.
? b b b 44
bb
Elec. Bass.
4
b
& b bbb
∑
er
j
œ ˙
œ.
∑
∑
œ
œ
œœ ˙
œœ œœ œœ œœ œœ ˙˙
œœ œ œœ ˙
nev
œœ ..
œ.
-
œœ ˙
œœ œœ œœ œœ œœ ˙˙
œœ œ œœ ˙
er
nev
∑ œœœ ˙˙˙
∑œœœ ..
j
œ ˙
∑
∑
YT: zWzy5q_M5Ho
er
œœ ∑ ˙˙
œ ˙
J
.
J
œ.
-
j
œ ˙
œ.
∑
∑
∑
Figure 14.4.4 Holly Knight, Gene Bloch, Ann Wilson, and Nancy Wilson,
bb
b “Never”
∑(1985) ∑
∑
∑
∑
∑
∑
∑
& bb
? bb
bbb
? bb b
bb
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
©
55
CHAPTER 14. ACCOMPANIMENTAL TEXTURES
4
D5
& b# 444 œ . œ
& 4 œ.
? 4 œ. .
b 4 œ œ
Keyboard 1
756
Œ ‰ j . C5 œ
œ œœ œ
œœ ˙˙
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j
Œ
‰
œ œ œ œ.œ œ œ
œ œj
E5
j
? Keyboard
# 44 œ . 2 œœ ˙˙
>œ . >
? 4 œœœœ . ‰ œœœœ Ó ˙
b 4
756
760
? b# 44
>œ
œœ
J
152
D5 E5
œjœ œ œ . œ . œ œ œ Œj‰ œj œ . œ
œœ ˙˙
œœ .. œœ ˙˙
œ œ œ œ . œ . œ œ œ Œ ‰ œj œ . œ
D5
œœ œœ œœ.
ww
œœ œœ œœ.
j
j
œœ ˙˙ > œœ .. > œœ ˙˙ > ww>œ
œÓ ˙ œœœ œ .‰ œœœ œÓ ˙ œœœ ‰wœœ Ó
J
J
J
œœ .. >œ
œ .‰ œœ
55
55
‰ jÓ
‰ jÓ
D ‰ j Ó D/F˜
G ‰ j Ó G/A
4
j
j
#
j
œ
& # 444>œœ . œ>œ ˙ j >œ . > œ ˙ >œ œ . >œ œ j˙ >œ >wœ
&
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œ.
œ ˙
œ.
j
j
j
? ## 444 œ . œœ ˙˙
ww
œœ ˙˙
œœ .. œœ ˙˙
?
.. iP6XpLQM2Cs
# 4 œœ .. œ ˙ j œœœYT:
j
œ
˙
˙
œ . Benny Blanco, w“Tik Tok”
. œ Gottwald,
œ ˙ Lukasz
œ . Kesha Sebert,
Figure 14.4.5
œ ˙
œ.
D5
E5
C5
D5
D5
E5
(2009)
760
762
A¯13sus
# # 4 E¯m9
j
b
b
4
j
& b b b4 4œ . ‰ Óœ ˙ ‰ j Ó
&
œœ .. œœœ œœœ œ ˙œœœ œœœ
œ œ
œ œ©
? ## 4 4
j
?
j
b b b b b4 4œ . œ ‰ œj Óœ ˙œ ‰ œ Ó
D/F˜
D
D¯: (ii
E¯m9
bb bb bbb b 44 œ ‰ œj Ó
&
& b b œœœ œœœ
762
766
V
A¯13sus
G
Fm7
œœœœ..
œœ.
G/A
‰ œj Ó œœj
œœ œ
j
œœœ˙˙˙œ ‰ œœœœ Ó
B¯9sus
‰ j Ó j œ ‰ œj Ó
œœ. œ œ ˙
iii
Fm7
‰ œj Ó
œœ ‰ œjœ Ó
œ
œœ œœ
œœ PMivT7MJ41M
œœ
YT:
vi)
B¯9sus
j
œœœœ ‰ œœœœ Ó
? b b 4 ‰ jÓ
‰ œj Ó ∑
‰ jÓ
‰ œj Ó
?
bb b bb b 4 œ œ
œ
œ
œ œ
bb
Notice that the example above (“That’s What I Like”) has the same pro-
Figure 14.4.6 Bruno Mars, Philip Lawrence, Christopher Brown, James Fauntleroy,
Johnathan Yip, Ray Romulus, Jeremy Reeves, Ray McCullough II, “That’s
What I Like” (2017)
(ii
V Wind, and Fire.
iii
gression as D¯:
“September”
by Earth,
766
b
& b 44 œ . œj
œœ .. œœ
j
? b b 44
œ
.
œ
Gm B¯
B¯: vi
I
˙˙
˙
˙
E¯
œœ ..
œ.
œ.
IV
j
œœ
œ
j
œ
B¯
I
˙˙
˙
˙
j
œœ
œ
j
œ
Gm B¯
œœœ ..
.
œ.
vi
I
vi)
˙˙
˙
˙
j
œœ
œ
j
œ
œ.
E¯
œœ ..
œ.
IV
B¯
I
˙˙
˙
˙
YT: RgKAFK5djSk
Figure 14.4.7 Charlie Puth, Cameron Thomaz, Andrew Cedar, Justin Franks,
Dann Hume, Josh Hardy, and Phoebe Cockburn, “See You Again” (2015)
CHAPTER
14. ACCOMPANIMENTAL TEXTURES
2
8
153
(notated at pitch in grand staff)
bb 4Ac.‰Gtr.
r‰ j
r
r
.
& 4 œœ œ ˙ ‰ . œ ‰ œj ˙ ‰ . œ ‰ œj ˙ ‰≈ œr‰ œj œ œ œ .
œ ˙ œ œ ˙ œ œ ˙ œ œ œœ
? b b 44 œœ .. œj ˙
j
œ . œ ˙ œ . œj ˙ œ . œJ ˙
b 4 Organ
b
& 4 ww
ww
ww
w
ww
w
w
? b b 44 w
w
w
w
B¯: I
&b
12
b
V
∑
vi
IV
∑
∑
YT: 0yW7w8F2TVA
∑
Figure 14.4.8 James Arthur, Neil Ormandy, Steve Solomon, “Say You Won’t
Let Go” (2016)
?Theb b example∑below has the “1∑(2) &” rhythm in∑ dimininution. ∑
56
770
equivalent to:
#### 4
j
j
Œ
Œ
& b 4 œ. œ œ. œ œ. œ Œ Ó C œ. œ Ó œ. œ Ó
∑
∑
∑
&b
? #### 4 œ Œ œ Œ œ Œ Ó
4
?
bb
∑
C ˙
∑
Ó
∑
˙
Ó
j
œ .∑ œ Ó
˙
Ó
∑
YT: oyEuk8j8imI
#### 4
& 14.4.9
4 Justin Bieber, Benny Blanco, and Ed Sheeran, “Love Yourself”
Figure
775
(2015)
#
? # # The
# 44 “Barbara
∑ ∑ Ann”
∑ ∑ Rhythm
∑ ∑
14.4.2
∑
∑
∑
∑
It is easier to describe the next block chord accompaniment pattern as the
“Barbara Ann” rhytm than the “1 2 3 (4) & (1) & (2) & 3” rhythm. Below
are six examples of pieces that use this rhythm, whether with block chords or
785 in the bass line.
solely
&
####
? ####
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
##
& ##
791
? ####
F TEXTURES
A
CHAPTER 14. ACCOMPANIMENTAL
b b D4
∑
∑
& b b bb 4
? # # 44 œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ
? b b b œ4 œ œŒ œ . œÓ œ œ œ ˙
bbb 4
J J J
411
Bm
Baa, baa, baa, baa,
154
j j j
œœ œœ œœ .. œœ œœ œœ œœ ˙˙
œ œ
œ œ
œBaa,œ baa,œ baa,œ œbaa,œ œ œBar -œbar' œAnnœ œ
œœœ œœ Œœœ .. œœ Óœœ œœ œœ ˙˙
J J J
F˜m/C˜
Bar - bar' Ann, G Baa, baa, baa, baa,
Bar - bar' Ann
5
?
# #b bœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ
∑
∑
& b b œb b
Œ ∑ Ó YT: -bSnI-a0BSc
η
Ó
œ
Figure 14.4.10 Fred Fassert, “Barbara Ann” (1961)
413
??bb b b44b b b
415
9
b
& b bbbb
∑
∑
∑ ‰ ‰ ∑
j ‰ j‰ j
j j j
œ œ œ. œ œ œ œ œ œ œ œ. œ œ œ œ œ œ œ
∑
∑
∑
YT: w6MQrdfj638
∑
∑
∑
? bb b b ∑
∑
∑
∑
∑
∑
bb
? ## #
j Œ‰ j ‰ equivalent
jÓ Cto: j Ó
j ‰j Ó j ‰ j j Ó
## # 4
Œ
Œ
.
.
œ. œ
15&
œ. œ
œ 4 œœ œœ œœ. œ œœ . œ œ œ œ œ
bb b b . b . ∑. . .∑ œ. ∑ œ. œ. ∑ œ . œ. ∑ œ. œ. œ ∑ œ
& b
423
?? #### # # 44 œ Œ œ Œ œ Œ Ó C ˙ Ó ˙ Ó ˙ Ó
YT: yRYFKcMa_Ek
? bbb ∑
∑
∑
∑
∑
∑
b b14.4.12
Figure
Sara Allen, Daryl Hall, and John Oates, “Maneater” (1982)
b
Figure 14.4.11 Brian Holland, Lamont Dozier, Eddie Holland, “You Can’t
23
Hurry Love” (1966)
419
56
770
? # #b b 4
& 4 œ œ œ.
œœ œœ œœ ..
? b b 44
437
? ##
œ œ œ.
431
775
‰ œj ‰ œj ˙
œœ œœ ˙˙
j ‰ j‰ j
œ œ œ ˙
B¯
B¯: I
b
?&# #
779
443
E¯
j
œœ
œ
F
E¯
IV
V
IV
b
j
œœ œœ œœ .. œœ
œ œ œ. œ
‰ œj ‰ œj ˙
œœ œœ ˙˙
‰ ‰
œ œ œ . œj œj œj ˙
YT: iPUmE-tne5U
Figure 14.4.13 Kimberley Rew, “Walking On Sunshine” (1985)
? bb ∑
? ##
449
bb
&
455
? ##
? b
791
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
? b 4
b 4
j ‰ j‰ j
œ
œ œ ˙
œ œ œ.
j ‰ j‰ j
œ œ œ. œ œ œ ˙
CHAPTER
TEXTURES
B¯:14.
I ACCOMPANIMENTAL
IV
V
A
œœ
4
#
#
V #4# # œœœc
&
œ.
Elec. Bass
? 44
? #### c
œ.
Elec. Gtr.
56
779
770
œœ œœ ..
œœ œœ ..
œœœ . œœœŒ..
.
C
j j j
.
œœ œœ œœ œœ œœ œœ œœ œœœ
œœ ‰ # œœ ‰ equivalent
œ œ œ œ œto: œ
œœœ. œ Œ œœ . œœœŒ œœœÓ œœœ œœœCœœœ œ œœ.
.
.œ œ -
‰ ‰
œ Œ œ j Œ œj Œj Ó
œ. œ . œ.
œ. œ- œ
œœ. œœ ..
œœ œœ ..
œj œ .
œœ Ó œ .
C ˙
Ó
œ œ. œ. œ .
IV
œœ. œœ. œœ- œœ œœ œœ œœ
œœ ‰ œœ ‰ œœ œœ œœ œœ œœ
œ jœ œ œ œ œ œ
œœ. œ œÓ œ œ .œ œœj Óœ œ
J J J
‰ j‰ j
Ó ˙
Ӝ
. œ. œ- œ
˙œj
23
783
V bb c
j ‰ YT:
j ‰ tuK6n2Lkza0
j
j ‰ j‰ j
?&# # 14.4.14
œœ œœ œœ“Are
.. jœœYou
œ
œ
œœ ˙˙ Muncey,
œœ‰ jœœ Be
˙ My
Figure
Nic
Cester
and
œœ œœ œœ ..j œœ‰ j ‰œœ jCameron
œ œ œ . œ ‰ jGonna
œ ˙
œ œ ˙˙
Girl” (2003) œ œ œ .
œ œ œ . œ. œ. œ. œ œ œ. œ. œ . œ. œ. œ. œ œ
?
∑b .c ∑.version
∑ of∑ this
∑j ‰ ∑joccurs
∑ in∑ Deep
∑ Purple’s
∑ j ∑‰“Smoke
?A slower
j∑ ‰rhythm
j∑‰ j∑ on ∑the
b
Water.”
œ
œ
œ
. œ œ œ ˙
œ . œ œ. . œ œ bœœ ˙
.
œ
˙
œ.
? b b 44B¯:œœ. I œœ œ . œœIV ‰ œœ ‰ b œJ ˙ Vœœ. œœ œ . IVœœ ‰ œœ .. ˙˙
J
J J
A
C
j j j
. .
. . Elec. Gtr.
œœ œœ œœ .. œœ œœ œœ œœ œœ œœ œœ œœœ œœœ œœœ ... œœœ œœœ œœœ œœœ œœœ œœœ œœœ
427
c # œ œ œ . œ ‰ # œ ‰ œœœ œœœ œœœ œœœ œœœ œœ œœ œœ .. œœ ‰ œœ ‰ œœ œœ œœ œœ œœ
?Vb b œœœ œœœ œœœ ... œœœ œœœ YT:
œ- œ_zO6lWfvM0g
œ œ œ œ œ œ . œJ œJ œJ œ œ œ œ
.
.
.
.
Figure 14.4.15 Ritchie Blackmore, Ian Gillan, Roger Glover, Jon Lord, and
Elec. Bass
Ian?
Paice, “Smoke on the Water” (1973)
c
j ‰ j‰ j
j ‰ j‰ j
437
œ œ. œ. œ . œ. œ. œ- œ œ
œ. œ. œ . œ. 8th-note
œ. œ- œChords
14.4.3
? b Repeated
b
B¯
775
419
423
779
E¯
F
E¯
Repeated 8th-note chords occur regularly in “classical” music textures.
783
155
&c
? bb
443
?c
? b
b
r
#œ
œ œ .œ œ œ . r
œ œ #œ
f
œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ
˙
œ . œ œ œ .œ œ œ œ œ œ œ œ
œœœœ œœœœ œœœœ œœœœ œœœœ œœœœ œœœœ œœœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ
r
œ
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Figure 14.4.16 W.A. Mozart, Piano Sonata K. 310, I (1778)
? bb
œ. œ
œœœœ œœœœ œœœœ œœœœ œœœœ œœœœ œœœœ œœœœ
449
455
˙
19
CHAPTER 14. ACCOMPANIMENTAL TEXTURES
177
177
177
177
180
180
180
180
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&b
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2 Œ
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184
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19
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œ œœœ.
œœ œ
œœ π.
œ ∑œœ.
œ
œ
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œœ
œ.
œ.
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∑.
Figure 14.4.17 Franz Schubert, Winterreise, D. 911“Gute Nacht” (1828)
184
184
184
b ∑
&
&c Ó
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∑F ∑
‰ œj
∑ ∑
& cb œœ œœ œœ œœ œœ œœ
>œ œ œ œ >œ œ
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∑
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∑
Ich grol- le nicht,
˙
˙
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∑
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‰ œ œ œ b˙.
und wenn das
Herz
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∑
œœ ˙
auch bricht.
∑
Ó
∑
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œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœœ œœœ œœœ œœœ œœ œœ œœ œœ œœ œœ œœ œœ
œ œ œ œ œ œ >œ œ œ œ b >œ œ œ œ >œ œ œ œ >œ œ œ œ # >œ œ œ œ
>
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Figure 14.4.18 Robert Schumann, Dichterliebe, “Ich grolle nicht” (1844)
The next example is from the musical Annie. Note the “1 (2) &” rhythm
in the bass line.
20
CHAPTER 14. ACCOMPANIMENTAL TEXTURES
b
& b œ.œ œ œ
188
It's a hard - knock
b
&b ‰
188
Œ
? b ‰
b
&b
191
b
for us,
œœœ œœœ œœœ
. . .
j
œ‰‰
œ
>
Œ
∑
j
œ ‰ œ œ ‰ œ. œ œ œ.
j‰ œ ‰ œ . œ œ œ
œ œ
life
∑
It's a hard - knock
œœœ œœœ œœœ
. . .
j
œÓ
œ
>
œœœ
.
life
∑
for us
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157
∑
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. .
j
œ Ó
œ
>
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.
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.
∑
œœœ
.
∑
Figure 14.4.19 Charles Strouse and Martin Charnin, Annie, “It’s the Hard
191
Knock
Life” (1977)
bb
∑eighth notes∑ are a standard
∑ accompanimental
∑
∑texture in rock.
∑
&Repeated
? b b c ∑œœ œœ œœ œœ œœ œœ∑œœ œœ œœ œœ œœ ∑œœ œœ œœ œœ œœ œœ∑œœ œœ œœ œœ œœ œœ∑œœ œ œ œ œ∑ œœ œœ
bb
œœœœ
F5
787
787
791
E¯5
D¯5
B¯5
C5 E¯5
? bb c
bb
œœœœœœœœ œœœœœœœœ œœœœœœœœ œ œ œ œ œ œ
F5
E¯5
D¯5
B¯5
C5 E¯5
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
? b b 4 œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œœ œœ œœ œœ œœ œœ œœ œœ œ œ œ œ œœ œœ
4
œœœœ
791 b b
? bb b
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b
Figure 14.4.20 Geoff Gill and Cliff Wade, “Heartbreaker” (1979)
? b b b 44
The brepeated eighth-note rhythm is also common in recent popular music.
œ œ œ œ œexample
œ œ œ œ œ œ œtheœ œ1950’s
œ œ œ œ œ œ œ œ œ(i.e.,
œ
Note
? that
bb b b the∑ following
∑ ∑ ∑ ∑ uses
∑ ∑ ∑ ∑ progression
∑ ∑ ∑ œ ∑œI –œ∑viœ –œIV
∑œ – ∑V ).
F
Am/E Dm7
œ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ
Piano œ
œœœœœœœœ œœœœœœœœ œœœœœœœœ œœœœœœœœ
4
b
& 4
? b 44
œœœœœœœœ œœœœœœœœ œœœœœœœœ œœœœœœœœ
Elec. Gtr.
Elec. Bass œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ
&b
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Figure 14.4.21 Nate Ruess, Andrew Dost, Jack Antonoff, and Jeff Bhasker,
“We Are Young” (2011)
?
b ∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
57
∑
∑
57
CHAPTER 14. ACCOMPANIMENTAL TEXTURES
158
14.4.4 Repeated
Quarter-note
Chords
F5
E¯5
D¯5
787
447
787
791
452
791
795
795
457
799
462
Test 2 Review
Analysis
œ œ œ œ œchords
œ œ œ are
œœ œœaœœcommon
œœ œœ___œœ œœ œœaccompanimental
œœ
œœ œœ ___
œœ œœ œœ___
œœ œœ___
œœ rhythm
Repeated
quarter-note
inœ “clas?Lead-sheet:
4
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
___
___
___
b
b
œ
4
sical” band
music. ( )
( ) œ œ œ œ
b popular
( )
3
## 3
& 44 ˙ .
œ
?
œ œ œ œB¯5˙˙ .. C5 E¯5
D¯5œ œ œ
b b b b 4 p œF5œ œ œ œ œ œ œ œ E¯5œ ˙ .
œœœœœœœœ
œ
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? # #b 43 Fœ œ œ
œ Dm7
œ œœ œ œ
œœœ œœœœ œœœœ œ œœœ œœœœ œœœœ œ œœœAm/E
œ
œœœ œœ œ œœ œœ œœ œœ œœ œœ œœœ œœ œœœ œœ œœœ œœ
œ
œ
œ
Piano œ
œ
œ
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œ
œ
œ
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4
b
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&
b
œ œ œ œ œ œ ___
œ œ œ œ œ œ ___
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D: ___
œœœœ
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œ œ œ œ œX9yTjXM6m50
œ ___
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œ œ Dm7
œœ œœ
œœ œœ œœ œœ___
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Elec. Gtr. œ œ œ œ œ œ œ œ œ œYT:
œ
œ
œ
œ
œ
œ
#
œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œ œ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœœ œœ œ œœ œ œœ
Elec.Piano
# 14.4.22
.œœ œœ œœ George
.
. “Ombra mai fu,” Xerxes,
Figure
Frideric
Handel,
& bBass
œ œ 40
œ HWV
4
œ̇
œ
(1738)
& 4 œ œ œœ œ̇œ œœ œœ œ̇œ œœ œœ œ̇œ . œœ œœ œ œ œ
F
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4
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œœ œ œœ œ œb œœœ œœœœœ œœœœœ.. œœœ œœœœ œ
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4
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. .
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4
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. œ. ___
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Figure 14.4.23
œ. œ. œ.Joeœ.Raposo,
œ. œJon
œ.Stone,
œ. andœ. Bruce
œ. œ.pHart,
œ. œ “Can
œ. œ.Youœ. Tellœ. Me
?
#
.
œ
Œ
How to#Get to Sesame Street?”
(1969)
˙
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œ
œ
œ
œ
˙
? ∑
∑
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œEm∑ G7/D
G
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œœœ œœ___œœ ___œ ___
___ ___
& 44___œœœ œœœ ___œœœ œœœ(skip œœœthis œœœbar)œœœ ___
œ œ œœ œœœ œœœ œœœ n œœœœ œœœœ
Lead-sheet: ___
___
___
___
___
___
___
.
424 œœ (œ ) ∑ œœ (œ) œœÓ (œ) œœŒ (œ‰) œj(œœ )˙ œ œœ (œ )
˙
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œœ
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œ
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Figure 14.4.24
“She’s ___
Got a Way”
F: ___ Billy
___ Joel, ___
___ (1971)
___
B¯5
C5 E¯5
œ̇ œ (œ ) œ
˙
˙
( )
˙˙
___
57
33
57
CHAPTER 14. ACCOMPANIMENTAL TEXTURES
bb 4
& b b b b 4 œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ
E¯sus4 E¯m
58 803
? bbb
bb bb
& b b bbb
58 803
? bb b b
b
&
& b bb bbb b
58 803
807
E¯sus4 E¯m
159
A¯m/C¯ C¯
A¯m/C¯ C¯
œœ œœ œœ œœ œœ œœ œœ œœ
œ œ œ œ œ œ œ œ
E¯m
E¯sus4 E¯m
4 E¯sus4
4 œ Œœ œÓ œ Óœ œ œ‰ j œ
4 œœ œœ œœ œœ œœ œœ œœ œ œœ œ
Œ
œœ
œ
A¯m/C¯ C¯
Ó
Ó ‰ j
œ
œœœ œœœ œœ œœœ œœœ œ œœœ
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œ
44 Œ Ó
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Ó
44 œœ œœ œœ œœ YT:
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œ œ œ œ œœœ œœmjwV5w0IrcA
œ œ
E¯sus4 E¯m
E¯sus4 E¯m
A¯m/C¯ C¯
Figure 14.4.25 Lou Gramm and Mick Jones, “Cold As Ice” (1977)
E¯
Dm
?
44 Œ Ó Dm/F
? bbbbb b bb b bb Gm
∑œj j j ∑ j Ó j ‰j∑ jj j ∑jŒ jÓ j ∑ Ój
j
4
b
& b 4b œ ‰ œ ‰ œ ‰ œ ‰ œ ‰ œ ‰ œ ‰œœ œ‰ œœœ ‰œ œœ ‰ œœ ‰ œœ ‰ œœ ‰
807
œœ œœ œœ œœ
. . . .
? b 44 Gm
j
813 b
bb b 4b ‰j‰œ œ.j‰ Ój‰ j‰
& b b 4b b œœ œœ œœ œœ
&
œ. œ. œ. œ.
? b 4 ‰ j Ó
811
? bb b 4b b œ œ.∑
b
807
&
b
‰ j
œœœ œ œœœ
A¯m/C¯ C¯
j ‰‰ j∑j‰ j‰
œœœ œœœœ œœœœ
. . .
œœ œœ œœ œœ œ. œ. œ. œ. œ.
. . . .
Dm/F
E¯
‰ j Ó
‰j j j Ój j Dm
‰
Ó
j ‰œ œ.j‰ j‰ j‰ œ ‰œ œœ ‰ œ ‰ œ ‰ œj ‰œj œj ‰ œj ‰ œj ‰
œœ œœ œœ œœ œœ. œœ.. œœ. œœ. œœ œœ. œœ œœ
. . . .
œ. œ. œ. œ.
‰ j Ó
‰ j Ó
‰ j Ó
œ. 3T1c7GkzRQQ
œ œ.∑
∑ œYT:
∑
∑ œ œ. ∑
Figure 14.4.26 Gordon Sumner, “Roxanne” (1978)
811
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& b bbbbb 4
&bbb
819
D¯
œœ
œ.
∑
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œ. œ.
∑
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œ.
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.
3
j
>
819
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4
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b
œ Œ Œ
Ó
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& bb bb b bb b 4 œ∑ œJ œ œ.∑
œœœ
.
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bbb ∑
b
& b
∑
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.
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∑
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∑
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. .
3
3
3
j 3j
j œ œ.
. j
œ
œ
œ
Œ œ∑ œ œ Ó ∑ Œ œ œ œ∑ Œ Œ œ Œ œ∑ œ
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3
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.
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∑
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∑
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Figure 14.4.27 Michael Bublé, Alan Chang, and Amy Foster-Gillies, “Haven’t
Met You Yet” (2009)
? bb b ∑
bb
∑
∑
∑
∑
∑
∑
∑
∑
∑
˙
? #### œ
Sara
Bareilles
"Love
Song"
nœ
œ
˙
œ
#˙
CHAPTER 14. ACCOMPANIMENTAL TEXTURES
F/A B bsus2
&b œ œ œ œ
œœ œœ œœ œœ
?
j j
b œ Œ ‰œ ‰œ
œ œ
œ
Gm
67
71
& www
C
C
œœœ œœœ œœœ œœ
jœ j
Ó ‰œ ‰œ
œ œ
Dm
∑
w
∑
160
D/F #
"second inversion"
E
w
wC
˙
œœ œœ œœ œ
œ œ œ œ
#œ
Ó ‰ j‰ j
#œ œ
#œ
ww
wG
Figure 14.4.28 Sara Bareilles, “Love Song” (2007)
?
˙
F
œœœ œœœ œœœ œœ
œ
j œj
Ó ‰œ ‰
œ œ
"first inversion"
ww
w
˙
C/E
ww
ww
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w
"root position"
œ
∑
www
w
In the next section, we will examine accompanimental textures consisting
E
of afterbeats and offbeats.
G
David Foster, Jay
Graydon,
Goodrum
fifth
of chordRandy
is lowest
note
"Who's Holding Donna Now"
77
of chord is lowest note
third of chord is lowest note
14.5rootAfterbeats
and
Offbeats#
Badd2
D m7
G m7
#### 4
œ
˙
œ
˙
j
j
œ ˙
# 4 œœ .
14.5.1
& Afterbeats
œ
œ
œ
J
œœ ˙˙˙
œ ..
œ œœ
The term “afterbeats” is from Fundamentals ofœ.Musical
Composition by noted
. œ
? # # # #and4 pedagogue
w
j are repeated
composer
Arnold Schoenberg.œ “Afterbeats”
4 w
#
œ occur
˙ after the
J notes) that
chords (usually eighth notes, sometimes quarter
#
downbeat.
b
& b bb C
815
sempre piano e dolce
w
˙
œ n œ œ œ œ œ b œ Œ œ.
˙.
˙
œœ œœ œœ
œ œ œ
œ œ œ
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b
820
b
œ
.
& b bb œ œ Œ œ œ œ œ œ œ œ œ ˙
T
œœ œœ œœ
œœ œœ œœ
Œ œ œ œ Œ œ œ œ
œ œ ˙.
œ œŒÓ
œ
œ œ
œ œ œ
? b b b Œ œœœ œœœ œœœ Œ œœœ œœœ œœœ Œ œœ œ œ Œ œ œ œ Œ œ œ
b
825
829
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2 j ˙
& 4 14.5.1
œ Ludwig van Beethoven, Piano Sonata Op. 2, No. 1, IV (1796)
Figure
In thepnext example, the afterbeats are not repeated chords but instead are
passing-tone
figures harmonized in thirds.
œ œ #œ
‰ œ œ
‰
& 42 ‰
œ œ œœ
œœ œœ œœ œ
œ œ œ
&œ œ
œ #œ œ
&œ
?
˙
f
‰ œœ œœ œœ
˙
‰ œœ œœ œ
59
? b b b Œ œœ œœ œœ Œ œœ œœ œœ Œ œ œ œ Œ œ œ œ Œ œ
b
CHAPTER 14. ACCOMPANIMENTAL TEXTURES
825
829
2 j
&4 œ
p
& 42 ‰
˙
˙
‰ œ œ
œ œ œœ
‰
œ œ œ œ œ œ œ œ
œœ œœ œ
œ
œ œ œ
& œ œ
œ #œ œ
& œ
?
œ
161
œ
œ
˙
f
‰ œœ œœ œœ
œ
#œ
˙
‰ œœ œœ œœ
YT: ZixdOZh7zo4
Figure 14.5.2 W.A. Mozart, Piano Sonata K. 279, III (1775)
14.5.2 Offbeats
Offbeats are typically chords that occur regularly on upbeats, avoiding downbeats. While there are many styles of music that use chordal offbeats, in this
section we will consider only polka and reggae styles.
14.5.2.1
Polka
The polka, which originated in Bohemia, has connotations with Germary and
Oktoberfest. The polka in the United States is often associated with Frankie
Yankovic, who was known as the “Polka King.”
60832
b
œ
œ.
œ.
œ.
& b b 44 œ œœ. ‰ œœ ‰ œœ ‰ œœ
J
J
J
.
.
.
.
‰ œœœ ‰ œœœ ‰ œœœ ‰ œœœ
J
J
J
J
Accordion
? b b 44 œ
b œ
Piano & Ac. Bass
œ
œ
œ
œ
b
&bb
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
834
YT: jF-5zBjEIDM
Figure 14.5.3 Jaromír Vejvoda, “Beer Barrel Polka” (1927)
? b b ∑Reggae
∑ ∑
b
14.5.2.2
∑
∑
∑
∑
∑
∑
∑
∑
∑ ∑
Reggae is associated with the island of Jamaica and, in terms of texture, is
characterized by offbeats, often played on an electric guitar. Bob Marley is
CHAPTER 14. ACCOMPANIMENTAL TEXTURES
162
closely associated with reggae music.
17
# # 4 œœ ..
& 4
œ œœ
œ ≈œœ Ó
Clavichord
√
j
œ
œ
? # # 44 œ œ ≈ œ ‰ . œ œ œ œ œ œ
R
? ## 4
4
j
j
j
œœ ‰ œœ ‰ œœ ‰
œ
œ
œ
‰ ‰.
Elec. Bass.
60832
œœ
Accordion
b b b 44 œ œœœ
19&
# # ∑ ∑.
&
r ‰ ‰.
œ œœ
.
.
‰ œœœ ‰ œœœ ‰
∑J ∑ J ∑
œ≈œ œ
œ œœ
Ó
œ œ ≈ œ ≈ œ ≈ œ œ œ œ œJ ‰
Muted Elec. Gtr.
Gtr.
# #Elec.
4 ‰
& 4
œ.
œ.
j
œœ
œ
‰ œœj ‰ œœj ‰ œœj ‰
œ
œ
œ
‰ ‰ ≈ r ‰
r
œ œœ
œ œœ
.œ
.œ
.œ
.
œœ ‰ œœ ‰ œœ ‰ œœœ ‰
J∑ ∑J ∑ J ∑ J ∑
YT: g3t6YDnGXAc
œœ.
œ
J∑
? b b 44 œ
œ
œ
œ
œ
œ
œ
œ
b
By the lateœ 1970s,œBritish bands like The Police
and
UB40 were recording
œ
œ
œ∑ ∑œ ∑ style.
? #that
∑ reggae
∑ accompanimental
∑ ∑ ∑œ ∑ œ ∑
songs
# ∑used the
Piano & Ac. Bass
Figure 14.5.4 Bob Marley, “Could You Be Loved” (1980)
834
Œ
j
œœ
œ
#b# 4 ∑Œ
&
& 4
j
j j j j
œ
‰∑ œœ ‰∑ œœ ‰∑ œœ ‰ ∑œœ ∑ ‰ œœ ∑ ‰
œ. œ. œ. œ.
œ.
Dm
Elec. Gtr.
∑
? #b 44 ∑ ∑ ∑
?
#
œ. œ œ ˙ .
Elec. Bass
&b
B¯/C
∑
∑ œ∑ ∑ ∑
. œ œ ˙.
j
œœ ∑‰
œœ
.
∑
j
œœ ‰
œœ ∑
.
j
œœ
œœ ∑
.
∑
∑
C
∑ ∑
œ. œ œ
837
YT: mbv-LcdLY-Y
Figure 14.5.5 Gordon Sumner, “Walking on the Moon” (1979)
?
b ∑
∑
∑
∑
∑
∑
∑
∑
? b 44
œ
Elec. Bass
œ
œ
œ
œ
œ
œ
œ
œ. œ œ ˙ .
C œ œ œ163
œ. œ œ ˙ .
j. j
j
j
j
j
j
j
œ
‰ œœœ ‰ œœœœ
& b 44 Œ D¯ ‰ œœœ ‰ G¯œœœ ‰ œœœ ‰ œœœ A¯/E¯‰ œœœœ ‰ œœœœ G¯/A¯
Elec. Gtr.
. . . .
. . . .
bb b b 4 ‰ œj ‰ œj ‰ œj ‰ œj ‰ œœj ‰ œœj ‰ œj ‰ œj
& b Elec.
4 Bassœœ
œœ
œœ
œœ
œœ
œœ
œ
œ
? b 44
œ. œ œ ˙ .
Elec. Bass
œ. œ œ ˙ .
œ. œ œ
? b b b 44
œ œ
bb œ œœ œ
œ œ
œ
œ
.
œ
œ
.
D¯
G¯
A¯/E¯
G¯/A¯
.
Elec. Gtr.
œ. œ
j
jœ j œ j
bb b b D¯:4 I‰ œj ‰ œj IV‰ œj ‰ œj V/5th
‰ œœ ‰ œœ
& b 4 œœ
œœ
œœ ‰ œœœ ‰ œœœ IV/5̂
œœ
œ
œ
839
b
b b b bBass
& Elec.
? bb 4
œ œ
œ œ YT: GVVZ_O0_vUc
bbb 4
œ œ
œ
œ
.
œ
œ in 1983
œ . Diamond,
œ
Figure 14.5.6 Neil
“Red Red Wine” (recorded
by
.
œ
œUB40)
œ
œ
.
?Reggae
∑
∑ is fairly ∑common
∑in the IV/5̂
∑
∑ as
accompanimental
texture
present
day,
b b b b b D¯:
I
IV
V/5th
834
Dm
B¯/C
CHAPTER 14. ACCOMPANIMENTAL
TEXTURES
Elec. Gtr.
837
837
can be heard in the following examples.
E
839
Gtr.
# # # # Elec.
4 ‰ j‰
&
4 œœ
œ.
? # # # # 44
Elec. Bass
œ
F˜m/C˜
j
j
œœ ‰ œœ ‰
œ.
œ.
œœ≈œœ œ
. .
.
Œ
E
F˜m/C˜
j
j
j
j
œœ ‰ œœ ‰ œœ ‰ œœ ‰
œ.
œ.
œ.
œ.
œ
œœ≈œœ œ
. .
.
‰
j
œœ
œ.
œœ
YT: luzciaIHL04
Figure 14.5.7 Gwen Stefani and David Stewart, “Underneath It All” (2001)
CHAPTER 14. ACCOMPANIMENTAL TEXTURES
j
Gtr. j
# # # # Elec.
4
œ
œ
‰
œ
‰
œ
V # 4 œ.
œ. ‰
Elec. Bass
? # # # # 44
Œ
≈
#
œ œ
œ
B
841
843
V
####
? ####
845
2
V
####
# œ œ Œ
≈
#
‰ œœj ‰ œœj ‰ œœj ‰ œœj
œ.
œ.
œ.
œ.
‰
Œ
≈
‰ j
œ
œ
œ
œ
‹œ
œ
#
œ
œ
œœ
‰
j
Œ
#œ œ œ
≈
œœ œ œ
YT: BFG0aiDrmUk
? ####
#
∑
G¯
A¯
? b b b 44
bb
D¯
Elec. Bass
œ.
D¯: IV
V
B¯m
A¯
j
j
j
j
‰ œœœ ‰ œœœ ‰ œœœ ‰ œœœ
.
.
.
.
j
j
œœ ‰ œœ
œ.
œ.
Œ
œ
œ
œ
.
œ
∑
œœ ‰ œœ œœ œœ œœ ‰ œœ œ ‰ œ
œ œ
œœ ‰ œœ œœ œœ œœ ‰ œœ œœ œœ
Elec. Gtr.
b b b 4 ‰ œj ‰ œj ‰
b
& b 4
œœ
œœ
.
.
12
j
j
œœ ‰ œœ
œ.
œ.
Figure 14.5.8 Jason Mraz, “I’m Yours” (2007)
b
& b b b b 44
12
F˜
.
.
.
j
j
j
j E œ.
# ‰ œœ ‰ œœ ‰ œœ ‰ œœ ‰ œœ ‰ œœœ ‰ œœœ ‰ œœœ
œ.
œ.
œ.
œ.
J
J
J
J
G˜m
Muted Elec. Gtr.
12
164
≈œ œ
Œ
œ œ . œ œ œ œ.
I
‰
vi
V
œœ
b
∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
& b b b b ∑ ∑ ∑ ∑ ∑ YT:∑ PIh2xe4jnpk
14
Figure 14.5.9 Nasri Atwey, Adam Messinger, Mark Pellizzer, Ben Spivak,
Alex
Tanas, “Rude” (2013)
14
b
& b bbb ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
14.6 The 3–2 Son Clave
? bb b ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
bb
14
The 3–2 son clave (and the 2–3 son clave) are essential rhythmic elements in
Afro-Cuban music. In this section we will see how cross rhythms implied by
the 3–2 son clave can be viewed as a possible source of cross rhythms in popular
music. Here is a video demonstration of a 3–2 son clave.
b
& b bbb
30
b
& b bbb
30
∑
∑
∑
∑
61
CHAPTER 14. ACCOMPANIMENTAL TEXTURES
165
YouTube: https://www.youtube.com/watch?v=dxVeiPQ1juo
419
419
421
421
423
425
Here is rhythmic notation of a 3–2 son clave. Notice there are three attacks
23
in the first measure and 2 attacks in the second bar.
23
ã 44 Û
ã 44 Û
‰ Û Œ
Û
Œ
Û
J
‰ Û Œ
Û
Œ
Û
The
1 rhythm
2
3 underlying
1 J 2 the
3 first
1 bar2 is 3+3+2.
>
>
>
1 Û 2Û 3 Û 1 Û 2 Û 3 Û 1 Û 2 Œ
Û
Û
ã >
>
>
Û
ã 44 Û Û Û Û Û Û Û Û Œ
Û
Û
Û
Û
Œ
Œ
Œ
Œ
423
ã
ã 44 Û
The 3–2 son clave has also been called the “Bo Diddley Beat” because of
3+3+2
eighthsin
note
in sixteenth
notesabove as you
its use by
Bo in
Diddley
the 1950s. Look at3+3+2
the rhythms
shown
listen to the following examples.
440
‰ Û Œ
J
Û
44 Û ≈ Û ‰ Û Ó
J
3
1
2
ã 1> 2 3 1> 2YT: 9kAhqaPMsdQ
>
Figure
14.6.1 Willie Dixon, “Pretty Thing”
ã 44 Û Û Û Û Û Û Û Û
Ó
447
ã
ã
426
YT: 5OOcnPVdKrs
Figure 14.6.2 Bert Berns, Bob Feldman, Jerry Goldstein, and Richard Gottehrer, “I Want Candy”
454
ã
YT: LKdHy18rZcI
ã 14.6.3 Russ Ballard, “New York Groove”
Figure
454
YT: oOmUCbDofo4
Figure 14.6.4 George Michael, “Faith”
YT: z8rQ575DWD8
Figure 14.6.5 U2, “Desire”
419
419
421
421
421
423
423
423
425
425
425
426
426
430
432
23
4
Û
‰
Û
Œ
Û
Œ
Û
Û
Œ
ã4
23
J
CHAPTER 14. ACCOMPANIMENTAL
TEXTURES
166
Û
Û
Œ
ã 44 Û1 2 ‰ 3 Û 1 Œ2 3 Û 1 2 Œ
4
J
Û> ŒRhythm
Û> Œ
Û
Û
Œ
14.6.1
ã 4 Û> The ‰3+3+2
4 Ûexamples
J Û 3theÛ first
Û Œ
Û
Û
Œ
Inã the
41 2 Û 3 Ûbelow,
1 Û 2only
1 Û bar
2 of the 3–2 son clave is used. Below,
the >3+3+2 rhythm> is shown in both
eighth
notes
and
sixteenth
notes.
The
>1 2
1
2 version
3 1 is known
2
3 as tresillo.
sixteenth-note
Û
Û
Œ
ã Û >Û Û Û > Û Û Û > Û Œ
4 Û3+3+2Û in eighth
Û ÛnotesÛ Û Û Û 3+3+2
Πin sixteenth
Û notes
Û
Œ
ã4
44 Û ≈ Û ‰ Û Ó
Û
‰ Û Œ
Û
ã 443+3+2
in eighths Jnote
3+3+2 in sixteenth notes
J
Û 3+3+2
‰ in eighths
Û Œnote Û
Û 3+3+2
≈ Ûin sixteenth
‰ Û notes
Ó
ã The
example below shows the sixteenth-note subdivisions in the 3+3+2
1
2
3
1
2
3
1
2
44 Û ≈ Û ‰ J Û Ó
‰ J Û Œ> Û
rhythm.
ã 44 Û>
4 Û Û ÛJ Û Û Û Û> Û Ó J
ã4 1 2 3 1 2 3 1 2
4 Û1> Û2 Û3 1Û> Û2 3Û Û>1 Û2 Ó
ã4 >
4 Û Û Û Û> Û Û Û> Û Ó
ã4
44 Û ≈ Û ‰ Û Ó 44 Û ‰ Û ‰ Û Ó 44 Û . Û ‰ Û Ó 44 Û . Û . Û Ó
ã
Below are different ways of notating the sixteenth–note version 3+3+2
426
J
J
J
rhythm.
ã
3 + 3 + 2 3 + 3 + 2
3+ 3+2 3+ 3 +2
ã 44 Û1 ≈2 Û3 ‰1Û2Ó3 1 244 1Û2‰3Û1‰ 2Û 3Ó 1 2 44 Û . Û1 ‰2 3Û 1Ó2 3 1 244 1 Û2 .3Û1. 2Û 3Ó1 2
J
J
J
ã 44 Û . Û Û Û Û . Û Û Û 44 Û . Û . Û Û . Û . Û
454
The first example, by the Rebirth Brass Band, uses a “second line” drum430
ming
ã pattern, which is associated with second line parades in New Orleans.
ã 1 2 3 1 2 3 1 2 1 2 3 1 2 3 1 2
>
>
>
>
>
>
4
Û
Û
Û
Û
Û
Û
Û
Û
Û
Û
Û
Û
Û
Û
Û
Û
ã4
YT: cczwRUBxNL8
Figure 14.6.6 Reggie Calloway, “Casanova” (1987)
The well-known
3
+ introduction
3 + to “Eye
3 of the
+ Tiger”
3 uses+the 23+3+2
+ rhythm.
2
434
>
>
>
4 >Û Û Û >Û Û Û YT:>Û btPJPFnesV4
Û
Û
Û
Û
Û
Û
Û
Û Û
ã4
1
2
3
1
2
3
1
2
3
1
2
3
1
2
1
2
Figure 14.6.7 Frankie Sullivan and Jim Peterik, “Eye of the Tiger” (1982)
In the following example from Cyndi Lauper’s “Girls Just Want to Have
Fun,” the lead electric guitar riff emphasizes a 3+3+2 rhythm in 16th notes
on each downbeat.
CHAPTER 14. ACCOMPANIMENTAL TEXTURES
Elec. Gtr. 1 2 3 1 2 3 1 2
123 123 12
j
bb 4
Œ
& b b b b 4 œœ .œ œœ ‰ œœ œœ
Û
‰ Û patch)
Œ
Û
Œ
(Polysynth
ã 44Keyboard
j
J
bb 4 œ
‰ œœœ œœœ
Œ
& b b b b 4 œœ
.
1
2
3 1
2
3 1
2
>
>
>
Organ
.. .. .. ..
4
ã&4 b bÛb b b b Û44 Û‰ œœœÛœœœ ‰ Û œœœ œœœÛ‰ œœœÛ œœœ ‰ Û œœœ œœœ
419
421
167
œœ .œ œœ ‰ œœj œœ
Û
Û
Œ
∑
œœ
Œ‰ œœ. œœ.Û‰ œœ. œœ.Û‰ œ œŒ‰
œ œ œ œ œœ œœ
..
Muted Elec. Gtr.
. . œ. œ. œ. notesj .
œ. œ. ≈ œ.note
œ. œ. œ. ‰ ‰ œ 3+3+2
? b3+3+2
4in eighths
œ œ œin≈sixteenth
b
≈
≈
b
b
4
J
œ.Ó ‰ œJ
bb ‰ Û Œ
4
4
Û
Û
Û
≈
Û
‰
Û
ã4
4
J
Elec. Bass J
? b b b b 44
j2 3 1 2
j
1b b 2
3
1
œ
œ
>
>
>
œ
œ
˙
œ
œ
.
.
4
ã4 Û Û Û Û Û Û Û Û Ó
423
425
430
œœ œœ
œ. œ.
‰
bbb ∑
∑ Want∑ to Have∑ Fun” (1983)
∑
∑
&4 b b 14.6.8
b
Figure
Robert4∑Hazard, ∑“Girls Just
4
4
.
.
.
Û
≈
Û
‰
Û
Ó
Û
‰
Û
‰
Û
Ó
Û
Û
‰
Û
Ó
Û
Û
Û
Ó
ã 4Below is an example4 showing the 3+3+2
4 rhythm (in 16th4 notes) immediJ
J
J
ately repeated. The rhythm is shown in two possible notations below.
bb
∑ 3 + 3∑+ 2 3∑ + 3 +∑2
& b b 3b b + 3∑ + 2 ∑ 3 + ∑ 3 + 2∑
3
426
23
YT: PIb6AZdTr-A
ã 44 b bÛ .b b Û ∑Û Û ∑ Û .
& bb
Û Û Û
∑
∑
? b
ã b bbbb
∑
1 23 1 2 3
12 123 1 2 3 12
44 Û . Û . Û Û . Û . Û
∑
∑
∑
∑
12312312 12312312
The following three examples all use the (3+3+2)+(3+3+2) rhythm as a
432
rhythmic
ostinato or groove.
∑
∑
∑
∑
∑
∑
? b 14.6.9
∑
∑ Toby∑ Gad, “All
∑ of Me”
∑ (2013)∑
443
Figure
and
b b b b b ∑John Stephens
ã Notice that this progression is from the Best-Seller progression.
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450
ã
∑
∑
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Figure 14.6.10 Shawn Mendes, Teddy Geiger, and Scott Harris, “Treat You
Better” (2016)
J
4 Û>
ã4
425
>
Û
J
>
Û
1
2 ACCOMPANIMENTAL
3
1
2
3
1
2
CHAPTER
14.
TEXTURES
Û
Û
Û
Û
Û
168
Ó
YT: jVCxZlpj8dw
4
4
4
4
ã 4 Û ≈ Û ‰ Û Ó 4 Û ‰ Û ‰ Û Ó 4 Û. Û ‰ Û Ó 4 Û. Û. Û Ó
This rhythm
J also occurs in theJfollowing classicalJpiece by Ligeti.
426
Figure 14.6.11 Ed Sheeran, Steve Mac, Johnny McDaid, Kandi Burruss,
Tameka Cottle, and Kevin Briggs, “Shape of You” (2017)
3 + 3
430
+ 2
3 + 3 + 2
3+ 3+2
3+ 3 +2
44 Horn,
. Û ÛGyörgy
. ÛPiano,
. Û
Û Ligeti,
Û . ÛTrioÛ forÛ Violin,
Û . Ûand
Û . IIÛ(1982)
Figure
ã 44 Û 14.6.12
1 23 1 2 3
1 2 1 2 3 YT:
1 2 W6HQ2Za75k0
3 12
12312312 12312312
The following examples have the (3+3+2)+(3+3+2) rhythm in 8th notes.
>
>
>
4
Û
Û
Û
Û
Û
Û
Û
Û
ã4
432
1
2
1
3
2
1
3
>
>
>
Û Û Û Û Û Û Û Û
1
2
2
3
1
2
1
3
2
434
ã
YT: d020hcWA_Wg
Figure 14.6.13 Guy Berryman, Jonny Buckland, Will Champion, and Chris
Martin, “Clocks” (2003)
450
ã
24
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Figure 14.6.14 Grohl, Hawkins, Mendel, Shiflett, “Best of You” (2005)
3 + 3
+ 3 + 3 + 3 +
3 + 3 + 3 +2+ 2 +2+ 2
> > > > > >
> > > > > >
ÛÛÛÛ ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
ã 44 Û Û Û Û Û Û Û Û Û Û Û ÛYT:
PIh2xe4jnpk
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1
435
2 3 1 2 3 1 2 3 1 2 1 2 1 2 1 2
Figure 14.6.15 Nasri Atwey, Adam Messinger, Mark Pellizzer, Ben Spivak,
Alex Tanas, “Rude” (2013)
437
4
ã 4 Û.
1
14.6.1.1
3
+
3
+
4
+
2 3 1
2 3
1 2 3
Habanera and Reggaeton
Û
Û
Û
‰
4
3
1
Û
J
2
+
Û
3
3
Û.
1
2 3
The reggaeton beat is built from a 3+3+2 rhythm. We will see a relationship
between the reggaeton beat with the habanera. First, let us examine the
famous “Habanera” bass line from the opera Carmen.
438
440
? 2
b 4
?b
œ.
≈ œ œ.
œ.
œ.
≈ œ œ.
œ.
YT: iqlUlr2yzY8
Figure 14.6.16 Georges Bizet, Carmen, Habanera (“L’amour est un oiseau
rebelle”) (1870)
?
447
454
b
b 4
œ .
œ.
œ.
œ .
œ.
œ.
CHAPTER 14. ACCOMPANIMENTAL TEXTURES
169
23
( )
( )
Compare the habanera pattern above to the reggaeton beat below, notated
for bass drum and snare drum.
?b
≈ œ œ.
œ.
œ.
‰ Û Œ
Û
ã 44 Û
Snare Drum
J
4
ã 4 œ1 ≈2œ œ3 œ 1 œ 2 ≈ œ3 œ 1 œ 2
> Drum
>
>
4Bass
Û
Û
Û
Û
Û
Û
Û
Û
ã4
440
419
442
421
≈ œ œ.
Û
Û
œ.
Œ
œ.
Œ
œ œ
œ œ
œ ≈ œ
œ ≈ œ
Œ
Û
Û
Œ
Compare the “reggaeton” rhythm to the 3+3+2 of the first bar of a 3–2
444
son clave (refer to the second measure in the example below).
ã
423
ã 44 Û
3+3+2 in eighth notes
4 Û>
ã4
425
‰ Û Œ
J
>
Û
44 Û ≈ Û ‰ Û Ó
J
3+3+2 in sixteenth notes
Û
>
Û
Here are examples of songs with a reggaeton beat.
1
2
3
1
2
3
1
2
Û
Û
Û
Û
YT: VQqwea8ZSbk
Û
Ó
Figure 14.6.17 Wycliffe Johnson and Cleveland Browne, “Dem Bow” (1990)
426
430
ã 44 Û ≈ Û ‰ Û Ó
J
44 Û ‰ Û ‰ Û Ó 44 Û . Û ‰ Û Ó
J
YT:J 6vjv9O4c1do
44 Û . Û . Û Ó
Figure 14.6.18 Aubrey Graham, Paul Jefferies, Noah Shebib, Ayodeji Balo+ 3 Errol
+ 2Reid,3Kyla
+ 3Smith,
+ 2 Corey Johnson,
3+ 3+
2 Dance”
3 + 3 (2016)
+2
gun, Luke3 Reid,
“One
1 23 1 2 3 12 123 1 2 3 12
12312312 12312312
ã 44 Û .
Û Û Û Û.
44 Û . Û . Û Û . Û . Û
Û Û Û
YT: kJQP7kiw5Fk
>
>
>
>
>
>
4
Û
Û
Û
Û
Û
Û
Û
Û
Û
Û
Û
Û
Û
Û
Û
Û
Notice that the progression for “Despacito” comes from the Best-Seller
ã
4
progression.
Figure 14.6.19 Luis Rodríguez, Erika Ender, and Ramón Ayala, “Despacito”
1 2 3 1 2 3 1 2
(2017) 1 2 3 1 2 3 1 2
432
3
434
+
3
+
3
+
3
+
2
+
2
>
>
>
>
>
>
ã 44 Û Û Û Û Û Û Û Û Û Û Û Û Û Û Û Û
1 2 3 1 2 3 YT:
1 8ELbX5CMomE
2 3 1 2
3 1 2 1 2
Figure 14.6.20 Bieber, Michaels, Tranter, Moore, and Tucker, “Sorry”
YT: FjvxZO4BX38
Figure 14.6.21 Karen Marie Ørsted, Jonnali Parmenius, and Uzoechi Emenike,
“Final Song” (2016)
426
ã 44 Û ≈ Û ‰ Û Ó
J
44 Û ‰ Û ‰ Û Ó
J
44 Û . Û ‰ Û Ó
J
44 Û . Û . Û Ó
CHAPTER 14. ACCOMPANIMENTAL TEXTURES
430
ã 44 Û .
3 + 3
+ 2
3 + 3 + 2
Û Û Û Û.
3+ 3+2
170
3+ 3 +2
44 Û . Û . Û Û . Û . Û
1 2 3 1 2 3 1 2 1 2 3 YT:
1 2 DCBmhs4dYzc
3 12
12312312 12312312
Figure 14.6.22 Adam Levine, John Ryan, Jacob Kasher Hindlin, Justin Tranter, and Phil Shaouy, “Cold” (2017)
Û Û Û
In the next two sections, we will examine expansions of the 3+3+2 rhythm
1 2 3 1 2 3 1 2
>
>
14.6.2> 3+3+3+3+2+2
>
>
>
4
Û
Û
Û
Û
Û
Û
Û
Û
Û
Û
Û
Û
Û
Û
Û
4 section, we will see each number in the 3+3+2 pattern repeated,ÛgenInã this
432
1
2
3
1
2
1
3
2
erating the 3+3+3+3+2+2 pattern.
3
434
+
3
+
3
+
3
+
2
+
2
4 >Û Û Û >Û Û Û >Û Û Û >Û Û Û >Û Û >Û Û
ã4
1
2
3
1
2
3
1
2
3
1
2
3
1
2
1
2
Listen for the 3+3+3+3+2+2 rhythm in the following examples.
YT: co6WMzDOh1o
Figure 14.6.23 U2, “Beautiful Day” (2000)
YT: PKRuEY68BVA
Figure 14.6.24 Aluna Frances and George Reid, “You Know You Like It”
(2012)
YT: cLyUcAUMmMY
Figure 14.6.25 Janee Bennett, Jessica Glynne, Jack Patterson, and Ina Wroldsen, “Hold My Hand” (2015)
14.6.3 8 Groups of 3 Plus 4 Groups of 2
the 3+3+2 pattern can also be expanded to 8 groups of 3 sixteenth notes
followed by 4 groups of 2 sixteenth notes, as shown in the example below.
24
3 + 3
435
+ 3 + 3 + 3 +
3 + 3 + 3 +2+ 2 +2+ 2
> > > > > >
> > > > > >
ã 44 Û Û Û Û Û Û Û Û Û Û Û Û Û Û Û Û Û Û Û Û Û Û Û Û Û Û Û Û Û Û Û Û
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1
2 3 1 2 3 1 2 3 1 2 1 2 1 2 1 2
Listen for this rhythm in the examples below.
#
ã #
437
?
CHAPTER 14. ACCOMPANIMENTAL TEXTURES
1. c˜: N6
2. b: N
3. G: ¯VII7 4. d: viio65/V 5. F: N46
3 + 3 + 3 + 3 + 3 +
664
3 + 3
171
6. f˜: N6
+ 3 +2+2 +2+ 2
123 1 2 3 1 2 3 1 2 3 123 1 23 1 2 3 1 2 3 12 1 2 1 2 1 2
>
>œ œ > >œ > > >
# # 4 œ . > >œ œ > >œ . >
œ‰ J œ‰
œ ‰ J œ‰
œ œ #œ œ
& 4
61
F˜
j Jr., “Ghostbusters”
j
j (1984)
Elec. Gtr. j
# # #14.6.26
j j
j j
Figure
# # 4 ‰Rayœœ Parker,
œ
œ
œ
‰ œœ ‰ œœ ‰ œœ ‰ œœ
V
4 œ. ‰ œœ. ‰ œœ. ‰ œœ.
œ.
œ.
œ.
œ.
Elec. Bass
? # # # # 44
Œ
≈YT: XjVNlG5cZyQ
‰
Œ
≈
‰ j
#
œ “Raise
œ Your Glass”
œ œ (2010)
‹œ
œ
#
œ
Figure 14.6.27 œPink,
Max
Martin,
Johan
Schuster,
œ
œœ
B
841
YT: Fe93CLbHjxQ
.
.
.
j
j
j
j E œ.
‰ œœ ‰ œœ ‰ œœœ ‰ œœœ ‰ œœœ
V # ‰ œœœ ‰ œœœ ‰ YT:œœœ IIkqOLvuQNo
œ.
J
J
J
J
. Many
. Zooz, .“Warriors”
Figure 14.6.28 Too
(2016)
? ####
Œ
≈
‰ j
Œ
≈
# Other
14.6.3.1
œ œ Combinations
œ œ of 3s# œand œ2s œ
œ œ œ
œ
You will also find other combinations of 3s and 2s (or 3s and 4s).
####
843
G˜m
bb b 4 œœœ ... œœœ œœœ œœœ ‰ œœœ œœœ œœœ ...
& b 4
J
Fm
845
? bb 4
b b 4 œ . œ œ œ ‰ œj œ œ .
b
& b b3b
+ 3
? bb b
b
∑
œœ .. œœ œœ œœœ œœœ œœœ œœœ ...
œ. œ œ ‰ J
E¯
D¯
‰ j
œ œ œ.
œ. œ œ œ
847
24
+ 3 + 3 YT:
+ 3KQ6zr6kCPj8
+ 3 + 3 + 3 +2+ 2 +2+ 2
1 14.6.29
2 3 1 2 Stefan
3 1 2 Gordy,
3 1 2 3Skyler
1 2 3Gordy,
1 2 David
3 1 2 Listenbee,
3 1 2 3 1 Peter
2 1 2 Schroeder,
1 2 1 2
Figure
> (2011)
> > >
> > > > > >
“Party
4 >Rock >Anthem”
ã4 ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
435
∑
∑
∑
∑
∑
Notice that this progression is from the i–VII–VI–VII progression. The
rhythm in the above example is dissected below.
437
ã 44 Û .
1
3
2
+
3
3
1
Û
Û
2
+
3
4
1
Û
2
+
‰
3
4
3
1
Û
J
2
+
Û
3
3
Û.
1
Listen for the 3+3+4+3+3 rhythm in the following examples.
#
ã #
438
2
3
bb 4
&bbb 4 œ
œœ ˙
Voice
œ
œœ ˙
CHAPTER 14. ACCOMPANIMENTAL TEXTURES
b b b 4 œœœ œœœ œœœ œœœ œœœ ˙˙˙
b
& b 4
Keyboard
Nev
-
er
œœ œœ œœ œœ œœ ˙˙
œœœ œœ ˙
nev
-
er
œ
œœ ˙
œœ œœ œœ œœ œœ ˙˙
œœœ œœ ˙
nev
-
er
172
YT: SeIJmciN8mo
œ
˙
œœ Falk,
˙˙ Rami
œœ Wayne
˙˙
.
..
œ
œœ .. Yacoub,
? b b 14.6.30
œœ ˙˙NadirœœKhayat,
Figure
Maraj,
Carl
..
bb 44 œœOnika
œ ˙ œ.
œ ˙
œ.
b Bilal Hajji, “Starships”
Hector, and
(2012)
J
J
J
Elec. Gtr.
? b b b 44
bb
Elec. Bass.
œ.
j
j
œ ˙YT: iS1g8G_njx8
œ ˙
œ.
j
œ ˙
œ.
Figure 14.6.31 Max Martin, Savan Kotecha, Ilya Salmanzadeh, Amethyst
Kelly, Ariana Grande, “Problem” (2014)
One also finds the 3+3+4+3+3 pattern in the second bar of “Tik Tok,” an
example from earlier in the chapter.
4
& b 44 œ . œ œ œ Œ ‰ œj œ . œ œ œ œ œ œ œ . œ . œ œ œ Œ ‰ œj œ . œ œ œ œ œ œ œ .
j
j
? 4 .
b 4 œ œ œ œ Œ ‰ œ œ.œ œ œ œ œ œ œ. œ. œ œ œ Œ ‰ œ œ.œ œ œ œ œ œ œ.
Keyboard 1
>
? b 44 œœœ
Keyboard 2
? b 44
œ
>
>œ
‰ œœ Ó
J
‰ jÓ
œ
>
>œ
œœ
œ
>
>œ
‰ œœJ Ó
‰ jÓ
œ
>
>œ
œœ
œ
>
>œ
‰ œœ Ó
J
‰ jÓ
œ
>
>œ
œœ
œ
>
>œ
‰ œœJ Ó
‰ jÓ
œ
>
YT: iP6XpLQM2Cs
Figure 14.6.32 Kesha Sebert, Lukasz Gottwald, Benny Blanco, “Tik Tok”
(2009)
Notice that this progression comes from a rotation of the i–VII–VI–VII
progression.
14.7 Distinctive Bass Lines
©
Sometimes the identity of a song is in its repeated bass line (known as a “riff,”
which is a short repeated pattern). Listen to the distinctive bass lines in the
following examples.
YT: KjuF89RvfIA
Figure 14.7.1 Joseph Eastburn Winner, “Little Brown Jug” (1869)
YT: eeFpUDCyTUo
Figure 14.7.2 Lennon-McCartney, “Day Tripper” (1965)
CHAPTER 14. ACCOMPANIMENTAL TEXTURES
173
YT: Er9xGRolrT4
Figure 14.7.3 Bernard Edwards and Nile Rodgers, “Good Times” (1979)
YT: rY0WxgSXdEE
Figure 14.7.4 John Deacon, “Another One Bites the Dust” (1980)
YT: QYHxGBH6o4M
Figure 14.7.5 Rick James, “Superfreak” (1981)
YT: a01QQZyl-_I
Figure 14.7.6 David Bowie, “Under Pressure” (1981)
YT: JtpX8KBT768
Figure 14.7.7 Amethyst Kelly, Charlotte Aitchison, George Astasio, Jason
Pebworth, Christopher Shave, Kurtis McKenzie, “Fancy” (2014)
YT: a5qZOMQ1qys
Figure 14.7.8 Ben Haggerty, Ryan Lewis, Jacob Dutton, Eric Nally, Joshua
Karp, Joshua Rawlings, Darian Asplund, Evan Flory–Barnes, Tim Haggerty,
“Downtown” (2015)
14.7.1 Distinctive Guitar Riffs
You will also find distinctive riffs played by guitar in conjunction with bass, as
in the following examples.
YT: fTTsY-oz6Go
Figure 14.7.9 Ray Davies, “You Really Got Me” (1964)
YT: y8OtzJtp-EM
Figure 14.7.10 Jimmy Page and Robert Plant, “Immigrant Song” (1970)
CHAPTER 14. ACCOMPANIMENTAL TEXTURES
174
YT: 4c8O2n1Gfto
Figure 14.7.11 Steven Tyler and Joe Perry, “Walk This Way” (1975)
YT: pAgnJDJN4VA
Figure 14.7.12 Angus Young, Malcolm Young, and Brian Johnson, “Back in
Black” (1980)
This chapter is meant to give you ideas about animating chords and chord
progressions with accompanimental textures, including riffs. It is by no means
meant to be exhaustive, but rather to encourage you to listen closely to texture
and accompaniment.
Chapter 15
Creating Contrast Between
Sections
In this chapter, we will explore how a composer or arranger can create contrast
between different sections in a piece of music.
15.1 The Elements of Music
Creating contrast usually involves varying one or more of the “Elements of
Music,” which are listed and explained below.
Table 15.1.1 The “Elements of Music”
Melody
Harmony
Rhythm
Timbre
Texture
Articulation
Dynamics
Register
We all know what melody is, but don’t confuse
melody with ostinato! Melody lives and breathes
and has variety.
In this section, we will associate harmony with
key and mode (major versus minor).
What the most common rhythmic value is in a
section.
The different tone colors of different instruments,
and the different tone colors an individual
instrument can produce.
Described in the previous chapter as existing in
the vertical plane (the number of voices) and the
horizontal plane (rhythmic activity of the various
voices).
Staccato versus legato, or short, clipped notes
versus long, sustained or connected notes.
Loud versus soft.
High versus middle versus low.
In the next two sections we will look at how two different pieces exhibit
contrast between various sections using the elements of music.
175
CHAPTER 15. CREATING CONTRAST BETWEEN SECTIONS
176
15.2 Mozart, Eine kleine Nachtmusik, K. 525,
II.
The second movement of Mozart’s Eine kleine Nachtmusik is a five-part rondo
form (ABACA).
Let us examine the elements of music in the first section (the A section).
Vln. I
Violino I
Vln. II
Violino II
Vla.
Vc.
Viola
Violoncello
e Contrabasso
14
Vln. I
&
.
œ œ œ œ œ œ . œ œ œJ œ œJ
œ
œ
œ
.
J
J‰
& C J ‰J ‰
p
j j
& C œj‰ œj ‰ œ œ œ œ œ œ œ . œ œj‰ œ. œ œ
œ
œ
p
BC Ó
∑
∑
?C Ó
∑
∑
Figure 15.2.1
Vln. II
Vla.
∑
Œ œ œ œ
∑
∑
œ
œ
∑
Harmony
∑Rhythm
Texture
∑
∑
∑
Articulation
Dynamics
Register
The key is C major
The 8th ∑note is most
∑ common∑ rhythmic ∑value, ∑
though the phrase begins with quarter-note values
The top two instruments are grouped together
against a simple bass part
∑ legato ∑
∑
∑
∑
Generally
Soft
Neither extremely high nor low
∑
∑
∑
∑
∑
∑
∑
∑
&
∑
∑
∑
∑
∑
∑
∑
∑
B
∑
∑
∑
∑
∑
∑
∑
∑
?
∑
∑
∑
∑
∑
∑
∑
∑
21
Vln. II
∑ YT: o1FSN8_pp_o
∑
∑
Notice how Mozart expresses the various musical elements:
?
Vln. I
œ œ Œ œ
j j
œ. œ œ œ œ ≈ œ œ ≈ œ . œ œj‰
∑
∑
∑
∑
∑
∑
& ∑
Table 15.2.2 A Section, Second Movement, Eine kleine Nachtmusik
B
Vla.
œ œ œ œ
p
œ. œ œ œ œ œ œ œ . œ
œ‰
J J ≈ ≈
J
&
Here is the beginning of the second section (the B section):
Violoncello
e Contrabasso
Vc.
CHAPTER 15.
14
Vln. I
Vln. I
Vln. II
Vln. II
Vla.
Vla.
c.
Vc.
14
Vln. I
Vln. I
Vln. II
Vla.
Vla.
c.
c.
c.
17
Vln. I
Vln. II
Vla.
œ. œ.
&C
p
Violino I
&C œ œ
Violino
p. II.
. .
BC œ œ
œ
œ œ œ œ œ œ Œ œ Œ œ œ œ
œ C
p
CREATING CONTRAST BETWEEN SECTIONS
177
?C Ó
œ. œ.
&C
œ. œ. C
&
.œ œ.
œ œ œ œ œ œ œ œ. œ. œ. œ. #.œ
œ. œ. # œ. œ.
œ
‰
œœ .
œ ‰ œ ‰ œ . œJ œ œ œ œ œ . œ œJ ‰ J œJ œJJœ œJ œ œ ≈ œ œ ≈ œ . œ œ ‰ C
J J
J
p
œ. œ. œ.
j ‰ œ œ œ œ œ œœœ
œ
j
#œ ‰ ‰ œ
n
œ
œ
.
.
.
.
j
œ
j j ≈ .≈
j‰ œ œ
‰C
j j
œ œ œ œ œ œ œ. œ œ. œ .œ . œ. œ . œ œ. œ œ œ œ œ .œ . œ . œ œj
œ œ œ œ œ
œ œ œ. œ.
pœ
Œ
Œ
p. . . B. C Ó
œ œ œ œ œ
?
C
?C Ó
Violoncello
e Contrabasso
p
Viola
∑
∑
∑
Œœ œ œœ. œœ. œ.œ œ. œ Œœ œ ŒŒ œ
œ œ
p
∑
œ. œ. œ. œ.
œ
C
œ C
. .
∑œ. œ. œ. ∑œ. œ ∑œ œ œ œ œ∑ œYT:
∑œ. œ. #∑œ
. œ.o1FSN8_pp_o
œ∑ ‰ ∑œ. œ. # œ∑ œ b b∑b C
&
œ
C
&
J
Figure 15.2.3
B Section, Second Movement, Eine kleine Nachtmusik
p
C ∑ are the∑ most ∑noticeable
j ‰∑ œdifferences:
∑œ œ ∑œ œ œ œ∑
∑ œ. œ.∑ œ. b b∑b C
&Here
œ
œ
œ
œ œ œ Bœ Section,
#œ
Table 15.2.4
Second
Einen œkleine
. . Movement,
. .
œ œ. Nachtmusik
p. . . .
. œ. most
Rhythm
are
rhythmic
œ. œ. œ. œ. œ8th notes
œ. œthe
œ. common
œ
œ. œ.value,
œ.∑ œ. b b∑b C
B
C
Œ
Œ
with
some
16th-note
runs
B ∑
∑
∑
∑
∑
∑
∑
∑
All four voices move in the same rhythm at the
pTexture
.œ œ. œ. œ. beginning of each subphrase
œ. œ. œ. œ.
? CArticulation œFour Œstaccato
b C
Œ
notes start each subphrase
? ∑
∑
∑
∑ œ. œ. ∑œ. œ. ∑œ
∑
∑
∑ b ∑b
Now,plook at the beginning of the next contrasting section (the C section):
T
T
T
œ. n œ
œ. n œ
œ. œ
bb b C Œ
nœ J ‰ Œ Œ
nœ J ‰ Œ Œ
&
p
b
& b b C œœ œœœœœœ œœœœœœœœœœ œœœœœœ œœœœœœœœœœ œœœœœœ
p
B bbb C œ œ n œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ n œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ n œ œ œ œ œ œ
p
T
T
. n j
. n j
œ
œ
? bb C Ó
Œ
Œ
nœ œ ‰ Œ
nœ œ ‰ Œ
b
p
17
YT: o1FSN8_pp_o
Figure 15.2.5 C Section, Second Movement, Eine kleine Nachtmusik
The following elements are noticeably changed:
œ œ
œ #œ
œœ
j
j
j
j
œœ. ‰ œœ. ‰ œœ. ‰ œœ.178
‰
œ
‰
œ
‰
œ
‰
œ
‰
#
V
œœ
œœ
œ
œœ
œ
œ
œ
œ
J kleine
J Nachtmusik
J
J
Table 15.2.6 C Section,
Eine
.
. Secondœ. Movement,
.
This section begins in C minor
##
? # Harmony
Πaccompaniment
≈
‰ j
Œ
≈
#Rhythm
# œ œ The
œ œ # œmovesœ in œ16th notes and œtheœ œ
ornamentation of the second melody note (the
œ
####
G˜m
E
CHAPTER 15. CREATING CONTRAST BETWEEN SECTIONS
843
turn) in the outer parts sounds as four 32nd notes
The middle two parts (Violin
II and Viola)
are
E¯
D¯
paired together and the Violin I and Cello/Bass
part engage in imitation
The middle parts are played in a “separated”
manner (more staccato than legato) and the
motive in the outer voices starts with a staccato
note
bb b 4 œœœ ... œœœ œœœ œœœ ‰ œœœ œœœ œœœ ...
b 4
& Articulation
J
TextureFm
845
œœ .. œœ œœ œœœ œœœ œœœ œœœ ...
œ. œ œ ‰ J
? bb 4
b b 4 œ . œ œ œ ‰ œj œ œ . œ . œ œ ‰ j
œ œtransitional
œ œ.
Listen to how Mozart puts the entire form together, including
material to smooth out the changes from one section to another.
A
B
A
C
A
legato
8th notes
staccato
8th notes
legato
8th notes
staccato
16th notes
legato
8th notes
Vn1+Vn2 vs Bass
C major
All 4 together
C major
Vn1+Vn2 vs Bass
C major
Bass imitates Vn1
C minor
Vn1+Vn2 vs Bass
C major
YT: o1FSN8_pp_o
Figure 15.2.7 Formal Diagram of Second Movement, Eine kleine Nachtmusik
15.3 “Rude” by MAGIC!
2
Now we will examine contrast in recent popular music. Here is the musical
example of the texture from the reggae section of this song, as seen in the
previous chapter.
b
& b b b b 44
G¯
A¯
D¯
Muted Elec. Gtr.
12
œœ ‰ œœ œœ œœ œœ ‰ œœ œœ œœ
Elec. Gtr.
b b b 4 ‰ œj ‰ œj ‰
b
& b 4
œœ
œœ
.
.
12
12
? b b b 44
bb
Elec. Bass
œ.
D¯: IV
Œ
œ œ œ œ.
V
j
j
œœ ‰ œœ
œ.
œ.
B¯m
A¯
œœ ‰ œœ œœ œœ œœ ‰ œœ œ ‰ œ
œ œ
j
j
j
j
‰ œœœ ‰ œœœ ‰ œœœ ‰ œœœ
.
.
.
.
≈œ œ
Œ
œ œ . œ œ œ œ.
I
vi
‰
V
œœ
In Verse 1 there is no bass drum, snare drum, or electric bass. All we
hear
are the voice part and the two guitar parts from the top two staves in
14
b
& b bbb ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
b
& b bbb ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
14
14
CHAPTER 15. CREATING CONTRAST BETWEEN SECTIONS
179
the example above. There are fewer voices occurring on the vertical plane,
creating a light texture.
YT: PIh2xe4jnpk
Figure 15.3.1 Verse 1 of “Rude”
The bass guitar and drum groove enter in Verse 2, thickening the texture
and adding the backbeat of the snare drum.
YT: PIh2xe4jnpk
Figure 15.3.2 Verse 2 of “Rude”
In the pre-chorus, the guitars and bass have legato half notes and quarter
notes while the drummer plays cross-stick eighth notes (if one is counting in a
slow 44 ). Without the snare drum backbeat, the texture lightens.
YT: PIh2xe4jnpk
419
23
Figure 15.3.3 Pre-Chorus of “Rude”
ã 44 Û
The chorus has approximately the same accompaniment as Verse 2 but the
voice parts are in a higher register, repeating a 2-measure subphrase containing
the “hook.”
421
‰
Û
J
Œ
Û
Œ
Û
Û
>
>
>
4
Û
Û
Û
Û
Û
Û
Û
ã 4emphasizes a (3+3+2)+(3+3+2) rhythmÛ on allŒ instru-Û
The post-chorus
1
2YT: PIh2xe4jnpk
3
1 2
1
3
2
Û
Figure 15.3.4 Chorus of “Rude”
ments (guitars, bass, and the bass drum, snare drum, and hi-hat of the drum
set).
423
ã 44 Û
3+3+2 in eighth notes
425
‰ Û Œ
J
2
44 Û ≈ Û ‰ Û Ó
J
Û
1
3
Œ
3+3+2 in sixteenth notes
>
4 Û> YT:
PIh2xe4jnpk
Û Û Û Û
ã4
Figure 15.3.5 Post-Chorus of “Rude”
1
Œ
2
>
Û
1
3
Û
2
Û
Ó
Below is a formal diagram of the first five sections of “Rude.”
426
430
432
ã 44 Û ≈ Û ‰ Û Ó
J
ã 44 Û .
3 + 3
+ 2
2
3
2
3
1
2
44 Û . Û . Û Ó
3+ 3+2
3+ 3 +2
44 Û . Û . Û Û . Û . Û
Û Û Û
12 123 1 2 3
1
44 Û . Û ‰ Û Ó
J
3 + 3 + 2
Û Û Û Û.
1 23 1 2 3
1
44 Û ‰ Û ‰ Û Ó
J
12
12312312 12312312
1
2
3
1
2
3
1
2
legato
8th notes A: I
staccato
8th notes
legato
8th notes
Vn1+Vn2 vs Bass
All 4 together
Vn1+Vn2 vs Bass
? ###
J
staccato
ii16th notes
j œj œ œj Œ Ó
‹
œ
.
œ
œ
J
legato
8th notes
j œj œ œj Œ Ó
œ. #œ
œ
Bass imitates Vn1
Vn1+Vn2 vs Bass
C major
C major
C major
C major
E
A C minor
CHAPTER 15. CREATING CONTRAST BETWEEN SECTIONS
299
Verse 1
V
Verse 2
? ### 4
No bass/drums
4 w
303
16th notes
A: I
308
D
legato
E
whole notes
IV
Chorus
Post-Chorus
w
All instruments
legato elements
A
3+3+2 rhythm
I
w
All instruments w No snare drum
A staccato
staccato
8th notes
Pre-Chorus
180
staccato
E
16th notes
V
Open hi-hat
V
œ
YT: PIh2xe4jnpk
˙˙˙
˙˙˙
˙
˙
˙
˙
˙
Figure
15.3.6
First
5
Sections
of
“Rude”
˙
˙
&
˙
˙
˙˙
˙
˙˙
˙
˙˙˙
? 44 ˙
˙
˙
˙
I
This five-section unit repeats again with Verse 3, Verse 4, the Pre-Chorus,
C: I and vi
IV
V
versus
I
vi
ii/3rd V
Chorus,
Post-Chorus.
When you listen to the entire piece, you hear how the musicians designate
G
the form using the elements of articulation, C
rhythm,Am
texture, Fand dynamics.
One element that changes very little during entire song is the chord progression,
which we examined in the chapter on harmonic progression, and is a rotation
C: I
vi
IV
V
of the 50s progression.
309
311
G¯≤
? b b b 44
bb w
D¯≤: IV
? bb b
bb
A¯≤
D¯≤
B¯≤m
V
I
vi
w
w
w
While you are likely aware of successful songs in the which very few musical
315
elements change, it is worth considering how you can articulate the form of your
compositions and arrangements using the elements of music.
? bb b
bb
323
? bb b
bb
327
Chapter 16
Figured Bass
16.1 Historical Context
In the Baroque era in music (roughly 1600–1750 C.E.), a shorthand was developed for writing chords. (Lead-sheet symbols are the modern shorthand for
representing chords). Figured bass (also known as thoroughbass) consists
of a bass line notated on a staff accompanied by numbers representing intervals
to be played above the bass note within the key signature. (These figured-bass
numbers are traditionally notated below the bass line.)
Figure 16.1.1 George Frideric Handel’s handwritten manuscript of Recorder
Sonata in A minor, HWV 362, I. Larghetto
181
20
j
& œ . œ œ œ j‰ œ ‰œ œ . œ œ œ œœ ‰ œ œ œ ‰ œœ . œ œ œ .
œ #œ œ
œ . œJ œœ #œœ
œ œ
3
Œ
& 4 It's a hard-knock life for us, 6 It's a hard-knock life for us 'Stead of treat - ed
4+
6 3
7 6 6
7 6
6
bb ‰ Œ 6
7 6 2
&
œ œ œ œ œ œ œ . œ œœ œœ œœ œœ œ œœ. œœ œ œ œœ œ œœ
? 43 œ . œ œ œ œ œœ.œ .œœ.œœœ.œ .œœ.œ œœ. œœ. œ œœ. œ œœœ. . œ œ. œ. œ. œ. œ. œ œœ. . œ. œ.
œ œ.
j3 œj
3
? b ‰ Œ 3 j‰ ‰ j Ó 3
œ
‰‰ Ó
b
œ
œ
œ >œin A minor, HWV
Figure 16.1.2 George Frideric
Handel, Recorder Sonata
œ
œ
>
362, I. Larghetto, without
> figured
> bass realization
bb
188
CHAPTER 16. FIGURED BASS
863
188
867
191
191
&3
& 4 Œ
?∑
& 43
œ
J
œ.
œ
œ
œ
œ
œ
∑ ∑ ∑ ∑ ∑ ∑ ∑ œ ∑ ∑ ∑ œ∑
œœ œœ œ œ œœœ # œœœ œœœ œ œ œœ œœœ œœ œ
œ
œ œ œ œ. œ œ œ œ
œ
œ
œ
œ
.
.
œ
œ
œ
? 43
884
œ œ.
œ œ.
œ œ.
3
6
3
3
&
4+
7 6
6
?
&
195
œœ ∑
œ
œ #œ
182
3
7
6
∑
3
3
∑
6
2
∑
YT: ljj6URbK8Xg
∑
œ
œ #œ œ
3
œœ ∑
œ
œœ∑ œœ∑ œ ∑œ
œ
œ. œ œ œ œ
œ œ.
7
3
6
6
3
∑
Figure
16.1.3 George Frideric Handel, Recorder Sonata in A minor, HWV
195
362, I. Larghetto, with figured bass realization
∑
&Like lead-sheet symbols,
∑
?
∑
figured bass allowed a keyboardist or guitarist
freedom in choosing chord voicings. While some early music specialists perform
from scores with the original notation, editions of Baroque compositions by
composers like J.S. Bach and Handel that were originally notated with figured
bass have been “realized” or written out in modern editions.
In the present day, figured bass is taught in music theory courses primarily
as a shorthand for chord inversion symbols (although many music programs
also endeavor to teach students to perform at the piano music written with
figured bass notation).
∑
16.2 Figured Bass Inversion Symbols
Following are the figured bass inversion symbols most commonly used for triads
and seventh chords. (Remember that figured bass numbers represent intervals
above the bass note within the key signature.)
63
Figured
Figured
BassBass
"Bass
Position
Symbols",
or "bps")
(or (or
"Bass
Position
Symbols",
or "bps")
CHAPTER 16. FIGURED BASS
3
+
3
+ 183 4
437
1 2 3 1
2
3
1 2 3
For Triads:
For Triads:
4
ã 46 Û6. 6 6 Û
Û
4 4
Û
+
‰
3
1
Û
J
4
Root is the 3rd of the triad 5th of the triad
3rd of the
triad
of the
triadbass note.
Root isbass
the note.
is the
bass5th
note.
is the
bass note. is the bass note. is the bass note.
? b 42
7
≈ œ œ.
438
Figure 16.2.1 Figured Bass Inversion Symbols for Triads
7
?b
440
For Seventh Chords:
For Seventh Chords:
66
5
œ.
5
œ4.
34
œ.
Root of the seventh chord
Root of isthethe
seventh
chord
bass note.
is the bass note.
≈ œ ( œ. )
3rdseventh
of the seventh
The 3rdThe
of the
chord chord
is
the
bass
note.
is the bass note.
The 5th of the seventh chord
is the bass note.
The 5th of the seventh chord
is the bass note.
Snare Drum
3
The 7th of the seventh chord
is the bass note.
2
Figure 16.2.2 Figured Bass Inversion
Bass Symbols
Drum for Seventh Chords
572
&
C
ww
w
ww
w
C/E
&
ww
w
C/G
Am7
C:
ww
ww
www
Am /C
7
iii w
ww
w
www
w
Am7/E
w
www
Am7/G
vi
www vi
wwwwvi
&
w Bass versus Roman Numerals
Figure 16.2.3 Roman Numerals with Figured
C: 447
I
C: I
I6
I64
vi7
I/3rd
I/5th
vi7
vi65
7/3rd
vi43
7/5th
vi42
7/7th
579
with
Modifed Slash Notation
iii7used for seventh chords,
ii56 the “7”
are only
Because the figures 65 , 43 , and 42 C:
is omitted when labeling inverted seventh chords.
&
451
589
&
&
C:
wwww
V765
Figure 16.2.4 “7” is not included when 7th chords are inverted
(
œ ≈œœ œ œ
The 7th of the seventh chord
is the bass note.
444 Unlike original figured bass notation in the Baroque era, in music theory
courses, figured bass inversion symbols are placed after Roman numerals.
Compare figured bass symbols to the modified slash notation we have been
29
using in previous chapters.
≈ œ
œ.
4
4
ã 4 œ2 ≈ œ œ œ œ ≈ œ œ œ
4
442
Û
3
≈ œ
œ.
œ.
2
ww
w
ii6
wwww
IM43
J
J
p
Bass Drumfrag. a frag. b
frag. a frag. b
j
j
j
j
j
j
œ FIGURED
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
CHAPTER 16.
BASS
184
? # # # 68 œw. œ œ œ œJ œ . œ œ wwœ œJ œ œ œ œJ œww œ œ .
&
w
w J
J
w
Notice thatwit is essential with seventh chords to include symbols
like “M”
444
◦
6 3rd I/5th V
7 figured
Iiii
I/3rd and
V/3rd
V/3rd bass
I Iii/
(for a major
chord)
andV
beforevithe
C: A: seventh
ii67ø/5th
4numbers and
after the Roman numeral.
Half Cadence
447
493
www
phrase a w
www
www
ww
w
w
w
w
# # # œ .7 œ œ œ œ œ 6. œ œ œ œ M4 j œ œ œ œœ ø4œ œ œj
vii 2 œ œ
& C: iii
J ii5
J œI 3œ
J
J
Figure 16.2.5
451
p
j
j
j
j
j
j
&? # # œœ . œ œœ œœ œœ œœ . œ œœ œœ œœ œœ œœ œœ œœ œœ
J
J Chord
œ œ.
16.3 #The Cadential
Six-Four
J
J
J
&
I/5th V
A common term in music theory—the
phrase a' “cadential six-four” (or cadential
6
6
(HC)
)—is
used
to
refer
to
the
I
that
regularly
proceeds
the
V
chord
in
cadences.
4
4
497
##
œ œ œ. œ œ œ
& # œ. œ œ
J
j
j
j
œ œ œ œœ œœ œ œ œœ
? ### œ . œ
J œ. œ œ
j
œ œ œ œ œœ
J
œ
J
j
j
œœ œ œ œ
J œ œJ œ œ
J
A: ii6
œœ œœj œ ‰
œ œ œœ
œ
j ‰
œ œ
I46 V7 I
(Cadential 64 )
YT: vp_h649sZ9A
Figure 16.3.1 Mozart, Piano Sonata K. 331, I
185 17
CHAPTER 16. FIGURED BASS
F
152
152
b
& b 43 œ œ
b
& b 43 œ œ
O'er the
B b/D F B b
œ.
land
œœ ..
? b b 43 œ ( œ ) œ .
œ ( œ) œ .
B b/D G m C ø7/G b B b/F
œ œ (œ ) ˙
J
œ œ œ . ( œJ ) œ
j
œœœ œœœ ( œœœ ) ˙˙˙
of the
œœ œœœ œœœ ... ( œœœ ) œœœ
œ
J
free
and the home
157
of the
œ bœ œ. j
œ bœ œ. œ œ
œ œ
j
˙
œ œœ ( œœ ) ˙
œ ( )
B¯: I64
V7
(Cadential 64 )
V7
B¯: I/5th
157
F7
I
Bb
˙
brave!
˙˙
˙
˙
˙
I
dom.
ton.
b
& b bbb c Œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ
G¯
YT: LGvW6jHUHiY D¯
Figure 16.3.2 Francis Scott Key and John Stafford Smith, “The Star-Spangled
Banner”
It is worth remembering
that the cadential 6 (or I64 ) has
dominant function,
Now that it's rain - ing more than ev4 - er Know
that we still have each oth just like the V chord that usually follows it. Previously, we have called this
chord “ I/5th .”
We will use the term “cadential six-four” throughout the rest of this text,
now that figured bass has been introduced.
b
& b b b b c ww
w
ww
w
? bb c
16.4b Other
Chords
b b w Occurrences of Six-Four
w
159
159
Second-inversion
D¯: IVchords with the fifth of the chord
I in the bass, also known as
6
chords,
are
special
chords
found
only
in
four
situations
in classical89
music.
4
A¯ six-four (discussed in the previous
B¯m section)
1. Cadential
bbbbb œ œ
&
œ bass
œ œ line
œ œwillœ look
2. Passing six-four:
œ the
œ œlikeœ a œpassing-tone
œ œ œ figure,
œ œ œwith
œ
three stepwise ascending or descending notes, and the middle chord will
You can stand un - der my um - br - el - la You can stand un - der my um - br - el be a 64 er
chord
b
& b bbb w
ww
? bb
bbb w
V
& œœœ
?œ
C: I
& œœœ
œœ
œ
œ
ww
w
w
vi
œœ
œ
œ
V64
I6
(passing 64 )
œœ
œ
œœœ
?œ
œ
œ
CHAPTER 16. FIGURED BASS
C: I
V64
I6
œœ
œ
œœœ
œ
œ
186
3. Pedal six-four: the bassline will consist of 6three repeated notes, and the
(passing 4 )
middle chord will be a 64 chord.
& œœœ
? œ
C: I
IV64
I
(pedal 64)
4. Melodic bass six-four: in this situation, the bass voice has the melody;
when the fifth of the chord occurs in this bass voice melody, the result
will be a 64 chord.
16.5 Additional Information
Though we will not use them in our harmonic analyses, you will sometimes
encounter figured bass symbols containing all of the intervals above the bass
note in Baroque music containing figured bass. The common figured bass
inversion symbols in the sections above are abbreviations of the figures given
25
in the examples below.
452
455
&
www
w
7
5
3
5
3
ww
w
ww
w
www
&
wwww
6
5
3
6
3
wwww
6
4
3
6
4
w
www
6
4
2
Figure 16.5.1 “Full” Figured Bass symbols showing every interval above the
lowest note
Additionally, you may notice that figured bass numbers in actual music
(but not in Roman numeral labeling) may be altered chromatically with the
following symbols.
& . #bb wwww œ œ 7œ#.# www6 œ 2œ œ œ bbœwww. œ œ œ# wwwœ œ . œ# wwœw œ œ
ww
œ w œ œ # # ww
#w œ œ. #w
?&
œ
œ
.
.
43 C: œvii#œwo.7/ii
œ
œ
o
7
ø7
vii /iii
vii /IV
viiø7/V
viio7/vi
o7/iii
C: 16.
viio7FIGURED
/ii 3
vii
CHAPTER
BASS
867
543
543
547
547
b bbb
wwEo
4
&
n
&&
4 bb œœb # œœ n www n ˙˙
œ c: œviio/iv˙
o
## ˙˙nn wwww
#˙ ow
F˜o
F˜o
Eo
c: vii /iv
Dø7
Dø7
? 44 b bœ
& b bbb
&
b
viiø7/IV
3
www œ ˙
ww
wviiø7# /III n
vii /V
viio/V
b www ˙
nb ww 6
now7 4+
Eo7
Eo7
3viiø7/V
870
558
558
863
o
# ˙˙˙
vii /VI
viio/VI
w
# nn wwww˙6
#w
F˜o7
F˜o7
7
b
878
3.
870
16
? b
? bb
542
5.
b7
b 5/VI
viiø7
viiø7/VII
viiø7/VI
viiø7/VII
accidentals before a
____ affect that
____
number
____ above the
____
interval
bass
6
4
n
w
6. d: __________
#w
w
##
6
b5
& #
?
? ##
ww_____
w
w 6
1. E: IV
_____
Rom. num.: 1.
D: _____
b
3. F: _____
2. DAnalyze
¯_____
: IVM7/7th the
chords.
b ww _____
& w
b b w2. c: iiø4
3
w
7. B: _____
_____
2. b: _____
# key signatures. b
Include
b:_____
viio7/5th
Lead-sheet:
Write
the1.specified
____
7
3. _____
f ˜: Vwith
chords
#
w
?# w
# ww
_____
3. G: V56
_____
3. e: _____
____
accidentals_____
before a
number affect 4that
interval above the bass
w
w
##
8. D¯: _____
_____
4. D: _____
bbbb
&
bbbb
4. E:
iisymbols.
/3rd
_____
lead-sheet
ww
w
w
_____
4. d: viio6
_____
4. f: _____
_____
2. g: Roman
_____
Analyze the excerpt using
numerals with figured bass inversion
? below and lead-sheet symbols ?
symbols
above. Analyze non-chord tones.
##
& #1.#A: wwI6
_____
ww
#
?
#
#
? #
Lead-sheet:
550
4
#
Rom. num.: 5. E: _____
_____
874 4.
878
w
˙ n wwww
#5 nw
b˙wwww
b ww
C: ____
____+
____
C: accidentals
____
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Rom. num.: 1. c: _____
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merals with figured bass
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#
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3
4
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with lead-sheet symbols above and Roman
w
w
w ____
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____
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568
b bass
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874
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accidentals without
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63
CHAPTER 16. FIGURED BASS
64 882
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∑
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Figure 16.6.1 J.S. Bach, Chorale 175, “Jesus, meine Zuversicht”
Click here to download the homework assignment for this chapter.
PDF versions of the textbook, homework exercises, and practice exercises
can be found at musictheory.pugetsound.edu
Chapter 17
Secondary Dominant Chords
So far we have studied diatonic harmony (chords without accidentals, with the
exception of the use of raised 6̂ and 7̂ in minor, which are considered diatonic).
In the following chapters, we will study chromatic harmony.
2
b 44 œŒÓ 44
V
17.1 Examples with Secondary Dominants
? 4 ∑ 4
b 4 4
Secondary dominants are common in classical and popular music. Here are
16
16
examples with the chromatic chords noted. We will examine these chords
more closely later in the chapter.
17
4
Vb 4 œ
I
17
? 4
b 4
œ
œ œ œ
be - lieve
œœ œœ œœ
‰
j
œ œ
in
yes
n œœ œœ œœ
œ œ œ œ
œ
-
œ œ œ
ter - day.
Œ
œœ œœ œœ œœ œœ œœ
œ œ œ
Figure 17.1.1 Paul McCartney, “Yesterday” (1965)
Vb ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
19
?b ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
19
Vb
35
?
35
189
∑
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œ œ.
œ .
œ
œ œ.
œ œ.
63
4+
7 CHORDS
6
6
7 6 DOMINANT
6
CHAPTER 17. SECONDARY
2
b 4
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195
b
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195
? b b 44 Œ
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7
3
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190
Ó
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6
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Figure 17.1.2 Jesse Harris, “Don’t Know Why” (2002)
198
198
198
198
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Figure 17.1.3 Rick Nielson, “I Want You to Want Me” (1977)
202
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209
? 44# #
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& # œ œ ∑œ œ ∑ œ œ œ ∑ œ
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209
206
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206
Figure
17.1.4 Robert William Lamm, “Saturday in the Park” (1972)
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CHAPTER
17.
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4 ____5 CHORDS
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Figure 17.1.7 Tchaikovsky, The Nutcracker, “Miniature Overture” (1892)
17.2 Tonicization
In this chapter and the next, we will study tonicization, which means treating
a chord other than the I chord like a tonic by approaching it with its dominant.
In diatonic harmony, the V chord (the dominant) resolves to the I chord (the
CHAPTER 17. SECONDARY DOMINANT CHORDS
192
tonic). A secondary dominant is a major triad or dominant seventh chord that
resolves to (or tonicizes) a chord other than the I chord.
896
& 44 œœ
œ
? 44 œ
G7/B
˙˙ ..
˙.
˙.
I V56/ii ii V56/iii iii V56/IV IV V56/V V V56/vi vi V56
I
œœ
œ
œ
C: V56
œ
n œœ
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C A7/C˜ Dm B7/D˜ Em C7/E F D7/F˜ G E7/G˜ Am G7/B
œœ
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901
&
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∑
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∑
∑
∑
∑
∑
Figure 17.2.1
25
the bass line of the example above and notice that a secondary chord,
through its chromaticism, intensifies the drive to the next chord.
911Sing
452
455
&
&
?
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Principle 17.2.2 Secondary Dominants. The Roman numeral after the
slash is the chord being tonicized by the V chord before
. 4 the slash.
7
5
6
6
You may find
that you want to analyze
the D F in the example
above
3
3
4
6
6
6
as .
a II5 instead of a V5 V (which we pronounce as “ V5 of V ”), and the
4
7
E G as a III65 instead of V65 vi (“ V65 of vi ”). Notice, however, that a ii
&
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chord is typically
minor in a 6major key and diminished
in a minor6 key ( ii◦ ),
6
7
918
4
4 is V/V .
5
5
making uppercase
II a chromatic
harmony for which
the proper label
459
&
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925
3
3
3
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&While labeling D7 as II7 in C major makes the root clear, it does not
communicate
the function of the D7 , which is to progress to a G major chord
&
?V chord, or the dominant
(the
∑ ◦ in C major).
∑
Figure 17.2.3
464
Also, notice that the vii is not tonicized with its secondary dominant
in the example above. Listen to the following example to understand why
diminished
chords such as vii◦ and ii◦ in minor are not tonicized.
472
&
479
&
486
&
65
? 44 œ
CHAPTER 17. SECONDARY
C: V6 DOMINANT
I V6/ii ii CHORDS
V6/iii iii V6/IV IV
5
Ÿ
& # # œœœ ...
F˜7
901
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464
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Triads
inV/ii
MajorA7
C
D Dominant
E
C: 17.3.1
V/V Secondary
V/vi
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In C majorb w7
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#
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7
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w
& as VCwww7/V
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7
7
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#
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3
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#
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#
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& Dominant
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& 17.3.2
# www
473
# www Secondary
Figure
Seventh Chords
in Major
the chromaticisms in the example above. The raised notes generally
&Notice
C: V/V
V/vi
V/ii
V/iii
473
C: V7D
/IV
V7/V E
?
&
&
473
476
& bbb
492
&
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492
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# # www
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7
C7Secondary Dominant
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Figure 17.3.3
Triads
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____
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∑ ∑ ∑ ∑ ∑
I
B64
act as the leading–tone to the root of the chord being tonicized. In the major
7
D7 dominant with
E7 a lowered Achromaticism
485
mode,
theC7only secondary
isB7V7 IV .
The lowered note in V7 IV acts as 4̂ of the chord being tonicized in the same
485
way
the last flat of a key signature is 4̂ .
Below are all secondary dominant chords (triads and major-minor seventh
C: inV7the
/IV minor mode.
V7/V
V7/vi
V7/ii
V7/iii
chords)
468
481
Not as
I
25
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V7/viio
viio
3
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Figure 17.2.4
D7
459
# œ œ N ˙˙˙
b ww
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#
w
w
w
#
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7
7
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A
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w
w
w
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w
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6
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17.3
Minor
In
4
Label as V7/V
V7/vi
V7/ii
V7/iii
V7/IV
w
7
7
7
7
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Both
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triads and major–minor
seventh
chords
Not
IIw
III ww
VI
I7
In
Cas
major
w
w
w
w
7
7
7
7
7
&
w
w
Label
/V 918 V /vi w
V /ii
V /iii
V /IV
chords.as V w
7
7
7
7
7
7
D7
5
3
459
193 V V6/vi vi V6
V56/V
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b ww
ww
V7/VI
n wwww
F7
V7/VII
____
www
w
B¯7
V7/III
(same as VII7)
____
∑
∑
b
&bb
n www
# n www
C
D
n www
F
CHAPTER 17.
DOMINANT
c: SECONDARY
V/iv
V/V CHORDS
476
481
b
&bb
C7
D7
c: V7/iv
V7/V
www
w
F7
b www
w
# n wwww
n wwww
(same as IV)
n wwww
E¯7
V7/VI
194
V/VII
B¯7
V7/VII
V7/III
(same as VII7)
____
____
____
Figure 17.3.4 Secondary Dominant Seventh Chords in Minor
____
?Remember that both
vii◦ (on raised 7̂ ) and the subtonic VII (on the
lowered
7̂ ) occur in the minor mode. The subtonic VII can be tonicized with
V7 VII ,1.while
vii◦ , being2.diminished,
E¯: V/ii
g: V7/VI cannot.
3. e: V4/iv
4. A: V6/ii
Notice that an F major chord in C minor can be2 V/VII or IV , depending
on how it functions or progresses.
If the F major chord progresses to a B2
G7/B C A7/C˜ Dm B7/D˜ Em C7/E F D7/F˜ G E7/G˜ Am G7/B
896
chord, label the F chord as V/VII . If the F major chord has pre–dominant
4
œœ œœ theœœ
b œœ œœ œœor Bœœ◦ , label
function and progresses
chord
(in
œœ anyœœ inversion)
&to4a Gœœ major
œ
œ
#
œ
œ
œ œ nœ
F chord as IV .
œ œœ œ œœ œ œ œ œ œ œ 7 27
The B chord, on the other hand, can be labeled correctly asœ V
# œ IIIœ orœ
4
?
œ #œ
# œ œ # œto IIIœ inœminor.
VII7 because both V7 III4 orœ VIIœ7 progress
16
C: V56
I V56/ii ii V56/iii iii V56/IV IV V56/V V V56/vi vi V56
17.4538Analyzing Secondary
Dominants
_____
_____
F˜7 _____
Bo
901
Ÿ
?
When you encounter a chord
with a chromaticism
and suspect it is a secondary
...
& # # œœœprocess.
# œ œ N ˙˙˙
dominant, use the following
2. D¯: IVM7/7th
3. f ˜: V7
1. Stack the chord in
?thirds
# ˙ to determine the root and quality. If the chord
542 quality is major (if a triad)
˙ _____seventh chord,
_____or a major–minor
_____
go on to
step 2. If the chord
quality
is
not
major
or
major–minor
seventh,
the
7
o
o
? C: V /vii
?
&
&vii
chord is not a secondary
(notdominant.
recommended)
1. b: viio7/5th
# #1.# #E: IV6
902
ww
_____
&
?
? ####
w &
#w
6
546
1. A: I
? # ##
?
E: ____
_____ 4
# www
2. c:(stacked
iiø43 in 3rds)
_____
∑
2. F: ii42
_____
3. G: V56
_____
?
3. b: V65
?
&
_____
550chord in question is an F major triad in first inversion.
The
65
˙˙ ..
˙.
˙.
C
I
_____
4. E: ii/3rd
_____
4. d: viio6
_____
4. g: viio6
_____
&
2. Determine the note
& #that would be&a perfect 5th below the root of the
chord you are analyzing. If this note would be the root of a diatonic
chord, the chord you are
is a6.secondary
5.
iv64
B¯: viiø4 dominant.
7. f ˜: VII6
8. E¯: IVM65
# e: analyzing
904
554
? ## #
####
&
906
####
∑
# www
3
∑
w
F˜ down P5 is B; in E major, B is 5̂
556&4
Since B is 5̂ , the
F major
chord in first inversion is tonicizing V . There
fore the chord is?V6 V .
? #### ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
17.5 Writing Secondary Dominants
To write a secondary dominant, use the following procedure.
## #
&
5. e: iv
www
#
6
w3
6. B¯:195viiø4
1.554
First determine the note that is the root
of the chord
being
F down
P5 is
B;tonicized
in E major,
(the chord to the right of the slash).
556
556
&b
&b
d: V43/VI
(6ˆ is B¯)
2. Determine the 557
root of the V7 in the key of B2 (the Roman numeral after
the slash): F
d: V4/VI
3. Build a major–minor seventh chord on F:
3 F–A–C–E 2
4. Invert the chord accordingly.
in the bass.
557
4
3
&b
&b
(6ˆ is B¯)
inversion means the fifth of the chord is
b wwww
564
d: V43/VI
&b
558
2
17.6 Irregular Resolutions16 of Secondary Chords
4 4
V b 4 œŒÓ 4
? 4 ∑ 4
b 4 4
16
The roots of secondary dominants do not always resolve down a perfect fifth to
the tonicized chord. In many of the examples of popular music with secondary
dominants at the beginning of this chapter, the secondary dominants resolve
deceptively.
17
4
Vb 4 œ
Dm
I
17
? 4
b 4
œ
F: vi7
G
œ œ œ
be - lieve
œœ œœ œœ
‰
B¯
j
œ œ
in
yes
n œœ œœ œœ
œ œ œ œ
œ
V/V
IV
F
-
œ œ œ
ter - day.
Œ
œœ œœ œœ œœ œœ œœ
œ œ œ
I
Figure 17.6.1 Paul McCartney, “Yesterday” (1965)
19
19
7. f ˜: V
B is 5̂
#### w ˜
# ww
&
w
b
&
F˜ down P5 is B; in E major, B is 5̂
CHAPTER 17. SECONDARY DOMINANT CHORDS
4
In “Yesterday,” the V/V resolves not to V but to IV , which sometimes
acts as a substitute for the V chord (the dominant) in popularmusic.
This progression also happens in “Forget You,” where a V7 V resolves to
a IV chord.
Vb ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
?b ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
bb 4
887
198
198
& 44 ‰ ‰ œœj
œ
>
? 44 j œ
œœ
œ. œ. >œ
‰ j
œœ
# œœ
>
˙ ‰ œj œ
˙ œ œ œ
. . œ
>
˙˙ ..
˙.
˙
˙
œ
____
9
‰ j
œ ˙.
n œœ ˙˙ ..
>
‰ j
œœ
œ
>
‰ j
˙ œ œœ
˙ œ. œ. œ
>
‰ j
œ œœ
œ. œ. >œ
IV
____196
10
C
I
˙˙
˙
˙
˙
> . .
.
.
.
j
œ
œœœ œ. œœ œ œ œ >œœ œ ‰
b 4 œ ‰ œœ ≈ œœ YT:œ awVi2QXC0ZE
œ
b
œ
& 4 œ.
œ
œ œ œ œ œ œ œJ
Figure 17.6.2
Bruno Mars, CeeLo Green, Philip Lawrence, and Ari Levine,
π
“Forget You” . (2010) œ.
œœ n œœ b œœ. œœ. œœ. >œ œ œ. œ. n >œœ œ
œœ
œ
≈
œ the
œ V/V chord resolves
to Want Me” by Cheapb Trick,
?In b“Ib Want
44 J You
J ‰ to
‰
2
a subtonic VII chord in A major.
##
j
& # 44 œ œ ‰ œ œ œ
F˜m7
### 4
& 4 ˙.
˙ Œ ‰ œJ œ œ‰ œJ œ œ ˙
B
shine up my old brown
G
shoes.
œ #œ ˙ .
& 44 ˙ .
I'll
A
V/V
œ #œ ˙.
Ó
put on my brand new shirt
œ nœ ˙
œœœœ
œœœœ
A: vi7
202
˙˙˙ ...
˙.
V7/V
I
? # # # 44
œ œ œ œ
œ œ œ œ
202
œ
œ
œ
E¯: ____
____
____DOMINANT
____ ____ ____
____ ____
CHAPTER
17. SECONDARY
CHORDS
1
2
3
4
5
6
7
8
7
C
D
F
C:
892
œ
nœ œ
nœ œ
¯VII
œœœ w
œ œ œ œ œ œ
œ œ œ œ œ œ
œ nœ ˙.
I
œœ ˙
œœ
4
& 4 œœ œœ œœ œœ ‰ œœj Œ œœ œœ œœ ‰ 2 œœj Œ œœ œœ œœ ‰ œœj Œ œœ œœ œœ
Remember,
œ œ œhowever,
œ # œœthat the
œœ œœ nVII
œœ in major
œœ œœ can
œœ actœ as a substitute
œ œœ
# œœ subtonic
YT: -qgpewMCVjs
Figure 17.6.3 Rick Nielson, “I Want You to Want Me” (1977)
for the dominant (see the Harmonic Flowchart for Popular Music with Subtonic
VII chord in Major).
. 2
In “Baby Love” by the Supremes, a C7 B in C major ( V42 IV ) resolves
to an A7 chord ( V7 ii ), which
. 2then resolves to ii ( Dm ). In this example,
7
2
notice that the B in the C B is a lowered chromatic note that wants to
resolve downward by half step to A. Instead of this A being the third of the IV
chord (an F major chord), which
is the traditional and expected resolution, it
is the root of an A7 chord ( V7 ii ).
? 44
206
206
œœ œ
œœ œ
œ
œ
œœ œ
œœ œ
# ## 3
œ. .
& # # 8 œ . œJ œJ
# # # # 3 œ . œ œ. œ.
& # 8
La
don - na è
œ œ
? # # # # 38 # œ œœ œœ
#
œ
œ
œ >œ
R≈
r
#œ
œœ œ
œœ œ
œ œ œ
œ œ œ
œ >œ
R≈
œ . œ œ. œ.
J J
œ≈œ
œ.
œœ œœ
R
œ œ
œ œ œ ‹œ
mo - bil
œ
œ
qual
œ œ. œ.
piu - ma al
œœœ œœœ
r
‹œ
œ œ
œœ ≈ œœ
R
œ œœ œœ
ven - to,
21
22
CHAPTER 17. SECONDARY DOMINANT CHORDS
C7/B¯
C
210
j
& 44 œ œ œ ˙ œ œ
Ba
210
& 44 ‰
?4 ‰
4
-
by love, my ba
œœ œœ œœ œœ
œ œœœ
œ œœœ
œ œœœ
& ∑
∑
∑
∑
& ∑
∑
∑
? ∑
∑
∑
215
Figure
A7
j
j
œ œ bœ œœ œ œ
J
œœ ˙ œ œ
by love,
I
œœ œœ œœ œœ
œ œœœ
need
V42/IV
Dm7
œœ œ ˙ Œ
3
you oh
how
# œœœ œœœ œœœ œœœ
œ œ œ œ
bœ œ œ œ
bœ œ œ œ
C: I
215
-
197
3
I
n œœ
œ
need you
œœ œœ œœ
œœœ
œ
œ
œ œ œ œ
œ œ œ œ
V7/ii
œœœ
œœœ
ii7
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
YT: 9_y6nFjoVp4
17.6.4 Lamont Dozier, Brian Holland, and Eddie Holland, “Baby
Love” (1964)
Finally, a rather common deceptive resolution of a secondary dominant is
V7 vi to IV , which can be seen in the following three examples.
227
∑
∑
∑
∑
∑
∑
∑
227
&
∑
∑
∑
∑
∑
∑
∑
?
∑
∑
∑
∑
∑
∑
∑
&
# 4 ˙
œ œ
J
œœ w
˙.
D: _____
_____
_____
CHAPTER 17. SECONDARY DOMINANT CHORDS
#
j
V 44 œ œ .
G
228
œ œ œ œ
896
230
#
& 44 ˙˙
˙
? # 44
901
902
to
live
œ # œœ n œœ # # œœ
œœ œ # œ œ
œ
4
œ
& 4 œœ œœ œœ
G:
œ I œ œ
? 44 œ œ # œ
# Cœ œ œ
VC: V6 I V6/ii
˙
˙˙
for
And look like
Ó
œ
œ Cœ
œ
œ
œ
œ
œ
œ ˙.
œ œ #œ
# œœœ œœœ b œœœ œœœ œœœ œœœ œœ œœœ n œ ˙˙ ..
V/vi
œ ˙.
# œ œ œ œ A# œ œ # œ œ
œ œ Vb6/IV
œ IVœ V56/VŒV V56‰/vi œvi œ Vœ 56 œ I œ œ
V56/iii iii
5
C A7/C˜ Dm B7/D˜ Em C7/E F D7/F˜ G E7/G˜ Am G7/B
G7/B
5
230
no - thing
_____ _____
198
œ œ œ œ œ ‰ ‰ œj œ œ
B
I've had
228
˙
˙
œœ
œ
œ
œ
ii
5
Ÿ
& ## # œœœ˙...
& ˙˙
? #˙
?#
C: V7œ/viio
Fno˜7- thin's gon - na Bocome
my
# œ œ N ˙˙˙ œ # œ n œ
œœ œ n œ
œ bœ
˙
œ viio œ
œ bœ
(not recommended)
##
& # # ww
# www
IV
way
So
I'm just gon'
#œ
œ
œ
œ
œ
œ
Œ
Ó
œ
œ
œ
œ œ œ
V/V
(stacked in 3rds)
YT: rTVjnBo96Ug
? #### w
#
w
Figure 17.6.5 Steve Cropper and Otis Redding, “(Sittin’ On) The Dock of
the Bay” (1967)
?
E: ____
904
œ œ
œ
œ œ
œ
? œœ œ œœ œ œ œ œ œ œœ œ œœœ œ # œœ œ œœ œ œœ œ œœ œ œ œ œ œ œœ œ œœœ œ # œœ œ œœ œ
F
G
?˙
˙
˙˙
C: IV
V
E
908
E7
C
E
F
G
˙˙
I
˙˙
˙˙
˙˙
V/vi V7/vi IV
B7
C˜m
V
G˜7
œœ rAn-AWXtHv0
44 # ˙˙˙
# # œœœ #YT:
#
# # # ˙˙˙
&
œ
Figure 17.6.6 John Lennon, “Imagine”
(1971)
& 44 # ˙˙
dolce e molto ligato.
E: I
# # œœœ
# œœ
V
vi
# # # ˙˙˙
V7/vi
C
E
˙˙
˙˙
E7
V/vi V7/vi
I
A
#˙
˙
# ˙˙
IV
65
˙˙
˙
˙
˙˙
˙
˙
˙
˙
˙
˙
B7
C˜m
C: IV
V
I
V/vi V7/vi IV
V
CHAPTER 17. SECONDARY DOMINANT CHORDS
E
# ˙˙
4
&4 ˙
908
& 44 # ˙˙
˙
˙
˙
˙
V/vi V7/vi
199
I
G˜7
A
# # œœœ
œ
# # œœ
# # œœœ
# # # ˙˙˙
# œœ
#˙
˙
V
vi
# # # ˙˙˙
# ˙˙
dolce e molto ligato.
E: I
V7/vi
IV
YT: lbblMw6k1cU
Figure 17.6.7 Beethoven, Piano Sonata Op. 53, I (1804)
There are two ways to conceptualize this progression. The first is that the
progression of iii to IV (Em to F in C major) is not unusual, so E to F, which
appears to be III to IV but is in fact V/vi to IV , is a chromatic modification
of iii to IV . The other way to think of V/vi to IV is as V/vi to VI/vi , a
deceptive progression within the submediant area.
We can conclude that secondary chords do not always resolve strictly to
the chords they appear to be tonicizing.
17.7 Practice Exercises
Day One:
66
910
1.
26
26
Approach
4 each chord with its secondary dominant seventh chord (whose
& lies
4 ˙˙a perfect 5th above
˙˙
root
Label
˙˙ chord of resolution).
˙˙ the root of the
˙
˙
chords ____
with
numerals
below
and
lead–sheet
symbols
above.
˙ Roman
˙
____
____
____
____
____
____
Am7
C
? 4˙
? 4444 ˙˙˙ ˙
?
4C:˙ I
____
485
485
Dm7
˙
˙˙˙˙
˙
vi˙7
____
____
____
____
ton. 7
C: ____
V /____ ton.
____ prol.
V7/____
C: ____
V7/____ ____ V7/____
FUNCTION:
____
& 44____
˙˙
? 444 ˙˙˙ ˙˙
?
?444 ˙ ˙
C
912
489
489
____
____
2.
914
# ˙˙˙ ˙˙
˙˙
˙
˙˙
V7/____ ____
V7/____ ____
V7/ii
C: ____
C: ____
C: I
493
493
A7
____
____
____
____
˙˙
˙˙˙7
ii˙
˙
w
˙ www
w
V w
____
____
pre-dom.7
____
____
V /____ dom.
____
V7/____ ____
D7
____
____
˙˙ ____
˙ www
www
˙
V77/____ ____
n # ˙˙˙ ˙˙˙
˙˙
˙˙
V7/____
V7/____
G
____
____
V7/V
____
____
G
V /____
____
V
____
FUNCTION: ton.
prol.
pre-dom.
Analyze
the followington.
secondary
dominants.
Include dom.
lead-sheet symbols above.
?
____
____
?
##
ww b # ww b b b
&
w
w
501? #
b
501
? # #w b w b b
?
Lead-sheet:
b: _____ F: _____
1
2
b
?& b b b
?
b ww
w
w
____
#
____
ww
# # ww
c: _____
3
G: _____
4
∑
∑
####
bbbb
____
# ww
w
#### w
____
b ww
w
w
bbbb
E: _____
5
f: _____
6
920
508
508
? bb
bb
515
515
?
?
∑
∑
∑
∑
∑
3
3
3
459
2
ww
# wwww
w
#
w
#
w
w
w
w
& 17. SECONDARY
# wwDOMINANT CHORDS
# ww
CHAPTER
D7
3.
464
920
468
924
473
E7
A7
B7
bCww
ww
7
200
In C major
On
the empty staff below,
copy 7the notes from
the upper 7staff to
Label as V7/V
V7/vi
V /ii
V7/iii
V /IV
the
adding
the VI
specified
non–chord
tones. I7(Note:
7
7
Not aslowerII7staff while III
VII7
LNT = lower neighbor tone; UNT = upper neighbor tone.) Realize
the lead–sheet symbols using quarter–note accompanimental texture.
D
E
A
Below the lower staff, analyze the chords using
Roman numerals
# Bww with
w
#
#
w
w
67
w
figured
& bass
# www
# ww inversion symbols.
w
chro.
DN
PT
C:b V/V LNT PT UNT j V/viPT PT
V/ii
4
˙
˙
& b b C47 œ œ œ . Dœ7 œ œ ˙E7
A7
w
# www
&? b b wwww4
# wwww
# wwww
bb 4
C: V7/IV
Cm
bb
&&b bb b 44
V7/V
V7/vi
Fm
C
n www
# n www
D
D7/F˜
APP
w
V/iii
# # wwww
B7
V7/ii
V7/iii
G
n www
F
V/VII
DN
? b b 44 c: LNTV/IV
APP
PT UNT
(same as IV)
bb bb c
j PT PTœ ˙
˙
˙
7 œ
&
w B¯7
E¯7
F7
476
œC7 œ œ . Dœ_____
Rom. num.: _____
_____
_____ w
ww
b
www
b www
w
w
n
w
n
&?b bb n wwww
# ww
w
w
c
Day Two: 928 b b
b bc: V7/IV
7/III
V7/V dominants.
V7/VI IncludeV7lead-sheet
/VII
Vsymbols
4. Write
following secondary
& b the
(same as VII7)
7
924
Cm key signatures.
Fm
D /F˜
G
above. Include
____
____
____
____
b
481
bb b c
?
&
b
? b
? b b 1.cE¯: V/ii
2. g: V7/VI
3. e: V24/iv
4. A: V6/ii
b
933
5. For
alter the given_____
motives as specified.
Rom.the
num.:
_____ example, _____
_____ Add an
b following
b
accompanimental
texture
of
afterbeats.
Analyze
the
Roman
numerals
b
&
chro.
V/V
PT
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with figured bass inversion symbols below the staff.
928
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67
Chapter 18
Secondary Diminished Chords
69
4
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18.1 Secondary Diminished Chords
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_____
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The vii◦ chord has dominant function (see the Harmonic Function Flowchart).
Since chords of dominant function typically resolve to chords of tonic function, diminished triads as well as half–diminished and fully–diminished seventh
chords occur
diminished
chords. iv
d: i as secondary
III6
VI
III
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4
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Figure 18.1.1 A Harmonic Sequence with Secondary Diminished Chords in
C major
968
&
Below are some examples of pieces with secondary diminished chords. Notice that chromaticism is an “essential” part of secondary diminished chords
(“non–essential” chromaticism refers to chromatic non–chord tones).
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976
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962
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215
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CHAPTER 18. SECONDARY DIMINISHED CHORDS
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(1990)
18.2 Secondary Diminished Chords in Major and
Minor
28
Below are the secondary diminished chords that occur in major and minor.
28
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18.2.2 Secondary Diminished Triads and Seventh Chords in Minor
in minor is not included because it is ii◦ . Notice
also that vii III has no accidentals—it is the same as iiø7 but functions
differently. The iiø7 chord has pre–dominant function and progresses to V
ø7
whereas the vii III chord progresses to III .
Minor triads are tonicized by fully diminished seventh chords. Major triads
are traditionally tonicized by half diminished seventh chords but can also be
tonicized by fully diminished seventh chords.
CHAPTER 18. SECONDARY DIMINISHED CHORDS
204
18.3 Analyzing Secondary Diminished Chords
When you encounter a chord with a chromaticism and suspect it is a secondary
diminished seventh chord, use the following process.
70
1. Stack the chord in thirds to determine the root and quality. If the chord
quality is a diminished triad or a half–diminished and fully–diminished
seventh chord, go on to step 2. If the chord quality is not a diminished
triad or a half–diminished and fully–diminished seventh chord, the chord
is not a secondary diminished chord.
975
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chord.
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G up m2 is A; in D major, A is
(the chord to the right of the slash).
517
b
b
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b
b
&
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2. Determine vii◦7 in the key of C minor (C is the root of the iv chord,
◦7
which is the Roman
518 numeral after the slash): B is the root of vii in C
minor because it is a m2 below C.
3. Build a fully–diminished seventh chord on B: B–D–F–A2
5̂
&b
CHAPTER 18. SECONDARY DIMINISHED
g: viio42/ivCHORDS
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Figure 18.5.1 Freddie Mercury, “We Are the Champions” (1977)
CHAPTER 18. SECONDARY DIMINISHED CHORDS
206
Click here to download the first homework assignment for this chapter.
Click here to download the second homework assignment for this chapter.
Chapter 19
Mode Mixture
19.1 Mode Mixture
24
Mode mixture typically consists of borrowing chords from the parallel minor
during a passage in a major key. “Borrowed chords” refers to borrowing
chords from minor and is synonymous with mode mixture. In the examples
that follow, notice the lowered chromaticisms—26̂ is most common but 23̂ and
27̂ also occur in borrowed chords.
### 6
V
4 œ œ ˙ Ó 44 œ œ œ œ œ œ œ œ
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232
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˙
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235
&
Notice the emotional effect of switching to the minor mode.
A famous example that progresses from the major I chord immediately to
the minor i chord is Richard Strauss’s Also Sprach Zarathustra.
241
V
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207
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# 4
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I6
CHAPTER 19. MODE MIXTURE
235
235
b
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b
œ
œ
V7/V
‰œ œ
is so
œ
œ >œ œ
237
bb
& b
Cm
˙
V7sus4
œ. œ œ
won - der - ful
œœ
œ
bw
I
209
‰ . œr œ œ
œ
E¯7/D¯
3
œ
œ
Then sud - den - ly
œœ
> œ
œ
V24/IV
E¯: I
237
˙
‰.
b
& b b œœ
œ
œ
œ œ œ œ œ
? bb w
b
r
œ œ œ bœ
It's hard
to
breathe
œœ
> œ
vi
YT: f1zLSpzCh9E
Figure 19.1.4 Linda Perry, “Beautiful” (2002)
Fø7/C¯
˙
Ó
b œœ œ œ œ œ œ œœ œ
>
bw
iiø43
210 25
CHAPTER 19. MODE MIXTURE
#
& # 44 œ œ œ œ n œ œ œ
œ
#
& # 44 ‰
nev - er
239
? # # 44 ˙
241
241
&
##
‰
j œ
œ œ
nœ
˙
I64
a
G/B
word he
j œ
œ n œœ
n˙
œœ
œ
him
œ
œ
œ
a
-
drink
œ
œ
j
œ œ
said
¯VI
IV
j
œ
B¯
j
j
b
œ
œœ œœ n œœ
œ œ
j
œ.
bœ
sin - gle
V24/IV
D/A
#
& # œ
? ##
un - der - stood
D: I
helped
j
nœ œ
D7/C
D
239
œœ
œ
œ œ
But
œœ
œ
˙
œ
his
j
œ
wine
œ
œœ # œ
œœ
œœ
nœ
D
#œ
œ
I
œ
I
#
& # ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
243
YT: kyI1OImD7ow
# ∑ ∑ bass
This# same
∑ ∑line∑ can∑ be∑ found
∑ ∑ (in
∑ ∑the∑same
∑ ∑harmonic
∑ ∑ ∑rhythm)
∑ ∑ ∑in ∑“Part
∑
&
of Your World.”
Figure
19.1.5 Hoyt Axton, “Joy to the World” (1970)
243
? # # ∑ ∑ ∑ ∑ ∑ ∑ ∑ YT:
∑ ∑SXKlJuO07eM
∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
Figure 19.1.6 Howard Ashman and Alan Menken, The Little Mermaid, “Part
of Your World” (1989)
In the next example by Radiohead, the iv chord (borrowed from minor) is
preceded by the major IV chord.
A7
Dm
____
____
w
˙
# ˙˙˙ ˙˙˙ ø6 # ˙˙˙ w6 ˙˙
? 44C: ˙˙˙˙wIV
˙ ii 5 ˙ I4 ˙˙
CHAPTER 19. MODE MIXTURE
E7
____
C
____
583
I
C: ____
G
&
#
vi
V7/____
vi
____
B
#____
wwF
C7
ww____
w
wb ˙
˙
˙˙˙
˙˙
˙w
w
ww
w
? 44 ˙˙˙˙
?#
w
587
Am
____
C
____
I
C: ____
G: I
IV
V7/____
IV
____
V/vi
ii
V7/____
ww
w˙
# ˙˙˙
w
E7
____
vi
V7/____
ii
____
C
ww____
wAm
˙˙
˙
w˙
vi
____
IV
D7
____
# ˙˙˙˙
G
w ____
ww
ww
V
V7/____
V
____
Cm
ww____
b ww____
7
wD
wG
ww
# ˙˙˙˙
w
w
ww
V
V7/____
V
____
iv
211
ww
w
w
591
F____
˜o7/A
F____
˜ø7/C
B____
˜o7/A
www
YT: XFkzRNyygfk
?
# www # ColinwwwwGreenwood,
# # # # Ed O’Brien,
w
b
n
w
b
Figure
b b b19.1.7 Thom Yorke,
b b Jonnyn Greenwood,
# n # www
w
Eo7
____
Philip Selway, Albert Hammond, and Mike Hazlewood, “Creep” (1992)
o6/V
1. A¯: viio7
2. in
c: vii
e: band
viiø43/III
Mode mixture
is/vi
also found
the
the
Nirvana. 4. B: viio42/ii
5 music of 3.
595
D5
? # # 44 ˙
˙˙
D: I
F˜5
B5
˙˙
˙
G5
iii
vi
IV
˙˙
˙
˙˙
˙
n bb ˙˙˙
B¯5
¯VI
C5
n ˙˙
n˙
A5
C5
¯VII
V
¯VII
˙˙
˙
n ˙˙
n˙
YT: pkcJEvMcnEg
Figure 19.1.8 Kurt Cobain, “Lithium” (1992)
In the example above for “Lithium,” the Roman numerals are analyzed as
triads instead of “5” chords because the third of the chord is either implied or
occurs in the voice part (not shown).
In the next example from the third movement Brahms’s Third Symphony,
the I chord alternates twice with a borrowed chord. There are three flats in
the key signature because this movement began in C minor, but this section
occurs later in the movement and is in C major.
CHAPTER 19. MODE MIXTURE
Bo7/C (ped.)
C
b
& b b 38 œ n œ
π dolce
‰ œ
? b b 38 œœ ..
b
212
œ
C: I
Bo7/C (ped.)
b b œ A œœ œ œ n œ
b
&
œ
œ nœ œ
œ
‰
? b b œœ b n œœœ
)
b (J
ped. pt.
viio7
b
&bb
C
œ Aœ œ nœ œ
œ
b n œœœ
œ)
‰
œ
(œ
J
‰
œœ .
.
ped. pt.
viio7
nœ
œ
nœ
œ
I
C
C/E
F
Bo
œ œ
œ nœ
œ
œ nœ œ nœ œ
œ
œ
nœ
J
œ nœ œ œ œ
œ
nœ
J
‰œ
œ
I
I6
IV
viio
YT: UH324lgbxaI
Figure 19.1.9 Johannes Brahms, Symphony No. 3 in F major, Op. 90, III.
Poco Allegretto (1883)
alternation between the I chord and a borrowed chord (2 VII )
?A similar
happens
b b bin “Inchworm,” from the movie Hans Christian Andersen. Notice the
26̂
7
special quality of the borrowed
in the upper melody.
73
CHAPTER 19. MODE MIXTURE
23
b
& b b 43 œ œ
Two and
œ
two
? b 3 Œ œ œ
bb 4 œ
ˆ
(6)
bœ ˙
are four,
b 3
& b b 4 Œ ˙˙
˙
? b 3 ˙.
bb 4
E¯: I
œ œ
four and
ˆ
(6)
œ
bœ
four
are
Œ œ œ œ Œ œ œ œ œ œJ
3
Inch - worm,
E¯
213
3
Inch - worm,
meas - ur - ing
the
˙
eight,
œœ œ Œ
3
œ
mar - i - golds,
D¯7
b b ˙˙˙˙ ....
E¯
b˙.
Œ ˙
˙˙
˙.
b b ˙˙˙˙ ....
¯VII7
I
¯VII7
D¯7
b˙.
b
&bb
∑
? b
bb
∑
∑
∑
∑
∑
b
&bb
∑
∑
∑
∑
∑
? bb
∑
∑
∑
∑
∑
27
∑ YT: 6dd6e14ov2c
∑
∑
∑
Figure 19.1.10 Frank Loesser, Hans Christian Andersen, “Inchworm” (1952)
A famous example of mode mixture occurs in the “Waltz of the Flowers”
from Tchaikovsky’s Nutcracker.
b
? b ‰œœ b n œœœ
bb(
J ped. pt. )
œ
œ
œ
œ
nœ
J
CHAPTER
o7 MODE MIXTURE
vii19.
I
#
& # 43
? ##
#
& #
239
443
4
D
dolce cantando
p
œœ
D
œœ
D: I
# D
& # 44 ‰
#
& #
? ## P
44 ˙
? # # D:œœ I
œ
# # D/A
& nIœ
œœ
œœœ
239
241
241
&
##
? ##
helped
œ
˙
I6
C˜o7/D (ped.)
˙
b ˙˙˙
>
viio7
un - der - stood
j œ
œ œœœ
œœ œ
œœ œœ
œ
œ
-
214
œ
œ
I
his
j
œœ
>œr
œ
œ.
word he
IV
j
bn œœ
œ
j
bœ
said
nœ
But
œœ
œœ>
œ
œ
˙˙
˙
˙
f.
œœ ‰ ¯VI j ‰
J Dœ
.
j
I
œ
wine
œ
œœ
œœ
D
œœ # œ
YT: Kw0wLLVEMaA
œ
25
œœ œœ B¯
œœ œœ
œn œj
œ
œ œj œ œ œ
sin - gle
drink
˙˙ ..
˙.
G/B
‰ j œ
- œ >n œptœ
œ
bn ˙œœœ ( œ˙˙ .. )
bœ
œ
V24/IV œ
œ
œ
( )
ped. pt.
j
œ viiœo7 œ
œ
a
nœ
J
viio
IV
œœ ... œœ ˙˙ ..
œœ . œ ˙ .
C˜o7/D (ped.)
him
œœ
a
œ
D
œœ
œœ
D7/Cœœ
œ œœœ
œ œ œ (nœœ)ped.œpt.
œ
nev - er
œœ n œ
œ
#œ
>œœœ
œœ
I
œœ. ‰
J
œ
Figure 19.1.11 Tchaikovsky, Nutcracker, “Waltz of the Flowers” (1892)
A similar melody occurs in “One Day I’ll Fly Away,” which, though it has
a different Iharmonization,
still uses mode mixture.
6
I
4
243
243
# 3
& # 4
D
œ
One
# # 3 ˙˙˙ ...
& 4 ˙.
? # # 43 ˙ .
˙.
D: I
œ
day
œ
I'll
Gm
˙
˙.
b ˙˙˙ ...
fly
˙.
˙.
iv
œ œ
a
D
-
˙.
˙˙ ..
˙˙ ..
way.
˙.
˙.
I
YT: I8eNaVEEtC8
Figure 19.1.12 Joe Sample and Will Jennings, “One Day I’ll Fly Away” (1980)
CHAPTER 19. MODE MIXTURE
215
19.2 Harmonization of Borrowed Scale Degrees
Let us examine the ways 26̂ can be harmonized as root, 3rd, 5th, and 7th of a
borrowed chord.
30
30
b b www
&
b www
b ww
w
b www
w
b ww
ww
b b www
b www
b ww
w
b www
w
b ww
ww
bw
b ww
b www
b b www
b www
b www
C: ¯VI
ˆ
¯6 as: Root
599
&
&
iv
3rd
iio
5th
iiø7
5th
viio7
7th
b ww
b ww
¯VII7
7th
b ww
b ww
Figure
19.2.1 Harmonization of 26̂
605
Here are the ways 23̂ and 27̂ can each
be harmonized
as root,
3rd, and 5th
of
7
C: ¯VIchord (notice
iv some of these
iio chords are
iiø7 duplicates
viio7from the ¯VII
a borrowed
previous
¯6ˆ as: Root
3rd
5th
5th
7th
7th
example).
599
&
613
30
C: ¯III
¯3 as: Root
b b www
i
3rd
¯VI
5th
¯VII
¯7 as: Root
v
3rd
bw
b ww
¯III
5th
b www
b ww
b ww
b ww
b ww
&
w23̂ 27̂ ww
ww
b ww
Figure 19.2.2 Harmonization of and
&It C:is not
611
¯VI
iv
iio
iiø7
viio7
¯VII7
necessary
to
memorize
the
chords
in
this
section
so
much
as to
ˆ
Root
3rd of diatonic
5thchords will5th
realize
the quality
be altered7th
when a scale7th
degree
&¯6 as:that
from the minor mode is included in the chord.
bw
627
www
b ww
b www
b www
b
b www Chords
bw
b
&
19.3
& Analyzing and Writing Borrowed
615
b ww
¯III
i
¯VI
¯VII
v
¯III
& C:secondary
Unlike
chords, you merely note the root, quality, and inversion of a
605
620
599
605
¯3 as: Root
3rd
5th
¯7 as: Root
borrowed chord in your Roman numeral analysis.
So, for the following chord:
611
622
&
615
&
#
b wwww
?
G: ____
#
b wwww
A is root when
stacked in 3rds;
A is 2ˆ
b wwww
3rd
M3
m3
m3
quality is ø7
(m3-m3-M3)
5th
b wwww
iiø65
G: ____
(bass note is
3rd of chord)
Notice that the root is A when you stack the notes in 3rds, and A is 2̂ in
G major. The quality is half–diminished since the 3rds stack as m3–m3–M3,
making this a iiø7 chord. Since C, the 3rd of the chord, is in the bass, the
correct analysis is iiø65 .
To write a borrowed chord from a Roman numeral, be sure to pay close
attention
to the quality of the Roman numeral.
622
A: 2 VI
2 VI is built on 26̂ . Determine 26̂ in A major, which is F6, then stack 3rds
in the configuration M3–m3. The resulting triad contains F6–A–C6.
&
#
A is root when
quality is ø7
stacked in 3rds;
(m3-m3-M3)
A is 2ˆ
216
?
G: ____
CHAPTER 19. MODE MIXTURE
###
615
&
nw
n ww
A: ¯VI
Be careful of flats before Roman numerals. Flats mean to lower a root a
m2 in the key signature, not to literally put a flat in front of the root of a
chord.
#
# # Cadence with 2 VI
19.4 The Deceptive
&
616
26
The V –2 VI deceptive cadence is a deceptive realization of a deceptive progression. This V –2 VI cadence ties into the 2 VI –2 VII – I progression to produce an
“epic” (although somewhat clichéd) ending to the “Star Spangled Banner” as
performed at the Super Bowl and Presidential Inaugurations by artists such
as Whitney Houston, Beyoncé, and Lady Gaga, among others.
b
& b b b 43 œ œ
Dø7 B¯7/D A¯/E¯
246
And
œ.
home
? b b b 43 n œ œ
b
nœ œ
of the
j
œ œ
œ œ
œ.
œ.
A¯: viiø7 V56
I64
F¯6
œ œ œ . 44 w
J
esc. j
œœ .. ( œœ ) œœ
œ . œ œœ
the
b
& b b b 43 n œœœ œœœœ
œ
246
E¯7
V7
G¯add9
brave!
44 ˙
b ˙˙
44 b ˙
b˙
¯VI
U
A¯
w
U
b ˙˙˙
˙
ww
w
U
w
b˙
b˙
w
¯VII
I
vi
250
250
#### 4
&
4 œ œ ˙.
Am
Bsus4 B
E/B
C
D
E
œ w
J
Figure 19.4.1 John Stafford Smith and Francis Scott Key, “The Star-Spangled
##
& # # 44 n œœ (œ )
œ
? # # # # 44 n œ
nœ
œ YT:wKbkWuVUkPmYw
˙ ..
œ w˙ ˙
˙ ˙
w
n n ww
n www
ww
w
Vsus4–3
¯VI
¯VII
I
home
of
the
brave, at the 1991 Super
the brave!
Banner” (1814)And
as the
performed
by Whitney
Houston
Bowl
E: iv6
256
&
####
##
& ##
256
? ####
˙w.
w
( )
œ ˙.
œ ˙.
I46
œ ˙.
œ ˙.
n˙. œ n˙. œ œ w
n˙. œ n˙. œ œ w
∑
∑
∑
∑
∑
∑
iiø
G: ___
(bass n
3rd of
b
œ . ofœj the
œ
nAnd
œ theœ home
esc.
ø7 V6
b b b b A¯:
œœœ5œ œœœI64... ( œœœ ) œœœVœ7
&
43 viiœMODE
œ
CHAPTER 19.n œ
œ vi MIXTURE
j
? b#b #b 43 n œAm œ E/B œ . œBsusœ 4 B
b
& # # 44 n œœ œ œ ˙ . œ . œ œw œ
246
250
A¯: viiø7 V56
250
250
256
of
the
D˜m G˜ø7/D F˜/C˜
U
b ˙˙˙
˙
wwI
w
¯VII
b˙
b˙
44 bC˙
b˙
w
¯VI
C˜7
#### # 4
&
? # # ## 4 œ œ
˙. œ œ
∑
j
œ
home
of
the
# ## # 4
& # # 4 œœ n œœœ
œ œ
˙˙ ....
˙ ..
j
œœ ww
œ w
? # # # # # 44
#
œ nœ
œ nœ
w
w
#
256
V7
44 ¯VI
˙
b ˙˙
U
w
217
wœ w
J
D
˙ ..
¯VII
E
I
# # # # 4 vi
&
4 n œœ (œ ) ˙w. (œ ) w˙ ˙
ww
n Dwww
n wwwC
4 ˙B
w
˙
Am E/B
Bsus
E
œ
n
w
#### 4
œ
w
&
..
? # # # # 444 n œœ œ ˙œ . ˙ . œ wœ ˙ .
n w˙ . œ n ˙˙ . œ Jœ w
w
nAnd
œ the home
n brave,
˙ . œ n ˙ . œ theœ brave!
œ ˙ . of theœ ˙ .
#
#
4–3
¯VI
¯VII
I
& # # 44E: nivœœ6 (œ ) I˙w46 . (œ ) Vsus
w
ww
˙
w
w
˙
n
n
w
w
˙
˙
w
œ
w
nw
w
256
#
#
∑
?
& # ## # ## 44 n œ œ ˙ ∑.
n˙. œ n˙. œ œ w
˙.
YT:œ qGDH18R7GfA
. œ n˙. œ œ w
n œ œ ˙ . Smithœ and
˙ . Francisn ˙Scott
Figure
19.4.2 John Stafford
Key, “The Star-Spangled
256
6 performed
6
4–3 at the
# # #(1814)
Banner”
as
by
Beyoncé
2013
Presidential
E:
iv
I
Vsus
¯VI
¯VII
I
4
∑
∑ Inauguration
& #
And the home
250
I64
w
b brave!
˙ b˙
And
F˜: vi
the
iiø43
I46
˙ œ œ œœ ˙
w
w
V7
brave,
the brave!
D
w
>
>œ>
Œœ œ
n n www
>
Œ >œ œ >œ
brave,
nw
nw
¯VI
E
∑
˙.
F˜
œ w
>
>œ>
Œœ œ
Ó˙
n ww
˙˙
w
>
Œ >œ œ >œ
Ó
˙
nw
˙
nw
¯VII
the brave!
I
YT: GbXSZBnBOQ4
Figure 19.4.3 John Stafford Smith and Francis Scott Key, “The Star-Spangled
Banner” (1814) as performed by Lady Gaga at the 2016 Super Bowl
This same V –2 VI deceptive cadence with 2 VI progressing to 2 VII followed
by I occurs in epic fashion at the end of the animated film Beauty and the
Beast from 1991.
CHAPTER 19. MODE MIXTURE
218
19.5 The Picardy 3rd
It is rare to borrow from the major mode during a passage in a minor key. The
major tonic usually functions as V/iv if it’s not the last chord of a piece, and
raised 6̂ and 7̂ occur naturally as part of the melodic minor scale.
In minor, the one place to borrow from the major mode is at the end of a
piece in minor, with the use of the major I chord instead of minor i .
U̇
œœœœ
œ #œ
œ
œ
œ
3
œ
œ
#
œ
& b 4 œœ œœ œœ œœœ œœ b œ œœ œ œœ# œœ # œœ œ # œœ n œœ œœ œ # ˙˙
72
? b 43 œ œ œ œ
bw
b www
& d: b ww
30
599
&b
C: ¯VI
¯6ˆ as: Root
iv
3rd
b b www
œ œ # œœ
b ww
w
iio
5th
œœ œœ œ œ œ
b www
b ww7
w
Vw
w
iiø7
5th
viio7
7th
U̇
œ
˙
(œ)
b ww
viio7 bIw
w
Picardy
7
¯VIIthird
7th
b www
YT: fTwkVsECg9w
b www
b www
bw
b b www
&
b ww
Figure 19.5.1 J.S. Bach, French Suite No. 1 in D Minor, BWV 812, Sarabande
?While
¯VI
¯VII
v
¯III
the¯III
Picardy 3rdi (the major
third above
the tonic)
was most
comb ¯3C:as:
Root
3rd
5th
¯7 as: Root
3rd
5th
605
monly encountered in the Baroque era, it has been used from then until now,
though with less frequency.
611
&b
C˜o7/B¯
1.
615
#
w
616
634
2.
622
646
b wwww
M3
m3
m3
? ? # ww b b ww # w # # w b w
b # ## b ww b b b b w
# # www # # # n www b b ww
#
n
w
&
n ww
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b wwww
ø7/G
A˜o7/G A is root
C˜lead–sheet
E¯m/G¯
D/F˜ andø6Roman 31
when
ø76 above
Analyze
theC¯following
with
symbols
? ¯III chords
quality
is iv
o4/iii
ø4
6ii/V5
G: V____
viio42 G: ____
vii
ii
2 in 3rds;
stacked
3
numerals with figured bass
inversion
symbols
below.
(m3-m3-M3)
(bass
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ˆ
____
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____
____
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____
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____ 3rd of chord)
____
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5
b b b # n www
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6
b
&the
b ww symbols.
analyze with lead–sheet
w
# # www b b www
? staff,
# # # # and
n www b b wwww____ # # ww____ b b b b ww____ # # ____
w b ____
____
### w b b
##
#
b
b F:b ____ D: ____ E¯:b ____
bB¯:
&
E:
____
A:
____
____
?b
____
____
____the chord
____ on
Given the____
Roman numeral,
key,____
and key signature,
notate
1
A: iv
D¯/F
____
____
2
f: V34/V
A¯/E¯
____
____
3
D: ¯VI
o/E¯
C
____
____
4
F: iiø65
D/F˜
____
____
5
e: viio42/iv
Ao/C
____
____
6
B¯: ¯III
C
____
____
Analyze the
symbols above and Roman
ww following
ww lead–sheet
### b w excerpt
#b# #with
# ww that
w
ww #notes
bb bb b with
b
b b bAnalyze
b
#
?
w
#
numerals
figured
bass inversion
symbols
below.
w
b
b
b
#
n
w
w
#
w
#
nw
&
b
b
b
b
ww
are non–chord
tonesb wby putting parentheses around
them and specifying
them E¯:
by ¯VII
type.
7
ø4
6
o6 ¯III
b: V56N/iv
g: viio7
A¯:
G:Niio6
N6
iiA:
N6/V
viio6ii/VI
3
4
c: ____
e: ____
B¯: ____
c˜: ____
d: ____
b: ____
#
____
& # # ____ b ____ # ____ b ____ # ____
w
b
w
w
b w # b ww b b ww
& # # # www b b b ww
n # www b b ww
w
w
1
f˜: ____
1
2
3
f: ____
2
e: ____
3
4
B¯: ____
4
5
D: ____
5
6
d: ____
6
CHAPTER 19. MODE MIXTURE
74
219
__________
__________
œ.
b
& b b 12
8 œJ
œ œ œ œ.
__________
œ
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œ
œ
œ
J
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œ
œ œœœ
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œ
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.œ
.œ
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*
°
* °
*
°
°
E¯: __________
? bb
__________
espress. dolce
? b b 12
b 8 ‰
b
&bb
__________
nœ
œ
°
œ
J
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œ
*
__________
& 44 www
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__________
___________
œ
œ.
°
œ
œ
œœ
œ
___________
____
____________
œ bœ.
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__________
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œ
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____________
*
œœ
œœ
œ
*
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ww
w
____
Figure
19.6.1
Nocturne
in E-flat major,
Op. 9, No. 2
Rom. num.:
____ Frédéric Chopin,
____
____
____
(1832)
? 44 w
w
Function: Tonic
Mode mixture
Tonic
__________
(with ¯6) ____
____
____
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to download the
homework assignment
for this chapter.
PDF versions of the textbook, homework exercises, and practice exercises
can be found at musictheory.pugetsound.edu
& www
?
w
www
www
w
R.N.: ____
____
____
w
Func.:__________
Secondary of V
__________
__________
____
Chapter 20
The Neapolitan Chord
20.1 The Neapolitan Chord
The label “Neapolitan” is used in classical music for the 2 II chord and is
labeled as “ N ” instead of 2 II . For example, when the Neapolitan chord occurs
in first inversion—its most common inversion—it is labeled as N6 .
Being a chromatically altered ii chord, the Neapolitan has pre–dominant
harmonic function.
Notice the special character of the Neapolitan and how composers sometimes alter texture, register, and dynamics when the Neapolitan occurs, as in
the first movement of Beethoven’s Symphony No. 7, Op. 92.
&
###
? ###
œ œ œ œ œ œ
6 œœœœœœœœœœœœ
8
ƒ
œ
68
œ. œ œ. œ œ
œ.
A
A: I
œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ
œ œ œ œ œ œ œœ œœ œœ œœ œœ œœ
Bm7/D
œœ
j ≈œ œ
œ . œ œ œœ
œ.
œ.
œœ
œ.
œœ
ii65
# # # œœœ œœœ œœœ œœœ œœœ œœœ b œ ..
nœ.
œ œœ œ œ
œ
œ
œ
œ
œ
œ
b
œ
&
#œ.
cresc.
π
œœ œœ n œœb œ œœ œ œœ œ œœ œ œœ œ œœ œ n œœ œ œœ œ œœ œ œœ œ œ œ œ œ
? ###
≈
œ . œ œ œj
B¯/D
N6
##
& #
E7
V7
YT: -4788Tmz9Zo
Figure 20.1.1 Beethoven, Symphony No. 7, Op. 92, I (1812)
? ###
&
###
220
œ
A
ƒ
œ
œ
I
75
cresc.
ƒ
π
œœœœ n œœb œœœœœœœœœœœœœœœœ n œœ œ œœ œ œœ œ œœ œ œ œ œ œ œ
? ###
≈
j
œ œ NEAPOLITAN
œ
. THE
CHAPTER œ20.
CHORD
221
œ
20.2 Examples of the Neapolitan
Chord
6
7
N
##
& ## C
C˜m
3
3
3
V
C˜m/B
3
3
3
I
3
3
œ
œ
œ
œ
œ
œ
œ
œ
œœ œœ œœ œœ œœ œœ œœ œœ
sempre π e senza sordini
? #### C w
w
w
w
c˜: i
&
####
? ####
i42
A
D/F˜
G˜7
C˜m/G˜ G˜sus4 G˜7
C˜m
œ œ
œ
œ œ œ œ œ œ œ nœ œ œ œ #œ œ œ œ œ œ #œ œ œ œ œ
3
˙
˙
VI
3
3
˙
˙
N6
3
3
˙
˙
V7
3
i64
3
˙
˙
V4
3
œœ
œ
7
3
i
YT: bT6WmWVYPhI
Figure 20.2.1 Beethoven, Moonlight Sonata, Op. 27, No. 2, I (1802)
For comparison, play the example above from the Moonlight Sonata
and
4
4◦. 4
◦6
try other pre–dominant chords in its place, like iv ( F m ) or ii ( D
F ),
while noting the difference in effect.
The next example is a well-known movie theme.
CHAPTER 20. THE NEAPOLITAN CHORD
76
& 44 œ . œ œ. œ ˙
œœœ ‰ ‰ œœœ œœœ œœœ ‰ Œ
J
J
? 44 Œ
C:
76
I
C
V7
G7 (no 3rd)
D¯
œ. œ
bœ
œœœœ
b œœ ‰ ‰ œœ œœ œœ œœ ‰ Œ
J
N
D¯
œ. œ ˙.
œ. œ
.
œ
œœ ‰ œ œœ œœ
œ œœ
œ
œ. œ
bœ
œœœœ
Œ
b œœ ‰ ‰ œœ œœ œœ œœj ‰ Œ
J
Œ N œœ
‰ œœ Œ
7
& 44G œ(no. 3rd)
œ œ. œ ˙
œ
œœ ‰ œ œœ
œœ ‰
& œœ
œ
œœœ ‰ ‰ œœœ œœœ œœœ ‰
? 44 Œ
œ J Œ
œJ
? C:Œ
I
œ
œ
œ
& œœ
˙.
œ. œ
C
222
œœ ‰ œ œœ
œœ ‰ œ œœ œœ.
œ
œ
œ. œ
YT: ML-RqsAG09o
œœ ‰ œ œœ
œ
j
&
œ
œ
œ
œ
? Œ
Œ
‰ pre–dominant
As with theœ example from the
œ MoonlightŒ Sonata,
œ try other
œ Œ
Figure 20.2.2 John Williams, Raiders of the Lost Ark, “Raiders March”
(1981)
?
chords V
(like
IV , iv , or iiø65 ) in place of the Neapolitan chord in the example
7
above, and notice the difference in effect.
The next example shows the harmonic progression from main theme of the
recent Star Trek movies.
& b 44 w
ww
Dm
? b 44 w
w
d: i
ww
w
w
w
B¯
ww
w
w
w
VI
ww
w
w
w
E¯
b ww
w
bw
bw
N
ww
w
w
w
A
# ww
w
w
w
V
ww
w
w
w
&b
Figure 20.2.3 Michael Giacchino, Star Trek, “End Credits” (2009) (chords
YT: EO1FZEUbZJE
only)
?b
b 4
w
w
w
w
w
w
bw
w
w
w
d: 20.
i THE NEAPOLITAN
VI
N
CHAPTER
CHORD
4 ww
& 4 # ww
G˜o7/D Am/C
C˜o7/B¯
www
C¯
G˜o7/B Am
w
# www
ww
w
w
w
V
B¯/D
b ww
w
Am/C
ww
w
A˜o7/G
C˜ø7/G
E¯m/G¯
¯III
viio42/iii
iiø43
iv6
E
# ww
w
D/F˜
223
ww
w
? 44 w
w____
w ____w ____w
w
____ w
____
____
w
w
w
? # #w b wwww wb b b b b www # w# ww # # w# # wwww b b ww b b w
b A˜o7/G
# Cw˜wø7/G #E¯m/G¯
n w 6 6 b D/F
w ˜ 6b # n ww
C˜o7/B¯
C¯
6
o4o4
a: vii
vii
i6 ¯III viio6viio4/iiii
N
i iv
V V /V
iiø4
628
viio42
23
D: ____
____
1
628
634
5
A¯: ____
____
2
2
G: ____
____
3
3
B: ____
____
4
31
V6/V
B¯: ____
____
5
c: ____
____
6
www b b ____
bw
? # # b w____
www b b ____
ww b b b ____
# wwww # # # # #____
b b b ww # #____
n www
n
w
b
w
#
b ww
# # wwww b b www
? # # #D:# ____
# # G:rD5wQROo_bs
www b A¯:b ww____
w YT:
w b b b B:b www____ # #B¯:
w
n
____
____
b c: ____
w 2 and Antonius
Figure 20.2.4 w
Hans Zimmer
Tom Holkenborg, Batman v Su1
3
4
5
6
perman: Dawn of Justice, “The Red Capes are Coming” (2016) (chords only)
634
640
E: ____
____
1
F: ____
____
2
“ N ” instead6 of II .
646
2.
N64
G:____
____
2
iio6
B¯: ____
____
3
N6
c˜:____
____
4
viio6/VI
d:____
____
5
&
?
658
664
664
N
b:____
____
6
4
# ww
____
f˜: ____
1
1. E¯: N6
____
b ____
b ww
w
n # ww
____
b ww
____
f: ____
e: ____ B¯: ____
2
3
4
2. a: N
3. D: ¯III 4. c: viio7/V
____
____
____
w
____
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5
5. B¯: iiø4
____2
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____
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Click here
download the
homework____
assignment
for this chapter.
& to ____
658
B¯: ____
____
6
o6/VI D: ____
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____
f: ____
e: ____
____
____
____
____
N6 the
N6 numeral,
iio6 please
N6theB¯:
viiof
N andd:
____
____
____
____
Given
write
notes
the chord
lead–sheet
#
1
2
3
4
5
6
#
#
#
symbol.
# Include
# w key
b b b signatures. ww b b b w # b www b b w
&
652
A: ____
____
5
bw
? b b ww # b ww b b b www # # # # n ww b b www # # n www
____
____
____
____
____
b ____
w
# # # # w b b bbw
# ww b b bww # # b www b b w
& c: ____
ww d: ____w b: ____
w
n # ww c˜:b ____
# ww G:b____b www B¯: ____
w6
1
2
3
4
5
N
____
c: ____
1
640
652
E¯: ____
____
4
ww # # ww b b www
# b ww b bD/F
w ˜ # ____
A#ow
/Cw
C
b b ____
b ____
b ww
ww and
b www____lead–sheet
# # ____
www
? b b E:the
w____following
# F:b ww____
# #E¯:
# #B¯:Roman
Analyze
chordsb D:
with
A:babove
____
____
n wwwsymbols
w
n
b
b
b
numerals with
symbols
to6 use
1 figured
4w below.o Remember
5
b w 2bass Cinversion
o/E¯ 3
D¯/F
D/F˜
A /C
C
2A¯/E¯
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w
b wwww # C____
ow
# #____
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A¯/E¯
/E¯
20.3 Practice
____
1.
646
D: ____
____
3
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3. D: ¯III
1. E¯: N6
2. a: N
1. c˜:____
N6
7
2. b:____
N
3. G: ¯VII
____
w
w
____
d: ____
6
6. G: N6
____
____
4. c: viio7/V
5. B¯: iiø4
6. G: N6
o6/V
4. d: vii
____
5
5. F:____
N46
6. f˜: ____
N6
2
3 + 3 + 3 + 3 + 3 +
3 + 3
+ 3 +2+2 +2+ 2
3 + 3 + 3 + 3 + 3 +
3 + 3 + 3 +2+2 +2+ 2
123 1 2 3 1 2 3 1 2 3 123 1 23 1 2 3 1 2 3 12 1 2 1 2 1 2
>
#1.# c4˜: N>œ6. >œ ‰2. b:>œ N œ >œ 3.‰ G:>œ¯VII
. >œ7 ‰4. d:>œviio65œ/V>œ ‰5. F:>œN46>œ >œ6.#fœ˜: Nœ 6
& 4
J
J
123 1 2 3 1 2 3 1 2 3 123 1 23 1 2 3 1 2 3 12 1 2 1 2 1 2
# # 4 >œ . >œ ‰ >œ œ >œ ‰ >œ . >œ ‰ >œ œ >œ ‰ >œ >œ > >œ
œ #œ
& 4
J
J
31
Chapter 21
Augmented Sixth Chords
21.1 Augmented Sixth Chords
Augmented sixth chords are a special class of pre-dominant chords with
notes that approach the dominant (5̂ ) from a half-step below (44̂ ) and from a
half-step above (26̂ ) simultaneously.
705
707
˜4ˆ
? #˙
b ˙
?
C: ¯6ˆ
5ˆ
˙
˙
5ˆ
˜4ˆ
b b b # ˙˙
c: ¯6ˆ
5ˆ
˙
˙
5ˆ
Figure 21.1.1
In minor, 26̂ doesn’t require a flat because 6̂ is lowered in the minor key
signature.
?
714 of Augmented Sixth Chords
21.2 Types
There are three general types of augmented sixth chords—the Italian augmented sixth chord (“ It+6 ”), the French augmented sixth chord (“ Fr+6 ”),
and the German augmented sixth chord (“ Ger+6 ”). These geographic labels have persisted
722 throughout the years despite the fact that no reasoning has
been found for these designations. 1
All types of augmented sixth chords contain scale degrees 26̂ and 44̂ . To
these two scale degrees, the It+6 adds 1̂ . The three notes of the It+6 (26̂ , 44̂ ,
and 1̂ ) form the foundation of the Fr+6 and Ger+6 . The Fr+6 adds 2̂ to the
26̂ , 44̂ , and 1̂ , and the Ger+6 adds 23̂ to the
Italian augmented
730 sixth chord’s
26̂
44̂
Italian’s , , and 1̂ , as is shown in the example below.
?
?
1 The 1964 Harvard Dictionary of Music states these chords are “rather pointlessly. . . distinguished as ‘Italian,’ ‘German,’ and ‘French’ sixth. . . ”
?
738
224
33
C: ¯6ˆ
c: ¯6ˆ
5ˆ
5ˆ
CHAPTER 21. AUGMENTED SIXTH CHORDS
#w
b ww
707
&
705
711
5ˆ
˜4ˆ C: It+6
711
714
718
1
¯6
# w
b www
˜4
2
1
¯6
ˆ
Fr˜4+6
? # ˙ ˙ bb # ˙ ˙
bb ˙ ˙ # ww b ˜4 ˙ ˙ # www
w ¯61
w
&bb
ˆ
C: ¯6ˆ
707
˜4
b
&bb
&
714
˜4
2
1
¯6 5ˆ
c: ¯6
Fr+6
5ˆ
c: It+6
#w
b ww
5ˆ
# w
b www
225
b # www
b w
˜4
¯3
1
¯6
Ger+6
# www
w
# b # wwww
˜4
˜2
33
1
¯6
EnGer+6
˜4
Ger+6
¯3
1
¯6
b b # wwww
# b # wwww
Figure 21.2.1 The Three Types of Augmented Sixth Chords in Major and
Minor
˜4
˜4
˜4
˜4
2
¯3 +6
+6 ˜2
The final chord on the
German1
or EnGer —respells
1 first line—the Enharmonic
1
6
+6 1
the 23̂ as a 42̂ because ¯6
the EnGer+6 resolves
¯6 only to major¯6I4 . The EnGer ¯6
does not occur in+6minor.
+6
+6
+6
b
C: It
Fr
Ger
& bb b Analyzing
21.3
˜4 Sixth
˜4
# w ˜4 Augmented
# w
# ww Chords
729
EnGer
2
ww 1
www
ww ¯31
bb
&
1
¯6
Since our process for analyzing
chords has been to stack them up in thirds to
¯6
¯6
determine the root
and quality, it is +6
worth examing these
four augmented sixth
c: It+6
Fr
Ger+6
735
chords
as stacks of thirds.
b
&bb
&
b
& bb b
&bb
741
# b www
o3
C: It+6
# www
# b wwww
o3
Fr+6
# wwww
b #b wwww
o3
Ger+6
www
#w
# # b wwww
o3
EnGer+6
(don't forget about the key signature when in minor)
c: It+6
o3
Fr+6
o3
o3
Ger+6
b b that all augmented sixth chords contain a 3 when stacked in 3rds.
Notice
b
&
None of the chords we have studied so far contain diminished thirds.
Figure
21.3.1 Augmented Sixth Chords Stacked in Thirds
721
◦
Principle 21.3.2 Augmented Sixth Chords. When you encounter a chord
with a diminished third, it is an augmented sixth chord.
◦
741 Once you determine the chord you are analyzing has a 3, analyze the scale
degrees to determine which type of augmented sixth chord it is.
b
&bb
21.4 Lead-Sheet Analysis of Augmented Sixth Chords
When using lead-sheet symbols for augmented sixth chords, we will treat them
as major-minor seventh chords built on 26̂ , since that matches the sonic quality of the augmented sixth chords and is similar to how they occur and are
spelled in jazz and popular music. The chords in parentheses are enharmonic
respellings of the three augmented sixth chord types.
www
ww o
# ww 3
# w o3
CHAPTER 21. AUGMENTED SIXTH CHORDS
&
721
bbb
w
# ww
(don't forget about the key signature when in minor)
o3
c: It+6
#w
& b ww
C: It+6
Fr+6
b ww
(b w )
A¯7 (no 5th)
226
Ger+6
# www ∫ b www
b w ( b w)
b b www
( bw
b # www
b w
A¯7(¯5)
Fr+6
A¯7
Ger+6
)
b
&bb
Figure 21.4.1 Augmented Sixth Chords Stacked in Thirds
727
In the example above, we see a disagreement between “classical” analysis
and lead-sheet analysis. The fundamental concept of lead-sheet analysis is
to show root, quality, and inversion. The “classical” spelling and the classical analysis of augmented sixth chords show the direction of resolution (with
the chromatically raised notes), which necessitate the need for original labels,
since we don’t have a Roman numeral or a lead-sheet symbol that would communicate a chord containing a diminished third above the root (that is then
inverted!).
Therefore, when you are asked to provide lead-sheet symbols for augmented
sixth chords, analyze each one as if it is a dominant 7th chord with a misspelled
2
2 4
2
2 2
7th (A –C–E –F instead of A –C–E –G ).
21.5 Examples with Augmented Sixth Chords
21.5.1 The Italian Augmented Sixth Chord
The first examples, from the first movement of Beethoven’s Fifth Symphony,
shows an Italian augmented sixth chord ( It+6 ) in C minor with the “classical”
spelling.
bb 2 œ œ œ
b
& 4
˙
‰ œ œ œ
˙
? b b 42 ‰ Œ
b
b b œ œœ œœ
b
&
œ œ
j
œ cresc.
? b b n œ n œœ œœ
b
b
&bb
œœ
œ
œ
œ
i
˙
n˙
˙
œ˙ œ œ œ
A¯7(no 5th)
Cm
œœ
œ
f
œ
œ
œ œ œ œ
Œ
# œœœ
Œ
Œ
œ
œ
U̇
G
nœ
œ
œ
œ
Œ
It+6
Œ
u
U
Œ
V
YT: _4IRMYuE1hI
Figure 21.5.1 Beethoven, Symphony No. 5, Op. 67, I (1808)
?Theb b next example from popular music has an It
b
+6
b
&bb
spelled enharmonically
77
CHAPTER 21. AUGMENTED SIXTH CHORDS
227
29
as a major-minor seventh chord with the fifth omitted.
279
78
279
# c Em
Œ œ œj œ .
&
# c
&#
& c Œ
œ Œ ‰ œj œ
thing
if it
283
283
&
#
C7
∑
## b ˙ ∑
&
&
7
Em
œ
ain't
got
that
swing
Em
3
3
?# c
? # c Œœ # # œœ œœ. œ‰ # ##œœœ ˙˙ œ œ œ˙ œ
J
e: i
3
3
j B
œ œ œ
j
∑ 3 b ˙˙ 3 3 œ . 3n œœœ œœœ3
j
Œ œj œ Œ j œ ‰ œ œ ‰# œ .œ. ‰ œ œ ‰ œ
# œ œ.
. #œ . .
.
Don't mean a
∑
Œ
bœ.
C7
∑
∑
e: i
∑
œ Œ# œb
œ œ
It˙+6
V7
∑
3
b œ œ. œ b œ
œ œ ‰b œ
J
3
i
∑
YT: LYfF9VKMp4w
œ œ œ∑
Ó
œ (œ ) œ ∑
3
∑
∑
∑
∑
∑
∑
∑
œœ œœ œœ
œ. # œ. œ.
∑
œ. œ. œ.
∑
∑Gm
˙˙œ # œ n œ œ œœœ
∑
∑
œ
˙
3
Figure 21.5.2 Duke Ellington,
“It Don’t Mean A Thing (If It Ain’t Got That
(
)
Swing)” (1931)
? # ˙˙ ∑
21.5.2 The French Augmented Sixth Chord
˙
∑
˙
∑
The next example contains an example of a French augmented sixth chord
( Fr+6 ). Notice how the French augmented sixth chord has pre-dominant funcGer+6
tion and intensifies
the drive toward the V chord.
#
& b
&b
289
#
&
? bb
289
?#
&b
∑
2 œ
4 œ
π
∑œ
24 œ‰
g:
b
∑
∑
∑
œœ œœ œœ œœ œœ œj ‰
. . . .
œ. œ. œ∑. œ. œ œ∑j
œ œ œ œ œ. œ œ
Gm
i
∑
∑
F˜o7/E¯ E¯7(¯5) D
# œœœ
.
œ.
∑
viio42
Fr+6
∑
V
∑
i
YT: xti0xkrIZjQ
? bb
Figure 21.5.3 Schubert, Winterreise, D. 911, “Der Wegweiser” (1823)
21.5.3 The German Augmented Sixth Chord
The following example, from Rossini’s William Tell Overture, has a German
augmented sixth chord leading to a chord of dominant function, the I64 chord.
? bb
b
nœ œ œ
œ
œ
œ
Œ
Œ
It+6
CHAPTER 21. AUGMENTEDi SIXTH CHORDS
n˙
œ œ nœ œ
#
n
˙
œ œ nœ œ
## # 2
&
4
S
j
˙
œ
n˙
nœ
? # # # # 42 n ˙œ œ œ œ n œœ ‰ Œ
J
C/E
E: ¯VI6
œ
œ
Œ
V
#˙
#˙
E
S
˙
# ˙˙œ œ œ œ
I
228
œ œ œ
œ œ œ œ
œ
j
œœ
œœ ‰ Œ
J
œ nœ œ œ œ
˙
œ #œ œ œ #˙
œ nœ œ œ œ
œ #œ œ #˙
#### ˙
J
œ
&
S
S
j
j
j
˙
œ
œ
# œœ
? # # # # # ˙˙œ œ œ œ # œœœ ‰ Œ
n n n ˙˙œ œ œ œ n n œœœ ‰ Œ
œ
J
J
J
C˜
V/ii
C7
Ger+6
E/B
I64
YT: oGPys3sKBHw
Figure 21.5.4 Gioachino Rossini, William Tell Overture (1829)
John Coltrane’s minor blues, “Mr. P.C.,” contains a German augmented
sixth chord (spelled as VI7 in minor) progressing to the V chord. (Note: The
bass line in this example is a jazz “walking” bass, which doesn’t stick strictly
to chord tones.)
bw
w
IV7
¯VI
CHAPTER 21. AUGMENTED SIXTH CHORDS
229
b
j
& b b c œ œ œ b œ ‰ œ . œ . b œ ‰ œ œj œ œ
A¯7
Cm
275
275
b
&bb c Ó
G7
b ˙˙˙˙ ....
? bb c
b œ œ
œœœ n œœœ
œ œ
œ œ
œ
œ
B¯
Œ œ Œ
œœ
Cm
œ œœ
˙
j
œœ .. œœ
œ. œ
˙˙
˙
œ œ
nœ œ
Ger+6
c: i
Cm
œ œ nœ bœ
V
i
VII
i
YT: oHDsywpCHj4
Figure 21.5.5 John Coltrane, “Mr. P.C.” (1959)
The next example is a movie theme and features a German augmented
sixth chord spelled as a major-minor seventh chord ( VI7 ). In this particular
case, the third of the chord doesn’t occur until the fourth beat of the measure.
78
#
& c Œ
Em
Œ
3
3
3
j
Œ œj œ Œ j ‰ œ œ ‰ œ œ. ‰ œ ‰ œ
œ.
# œ œ.
. # œ œ. .
.
? # c Œ # # œœ œœ ‰ # # œœ ˙˙
J
˙
3
3
3
3
e: i
˙
3
3
b œ œ. b œ
Œ b œJ œ ‰ b œ
3
3
C7
#
& b˙
? # ˙˙
Ger+6
&
#
œ ( œ) œ œ œ Ó
(œ )
3
˙
3
˙
YT: KEt_FkMkaO4
Figure 21.5.6 Henry Mancini, “The Pink Panther Theme” (1963)
Fiona 3Apple’s “Criminal,” from 1996, features German augmented sixth
? # #Œœ#œœj
&
#
CHAPTER 21. AUGMENTED SIXTH CHORDS
28
271
chords in the verse ( F7 in the key of A minor) as well as in the pre-chorus,
seen in the example below.
C
I've come to you
?c œ œ œ
œœ œ
C: I
273
273
A¯7
B¯
& c ‰ œj œ . œ œ œ b œ œ œ œ .
&c ˙
˙
271
230
'cause I
b ˙˙˙
bœ œ
bœ œ
¯VII
need
œ
œ
F7
& bœ œ œ œ œ œ œ. œ œ œ œ
don't
& b www
?
w
w
IV7
know
where I
can
be - gin
G
œ œ œ bœ œ œ. œ œ œ
gui - dance to be true
b b ˙˙˙
n œœ ..
œ.
b˙
b˙
˙
˙
Ger+6
A¯
œ bœ. œ
w
bw
j
# œœ
And I just
V
‰ bœ œ œ œ
œ bœ
Ooh
bw
bw
¯VI
&∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
275
YT: FFOzayDpWoI
Figure
21.5.7 Fiona Apple, “Criminal” (1996)
275
A repeating
∑ ∑ ∑progression
∑ ∑ ∑of Am
∑ – F∑7 – E∑ ( i∑– Ger∑+6 –∑V in∑ Roman
∑ ∑ numerals)
∑ ∑
&
occurs in “Friend Like Me” from the movie and musical Aladdin.
?∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
YT: 0HdwdptrmQQ
Figure 21.5.8 Alan Menken and Howard Ashman, Aladdin, “Friend Like Me”
(1992)
21.5.4 The Enharmonic German Sixth
In the following example an “Enharmonic German augmented sixth” chord
2
2 2 2 2
occurs. While a G 7 chord would normally have the notes G –B –D –F , the
F2 is respelled as an E6, creating the interval of an augmented sixth, while the
fifth of the chord, D2, is respelled as a C4, creating the interval of a doubly
284
b œœœ
b
& b
Christina Perri jar of Hearts
œnœ œ œ
œ œ œ.
œnœ œ œ
œ
œ
œ
œ
œ œ œ œn œ œ œ
œ œ œ œ œ œn œ231œ
œ
œ
CHAPTER 21. AUGMENTED SIXTH CHORDS
œ œ œnœ œ œ œ bœ œ œ œnœ œ œ œ œ œ œ œnœ œ œ œ bœ œ œ œnœ œ œ œ
œ
? b
bb
augmented fourth. In fact, some music theory textbooks refer to the Enharmonic German augmented sixth chord as “the chord of the doubly-augmented
fourth.” The spelling is this way because the C4 will resolve upward to a D6,
the third of a major I64 chord.
288
288
b 6
&b 8
G¯7
b 6
& b 8 ≈ œ nœ #œ
p
? b b 68
b˙.
B¯:
B¯/F
∑
Œ
F7
‰ Œ
œ
œ bœ
EnGer+6
p
j
œ œJ . œR œJ
≈ nœ #œ œ bœ ≈ œ œ œ œ ≈ œ œ œ
œ
œ.
I46
B¯
Am
œ.
œ
V7
leuch - ten - den
≈œœ
œ œ.
œ
œœ
I
YT: PMFUeLdhhuM
Figure 21.5.9 Robert Schumann, Dichterliebe, Op. 48, “Am leuchtenden
Sommermorgen” (1840)
21.6 Distingushing Between Chromatic Harmonies
The following table provides a brief synopsis of what to look for when analyzing
chromatic harmonies.
Table 21.6.1 Distingushing Between Chromatic Harmonies
Chromatic Chord Type
Secondary Dominant
Secondary Diminished
Mode Mixture
Neapolitan
Augmented Sixth Chord
What to look for
QUALITY—M triad or Mm7
QUALITY— ◦ , ◦7 , ø7
ACCIDENTALS—lowered notes
2II
◦
3 interval
Chord Labels
V/ , V7/
vii◦ / , viiø7 / , vii◦7 /
ii◦ , iiø7 , iv , vii◦7 , 2 VI , etc.
N
It+6 , Fr+6 , Ger+6 , EnGer+6
21.7 Descending Chromatic Bass Lines
A common musical pattern is the descending chromatic bass line (1̂ –7̂ –27̂ –6̂
–26̂ –5̂ ). Composers harmonize descending chromatic bass lines with all manner
of harmonies, including secondary chords, borrowed chords, augmented sixth
chords, and rarely-used diatonic chords. Below are some examples from the
past four centuries.
CHAPTER 21. AUGMENTED SIXTH CHORDS
232
30
23
291
291
b
& b b 3243 ˙œ œ˙ ˙œ
b œ˙ ˙ ˙ n ˙ œ œœ . œ œ . œœj # œ . b œœj # w ˙
J
7
ˆD /F˜
(6)
Gm
G7/F
C/E
D7
Cm/E¯
ˆ
(6)
b
?
œœ œ
& bbb 3243 wŒ œ œ ˙œ Œ w œ ˙œ Œ w˙œ œ œ œ œJ
w œ
w
˙ œ ww Œ
b ww
˙
3
π Inch - worm, w Inch - worm, meas -3ur - ing the mar - i - golds,
˙ # w7 n ˙˙ n ww
? b b 32 E¯
b ˙˙ D¯7 ww
D¯
E¯
b 3w
Œ ˙
& b b 4 Œ ˙˙
˙
˙˙ .. 7
.
˙˙ 6
b
˙
.
6
4
b
˙
g: i ˙
V
ivb6b ˙
˙ .. V2/iv IV
˙ .. V
295
? b 3 ˙.
˙.
b˙.
b˙.
& b b ∑4 ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
Two andI
When
two
am
are
laid,four,
am four and
laid
four
in are
eight,
earth,
3
E¯: I
¯VII7
I
¯VII7
21.7.1 Henry Purcell, Dido and Aeneas, Z. 636, “When I am laid in
earth” (Dido’s Lament) (1688)
YT: s-F19lgB0Ow
b
&b ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
295
Figure
27
# 3 Ó
˙ ˙ ˙
?
& b b 2 ∑ œ œ∑ ˙˙ ∑# ˙Ó ∑ ∑˙Ó ∑n œ˙ œ∑# ˙˙ ∑ # œw∑# œ ∑ #∑˙ ∑ ˙ . ∑ # ˙ ∑œ ˙˙∑
cru - ci
-
fi
fi - xus,
b
?
& #b 32 ∑ ∑
310
b
& #b
& 32
? #b b 3
?
2
310
-
xus
cru - ci
∑
∑∑
-
e - ti - am
pro - no
fix
us
-
e
∑.
∑ ˙ ˙ ∑˙
Ó
-
-
ti - am
˙˙ ∑ ˙˙
cru
cru - ci
-
fi
bis
-
-
A˜o7/E∑ B/D˜ Dm7∑G˜o7/D A/C˜
∑ Am/C C7(¯5∑) Em/B B
˙˙ ∑
˙
˙˙ n ˙ n ˙˙
˙˙ ˙ # ˙˙ ˙˙ # ˙˙
˙ ˙˙ # # ˙˙
˙
#
˙
˙
n˙
˙
Em
ci
xus,
∑ B˙7
˙˙˙
∑ œ œ œ œ∑ # œ œ n œ ∑œ œ œ ∑
∑
∑
#œ œ nœ œ œ œ œ œ œ œ œ œ
œœ
e: i
viio43/V V6
vii7 viio43/iv IV6
iv6
Fr+6 i64
V
7
YT: hY7CGrR6sPc
Figure 21.7.2 J.S. Bach, Mass in B minor, BWV 232, Crucifixus (1733)
705
718
4ˆ
œ Itœ+65ˆœ œ n œ œ œ œ bFrœ +6œ˜4ˆœ œ n œ 5œˆ
? b b˜ 44C:
? # ˙b ˙ b b # ˙ ˙
œ œ n œ œ œ œ b œ œ œ+6œ
EnGer n œ œ
œ +6 œ
Ger
b ˙ (don't
b ˙ ˙ key signature when in minor)
bb b ˙ wwforget about the
w
&
#w
# wwww
# www
CHAPTER 21. AUGMENTED
SIXTH6 CHORDS
c: i
V6
i24
IV
i
V6
ˆ
o3
c: ¯6 o3
5ˆ
C: ¯6ˆ
5ˆ o3
+6
G/B
C7/B¯ GerF/A
c: Cm
It+6
Fr+6
707
721
727
714
718
730
(b w )
¯6
? bC:
b It43+6C:˙˙˙ ...It+6 n ˙˙˙ ...
b
A¯7
b w
5
( b w)
¯6
˙.
b n ˙˙˙ ...
+6
Fr+6
. +6
˙Ger
n ˙˙ ..
b¯61 w
Cm/G
( bw )
Ger#+6
˙˙ .. EnGer+6
b ˙˙ ..
1
¯6
j
œœ ‰
œœ
7/G˜
˜4
˜4
# www VAm/G
#IV
Fmaj7i6
6
4/iv
b Amc: #i ww ˜V14C+maj
www6 D/F˜
Ger+6
¯3
4
2 2
b
b
w
w
w
&
1
1
¯6
œ ¯6
œ œ œ+6 œ¯6 œ
‰
œ
+6
œ
c: It
Fr
œGer+6## œ˙ œ œ œ n œœœœ
V&44b b b˙ œ
#˙ œ
n˙
YT: UoWXRlw9vBA
b w IVWoO
w
w
M4
6
Figure
III+ 3 32
i4 inb C
& a: i21.7.3
o3
o3 2
# b wwBeethoven,
# b wwwVariations
# wwwminor,
o3
#80# b wwww(1806)o3 VIM7
+6
+6
? b b C:
It+6
Fr+6
Ger
EnGer
Gm/F
C7/E
E¯
j
j
b Gm
œœ ‰ forget
œ œabout
œœ œœ œ when Œin minor)
œœ œœ œ Œ œœ œœ œ
œ œ theŒ key‰ signature
b 4 (don't
œ
œ
œ
b
b
w
V b b 4 œ œww o œ œ œ wwœœ o œœ œœ nwwœœ œœ o œœ œœœ b œ œœ œ œœ
&
#w 3
# ww 3
#w 3
g: c:
i It+6
721
233
IV6
œ œ.
b 3 Œ œ .. A¯
œ 7 (no
œ. ‰ 5th)
œ n œ. ‰A¯œ ..7(¯5)
œ n œ œ # œJ. ‰ œ œA¯b œ7n œ œJ ‰
œ
œ
b
n
œ
‰
R
b
n
œ
J
.
& 4 # w R 4J œ #œ w
J
# ww b ww b ww ˜1 b www# www ˜∫124bbbwww# wwww œ . b ¯3˜4# www ##bœ#.wb wwwb www ˜˜24
& b w
711
i42
#w
& b ww
4 +6
iFr
2
b ww
(b w )
A¯7 (no 5th)
6
Ger
IV+6
5
# www ∫ b www
b w ( b w)
A¯7(¯5)
YT: VJDJs9dumZI
VI
b b # wwww
b bb wwww
(
A¯7
)
+6
C:21.7.4
It+6 George Harrison,
Fr+6
GerWeeps”
Figure
“While My Guitar Gently
(1968)
Am
727
C+maj7/G˜
Am/G
D/F˜
œ
‰
œ œ œ œ œ œ
œ
œ ## œ˙ œ œ œ
V 44 ˙ œ
#˙ œ
n˙
a: i
III+M43
i42
IV6
Fmaj7
œ
n œœœ
VIM7
730
V
YT: iXQUu5Dti4g
Figure 21.7.5 Jimmy Page and Robert Plant, “Stairway to Heaven” (1971)
g:
viio42
i
Fr+6
V
i
CHAPTER 21. AUGMENTED SIXTH CHORDS
30
291
291
234
D¯maj7(˜11) Fm
G7/F
C/E
b
& bb bb b3 c œœ œ˙œœ œ ˙œœ œ œœ œ˙ n œœ˙ œ nœœ˙ œ b œœ œœ. œœœœœ
& 2 ˙
J .
Fm
Gm
Cm/E¯
Dø7
D7/F˜
œœj œœ œœœj œœœ Ó œœœ
œ œ# œœ. œ œ# ˙ œ
When
I
am
# # # # c Cœ˜mœ Œ
V
laid,
am
laid
in
Œ
##
V ## œ
C˜7/B
on a
what
297
I
V7
Sun - day af - ter - noon
V6
œ
iv6
‰ œ œ # œ œ œ œ œ œ œ œ . ‰ œj
c˜: i
297
earth,
G˜/B˜
r
# # # # œ œ . œœ œ œ œ œ œ œ
c œ œ‰ œ ≈œ œ œ œ œ œ œ œ
V
œ œ œ œ œ œ œ œ œ #œ œ
t # # # # c œ œ ‰ . œr ≈ œ œ œ œ œ
œ œ #œ œ
Wait - ing
295
D7
? b b b3 c
j
j
j
& b 2 wœ . œ ˙œ . œ w n œ . ˙ œj b œ .w˙ œj œ . œ œ . wœœ œ
w
w
˙
w
ww
˙
6
ø7
M7
f: i
v
˜vi
VI
i
π
w
ww
˙ # w n ˙˙ n ww
? b b 32
b ˙˙
w
89dGC8de0CA
6
g: i
VYT:
V24/iv
IV6
Figure 21.7.6 Steven Tyler, “Dream On” (1973)
295
Cm/E¯
nœ œ œ œ œ œ #œ
read be - tween
# # # # œ œ ‰ . œr ≈ œ œ
V
œœ œœ œœ
# œœ œœ
the
lines
For
‰ . # œœœ ≈ œœ œœ œœœ œœœ œœ
œ
R œœ
‰ . œr ≈ œ œ œ œ œ œ
A˜ø7
j
œ œ.
Œ
r
œœ œœ œœ œœ œœ œœ ‰ ≈ œœ ≈ œœ œœ
œ œ œ œ nœ œ
œ œœ
r
t # # # # œ œ ‰ . œr ≈ œ œ œ œ œ
#œ œ ‰ ≈ œ ≈ œ œ œ
œ
œ
˜viø7
V24/iv
YT: yjJL9DGU7Gg
Figure 21.7.7 Robert DeLeo and Scott Weiland, “Interstate Love Song”
(1994)
CHAPTER 21. AUGMENTED SIXTH CHORDS
235
79
Cm
b
œ
& b b 44 œ
? b b 44
b
G/B
œ œ nœ œ œ
Cm/B¯ F/A
Cm
œ œ œ œ œ œ œnœ œ œ œ
G/B
œ œ nœ œ œ
Cm/B¯ F/A
œ œ œ œ œ œ œnœ œ
œ œ œ œ nœ œ œ œ bœ œ œ œ nœ œ œ œ œ œ œ œ nœ œ œ œ bœ œ œ œ nœ œ œ œ
c: i
V6
b
& b bb
i24
IV6
i
V6
i42
IV6
YT: 8v_4O44sfjM
Figure 21.7.8 Christina Perri, “Jar of Hearts” (2010)
? bb b
b
Below is a table comparing the harmonizations of these descending bass
lines.
Table 21.7.9
Bass Line
Purcell
Bach
Beethoven
Beatles
Led Zeppellin
Aerosmith
S.T.P.
Perri
1̂
i
i – vii◦43 V
i
i
i
i
i
i
7̂
V6
V6
V6
III +M
V6
V6
27̂
iv
vii7 – vii◦43 iv
V42 iv
i42
i42
i42
4
V2 iv
i42
V42
4
3
6̂
IV6
IV6
IV6
IV65
IV6
4 viø7
4 viø7
IV6
26̂
6
iv
iv6 – Fr+6
Ger+6
VI
VIM 7
VIM 7
( VI )
For the harmonization of scale degree 6̂ , remember that the concept of 4 vi◦
was introduced when Roman numerals in minor were introduced. The notes
of the 4 viø7 chord belong to the melodic minor scale.
21.8 Chromatic Pre-Dominant Chords
The table below shows how our study of chromatic harmonies in recent chapters includes the chromatic expansion of the pre-dominant harmonic function
category.
Table 21.8.1
Ton.
I
Ton. Prol.
iii
vi
Pre-Dom.
IV
ii
V/V
vii◦ /V
iv
iiø7
N6
+6
It , Fr+6 , Ger+6
Dom.
vii◦
V
Ton.
I
5̂
V
i64 – V6
i64
bb
w
b b b n www
ww
# # www b n ww
#
Ger+6 e: ____
N6
It+6
Fr+6
g: ____
B¯: ____
c˜: ____
CHAPTER 21. AUGMENTED SIXTH CHORDS
672
32
1
____
672
684
699
2.
____3
____4
# w
# www Include
sheet
? # symbol.
b ww signatures.
# b www
b b key
# b ____w b b ∫ ____
w
D: ____
1
A¯: ____
2
G: ____
3
1. c˜: Fr+6
2. F: It+6
____ 5
1. E¯:7 It+6
2. a: 8Ger+6
____
____
##
#
# # # # n # www ____
b b www
# n w b b # b n wwww b____
w
____
B: ____
4
3. G: EnGer+6
B¯: ____
5
4. a: viio65/V
c: ____
6
5. d: Ger+6
#
b n wfirst
Click here #to download
homework
assignment
www ____
#____#this
# ww____
w b b bthe
b b b ww for
wwww chapter.
b #____
nw
____
&
w
b
w
Click here to
download
the
second
homework
assignment
for this chapter.
w
w
b www
w
? here to download the Unit 4 Practice Test.
Click
f˜: ____
f: ____
G: ____
g: ____
b: ____
F: ____
?
&
1. 6.
c˜:f:FrN+66
1. E¯: It
1. E¯: N6
F¯/A¯
____
? b b b ww
bb w
1. E¯: N6
3. 9D: EnGer+6 10 4. c: V43/V 11
____
B¯
____
## n w
b b b # n wwww
w
n
w
2. a: Ger+6
3. D: EnGer+6
2. a: N
3. D: ¯III
7. A¯: viiø7/V
B¯
____
w
b ww
2. a: N
4. c:
## n w
n ww
3. D: ¯III
+6/iv
10.
viio4
5. cF:˜: Ger
2
ø7/B¯
C
____
b w
b b www
9. F: ¯III46
F˜o7
____
b b b # n wwww
____
A¯/C
____
# b b www
4. c: V43/V
5. B¯: Fr+6
ø4
5. B¯: ii 2
6. G: N6
viio7/V
8. b: Fr+6
F
____
o66/V
9. a:
F:vii
¯III
4.
54
F˜o7
____
F
____
12
5. B¯: Fr+6
____
ø7/V 3. G:
7. 2.
A¯:
8. b:
Fr+6 +6
F:vii
It+6
EnGer
?
? b b b ww
w
b b w b ww
+6
F¯/A¯
____
6. f: N6
699
____ 2
1
2
3
4
5
6
f˜: ____
f: ____
G: ____
g: ____
b: ____
F: ____
Given the 7Roman numeral,
please9write the 10
notes of the11chord and lead8
12
?
694
c: ____
____
6
# ww
ww
ww # # # w____
? b b w____
‹ www b n #____
w # n www ____ b b n ww____ # # # # ____
w
w
w
b
w
### # w bb b n w # w bb
# # # www b n w
www e: b____ww B¯: ____
ww
& g: ____
w
# b____
www
b www c˜:b____
d: ____
b:
w
____
1
&
678
689
____
numerals
D: with
____ figured
A¯: bass
____ inversion
G: ____ symbols
B:below.
____
B¯: ____
678
694684
3
____
viio65
b: ____
236
6
____
21.9 Practice
Exercises# w
? # # b # wwww b b b ∫ b www # b www # # # # n # www b b # n www b b ww
b
# w above
ww
b w and bRoman
1. Analyze the following chords with lead-sheet nsymbols
666
689
2
viio6/V
d: ____
4
5
____
____
ww
4. c: viio7/V
10. c˜: viio42/iv
ø7/B¯
C
____
b w
b b www
5. B¯: iiø42
A¯/C
____
# b b www
6. G: N6
Chapter 22
Modulation
22.1 Modulation
At its simplest, modulation is a change of key that happens within a composition. In popular music, the change of key will often be called a “key change”
instead of a “modulation.” Those who study classical music theory typically reserve the term “modulation” for the slower and more subtle change of key that
occurs in many classical pieces, although there are similarities between “key
change” in popular music and the classical music term “direct modulation,”
which we will study later in this chapter.
Here are examples of key changes in popular music.
YT: Ob7vObnFUJc
Figure 22.1.1 Beyoncé Knowles, Terius Nash, and Shea Taylor, “Love on
Top” (2011)
YT: Siz-xBfIqpg
Figure 22.1.2 James Horner and Will Jennings, “My Heart Will Go On”
(1997)
YT: lDK9QqIzhwk
Figure 22.1.3 Jon Bon Jovi, Richie Sambora, and Desmond Child, “Livin’ on
a Prayer” (1986)
22.2 Tonicization versus Modulation
Studying modulation will require us to distinguish between tonicization, which
we studied recently, and modulation. Tonicization, involving secondary chords,
can be as short as two chords ( V/V to V , for example) but can sometimes
encompass several measures as in the following example.
237
CHAPTER 22. MODULATION
299
299
299
299
299
299
302
302
302
305
305
305
305
305
305
bb
œœ œœ œ ‰ œœ œœœ œœ œœ œœ n œ œ œœ œœ œœ ‰ œœ
b
b
œ œ œœ ‰‰ œJJ
œ œ œ nn œœ œœ œ œ œ œœ ‰‰ œJ
bb
&
&
& b bb œœœ
J
œ JJ
trau
trau -- rig
rig ge
ge -- seh'n,
seh'n,
trau - rig ge - seh'n,
bb b
b
b œ
b
&
&
& b bb œœ œœ œœœ œœ
œœ œœ
j
?
?
? bbb bbb bb œjjj ‰‰‰ œœœjj ‰‰‰
b œœ
E¯:
E¯: II
E¯: I
so
so kann
kann
so kann
es
es auch
auch jetzt
jetzt nicht
nicht beim
beim
es auch jetzt nicht beim
œœ œœ œœ œ œœ œœ
œ œœ œ œœ œ œ œ œ
œœ œœ œœ œœ
j
j
jj ‰‰‰ œœjj ‰‰‰ jj ‰‰‰ œœjj ‰‰‰
œœj œ œœj œ
œ
œ
œœ
œ
œœ œœœ
œœ
œ
jj ‰‰‰ œœjjj
j
œœ œ
œ
Ab
Ab -- schied
schied ge
ge -- scheh'n,
scheh'n, so
so
Ab - schied ge - scheh'n, so
œ
œœ œœ
œœ
œ
œ
jj ‰‰‰ œœœ
œœj
œ
œœ
œ
œœœ
œœ
‰‰
‰
7
V
V77/vi
/vi
V /vi
vi
vi
vi
vi
vi
vi
jj ˙ .
bbb b œœœ œœ œœ œœ œ œ œœ œ œ
b
‰
œ
b
‰
&
œ œ œ œœ œœ œ œœ œœ œœ ‰ œœj ˙˙ ..
&
& b bb
œ
kann
kann
kann
302
302
302
238
es
es auch
auch jetzt
jetzt nicht
nicht beim
beim
es auch jetzt nicht beim
bb bbb bb
&
&
& b b œœœ œœ œœœ œœ
œœ œœœ
?
j
?
? bbb bbb bb jjj ‰‰‰ œœjj ‰‰‰
b œ œ
œœ
IV
IV
IV
bb b œœ
b
b
b
&
&
& b bb œ
mun
mun
mun
--
bb bbb bb œœ œ
&
&
& b b œ œœ
œ
jj
?
?
? bbb bbb bb œœœj ‰‰‰
b œ
ii
ii
ii
7
V
V77/IV
/IV
V /IV
œœ œœ œœœ
œ œ
tre,
tre, du
du fröh
fröh
tre, du fröh
œœ
œ
IV
IV
IV
--
œ
nn œœœ œœ œœœœ
nœ
cresc.
cresc.
cresc. j
œœ œœ œœjj ‰‰‰
œœ œœ œœ
œœ œœ
V/ii
V/ii
V/ii
ii
ii
ii
‰‰ œœœJ
‰ JJ
Ab
Ab -- schied
schied ge
ge -- scheh'n,
scheh'n, A
A -- de!
de!
Ab - schied ge - scheh'n, A - de!
œœ
œœ œœœ œœœ œ
œ
œœ
œ
‰‰ jj ‰‰ œœœ
‰ j ‰ œœ
œœ
œ
œœ bb œœ œœ
œ bœ œ
œœ
jj ‰‰‰ œœJœ
œœj JJ
œ
œ
œœ œœ œœ œœœ œœ
œœ œœ œœ
œœ œœ ‰ Œ
œ œ ‰‰ ŒŒ
œ œJJ
J
œœ œœ
œ œ
lili -- che
che
li - che
nn œœ œœ
nœ œ
œ
œœ
œœ œ
œœ œœ
V/ii
V/ii
V/ii
œ
œœœ œœ œœœ œœœ œœœ
œ œ œ
j
œœ œœjj ‰‰ ŒŒ
œœ œœ ‰ Œ
œœ
du
du
du
œœœ nnn œœœ œœ œœœ œœœ œœœ œœœ
œ œœ œ œ
j
j
œœjj ‰‰‰ œœ œœ œœjj ‰‰‰ œœ œœ
œœ œœ œœ œœ œœ œœ
œ œœ œœ œ œœ œœ
œœ
œ
ii
ii
ii
˙˙ ..
˙.
œœ
œ
V/ii
V/ii ii
ii
V/ii ii
œœ
œ
V/ii
V/ii
V/ii
œœ œ nn œœ œ œœ œ (( œœœ )) œœ œœ œ
œ œœ n œ œœ œ œœ ( ) œœ œ œœ
œ œ œ
œ
Stadt,
Stadt,
Stadt,
j
œœjj ‰‰‰
œœ
ii
ii
ii
A
A
A
œœ
œœ
œœ
œœ
œœ
œœ
V/ii
V/ii
V/ii
j
œœjj ‰‰‰
œœ
ii
ii
ii
œœ
œœ
œœ
V
V
V
--
de!
de!
de!
œœ œjjj ‰‰‰
œœ œœ
œœ
II
I
YT: Wod-JellQ88
Figure 22.2.1 Schubert, Schwanegesang, D. 957, “Abschied” (1828)
Below is a reduction showing the underlying diatonic progression of the
example above.
31
31
31
test
?
1. F: V5622.
/IV MODULATION
2. c˜: N6
CHAPTER
? b w
bb
(with tonicizations)
757
E¯: I
766
˙ ˙ w
vi
ii
w
w
IV
E¯: I
? bb
vi
IV
4. e: viio42/V
5. D: Fr+6239
œœœœ œœœœ œœœœ w
˙ ˙ w
tonicizations)
? b b (without
w
w
w w
b
775
3. A: iv6
ii
V
w
I
˙. œ w
V
I
b
Figure 22.2.2 Reduction of Harmonies from “Abschied”
A modulation to a new key requires an eventual cadence to confirm that new
key. This cadence will often (though not always) have the following cadential
formula:
Table 22.2.3 Cadential Formula to Establish a Key
ii6
Pre-Dom.
I64
Dom.
V
Dom.
I
Ton.
Figure 22.2.4 Audio Realization of Cadential Formula to Establish a Key
In his book Form in Tonal Music, Douglass Green defines a V – I authentic
cadence with a pre-dominant prefix as a “full cadence.”
The cadential formula above is found in the following example.
œœ b n œœœ
?
? bbbb œœ œœ œœ b œœœ
œ
nœ
bœ
œ œ œ b œœœ bbœœœ # œœ # œ œ n œœœœœ ˙˙ œ n œœ
œœœœœ
œœ œ ˙˙
CHAPTER
22. MODULATION
240
g: ______
______ ______ ______
______ ______ ______
B¯: ______ ______
______
______ ______ ______ ______
______ ______ ______
Lead-sheet: ______ ______ ______ ______
œ .m
3
b
b
&
& b 4 œœ
m j j
ret.
œ
˙
b
œ
n
œ
œ
œ
˙
œ
œ
œ
œœJœ œœœ. œœœœJ. œ( n œ) œ˙˙œ. œ œ (œ ) œœ(b œœ ) ˙œ (œ )œ œ(œœ) #œœœœ. œœ(œn) œœw ( n œœ )œœ ˙˙˙ ..
( )
( )
œ œœ œ œ b œ ˙œ
œœ
?
? b b 43œ œ œœ œ b n œœœ . œ œ œ œ b nœœœœ œ ˙œ# œ. œ œn œœœ œœ˙˙œ œ œ œ œ
b
œ
œ
g:F:______
I V7 I______
______ ______
modulating...
m j
œœ. œ n œ œ˙˙. œ
œ
m
3
b
&
& b 4 œœ œœ œ œœ
j
bœ
œ œ œ ˙˙˙
œ
ret.
œœœ ˙
œ ˙˙
..
n œ œ œ œ œ n œ (n œ)œ ˙
œ œ œ œ œ œ œ œ ˙˙
( )
..
______ ______ ______
C: I6 ii6 I64 V I
ret.
YT: 9WQbN91tpWI
Figure 22.2.5
English Suite No. 4 in F Major, BWV 809, Saraœ œ J.S.œ Bach,
œ ˙ œ œ œœ œœ œœ œ œ
œœ ˙ .
? (ca.
3 1715)
œ œ
œ.bœ œ ˙
bande
.
?b
b 4
ret.
nœ œ œ.
œ
œ
Notice that this cadential formula establishes a key more strongly˙ than
the simple V – I 7of an authentic cadence. This means there will be ambiguity
F: I V I
modulating...
between a tonicization and a short
modulation ending
6 iian
6 I6authentic
C: Iin
V I cadence,
4
especially in music with fast harmonic rhythm, like Bach chorales
(usually in
quarter-note harmonic rhythm).
#
& c œœ
? # c œœ œ
œœ
œœ
œ # œœ œœ
œ
sus.
4 -
œ œ œ œ œœ œ œœ (ptœ)
œ
œ
G: I
vi IV6 V7
I V42/V V6
G: I
vi IV6 V7
I
D: IV V42
I6
(œ )
#œ
œ (œ ) œ
œ
pt
3
œ
œ
œ
œ
œœ
V/V V7/V V
(as a tonicization of V)
V
V7
I
(as a modulation to D)
YT: tVJy904MiIY
Figure 22.2.6 J.S. Bach, Christmas Oratorio, BWV 248, “Ermuntre dich,
mein schwacher Geist,” (Chorale) (1734)
To determine pivot chords and the new key, listen to the music to hear the
cadence in the new key, then work backward from the cadence to see if the
dominant in the new key was approached by pre-dominant chords ( ii or IV )
in the new key. Then, analyze from the beginning of the phrase until you reach
the new key. Finally, look for a logical pivot point. Sometimes two successive
chords could logically be pivot chords. If so, include two chords on either side
of your pivot bracket.
CHAPTER 22. MODULATION
# # # 2 œf . œ œ œ œ
& 4 œ . œœ œ . œ œœ
241
j 3
œ
œœ œ œ œœ œ œ œœ œœ œ œ œœ œ
# œœœ
œœœ
œœœ
œ
3
fœ œ œ œ œ œ œ œœ
œ œ œ œ.
œ J
f
? # # # 42 ‰
V6 IV6 I46 V7
A: I
I IV I
I
œœ œœ
œ
œœ ..
œ.
œ. œ œ œ
V6 I
E: I6 IV
#
& c
83
I64 V7
œ
I
YT: Qy8NLd7d6VE
Figure 22.2.7 Robert Schumann, Album for the Young, Op. 68, No. 17,
“Little Morning Wanderer” (1848)
?Before
# c we start analyzing and writing modulations, we will examine key
relationships and pivot chords.
22.3 Key Relationships
&
#
In the Baroque and Classical eras, composers typically modulated to the dominant (when starting in a major key) or to the relative major (when starting in
a minor key). In the Romantic era, composers experimented with modulating
to more remote (or perhaps adventurous) key areas, described as “foreign” to
the home key.
“Closely related” keys have key signatures one degree “sharper” or “flatter” than the starting key. For any major or minor key, there are five closely
35
related keys, including the relative major or minor of the home key.
?#
&
#
?#
775
Home key
D
&
##
b
one degree
"flatter"
A
###
one degree
"sharper"
f˜
E
####
c˜
(relative keys with same key signature)
Figure 22.3.1 Closely Related Keys with A Major as Home Key
Key signatures that are not closely related are said to be “foreign” or
“distantly related.” We will see that some types of modulations from the
Romantic era, like common-tone modulations, exploit foreign key relationships
to dramatic effect.
22.4 Modulations with Diatonic Pivot Chords
Modulations with pivot chords will be analyzed using a pivot bracket, as we’ve
seen earlier in the chapter.
##
& ##
778
œ
? 3 œ œœ œ
b 4
œ
œ.bœ œ ˙
œ ˙
œ œœ œœ œ œ
œ
nœ œ œ. œ œ œ
œ œ ˙
˙
..
CHAPTER 22. MODULATION
242
F: I V7 I
modulating...
C: I6 ii6 I64 V I
In a diatonic common chord modulation, the pivot
chords will be
diatonic in both keys.
#
& c œœ
? # c œœ œ
œ # œœ œœ
œ
œœ
œœ
3
œ # œœ
œ (œ )
œ
œ
œ
œ
œ
œœ
V7
I
( )
œœ œ œ œ œœ œ œœ (ptœ)
œ
vi IV6 V7
G: I
sus.
4 -
pt
I
D: IV V42
I6
V
both I and IV are diatonic
Home
Homekey
key
(as a modulation to D)
I V42/V V6
V/V V7/V V
one
degree
YT: tVJy904MiIY
one
degree
D
E
one
degree
(as
a
tonicization
of V)
one degree
D
E
"sharper"
Figure 22.4.1 J.S."flatter"
Bach, Christmas Oratorio,
BWV
248,
“Ermuntre
dich,
"flatter"
"sharper"
mein schwacher Geist,” (Chorale) (1734)
G: I
###
&
& #
775
775
vi IV6 V7
AA
### ##
#
## # #
##
f˜
c˜
b
f ˜ Chords Between
c˜ Keys
22.4.1 Determining
Common
b
(relative
keys with
same key
signature)
In order to compose
a diatonic
common
modulation, you need to deter(relative
keys with
same chord
key signature)
mine which chords are diatonic—having the same root and quality—in both
keys.
G major: G Am Bm C D Em F˜o o
G major: G Am Bm C D Em F˜
D major: D Em F˜m G A Bm C˜o o
D major: D Em F˜m G A Bm C˜
Figure 22.4.2 Diatonic Common Chords in G major and D major
We can repeat this process with Roman numerals, aligning the roots of the
chords in the two keys.
R. N.:
I
ii
iii
IV V
G major: G Am Bm C
778
&
785
&
778
####
####
##
D major: G
R. N.:
A
IV V
D
Bm C˜o D
vi
viio I
vi
viio
Em F˜o
Em F˜m
ii
iii
Figure 22.4.3 Roman Numerals for Diatonic Common Chords in G major
and D major
3535
CHAPTER 22. MODULATION
243
If you are a composer wanting to write a diatonic common chord modulation, you need to determine the best place within a progression to pivot to the
new key. To do this, you need to consider the 3harmonic 3function of the pivot
chords.
# # # 2 œf . œ œœ œ œ
& 4 œ . œ œ . œ œœ
œœœ
œ
j
œ
œœ œ œ œœ œ œ œœ œœ œ œ œœ œ
# œœœ
œœœ
œœ ..
œ.
22.4.2 Harmonic Functions of Diatonic Pivot Chords
fœ function,
In terms of harmonic
composers
œœ œœ doœœ not œuse a pivot chord
œ new
œ œœkeyœ typically
#
œ œœ œœinœthe
?
#
2
.
that has
dominant
function
because
such a modulation
‰
# 4
J
œ . œ œ might
œ
sound abrupt and unconvincing. Instead, the pivot chord in the first key often
œ
f
has tonic or tonic prolongation function.
A: I
V6 IV6 I46the
V7 pivot
I IV
I Isimultaneously
V6 I
In the following
example,
chord
has tonic function
6 IV
in the first key and pre-dominant function in the
key.
a
E: Isecond
I64 This
V7 creates
I
more seamless and less jarring progression to the second key.
#
& c œœ
? # c œœ œ
œœ
œœ
œœ œ œ œ œœ œ œœ (œ)
œ
Harmonic function in G:
G: I
œ # œœ œœ
œ
&
#
?#
œ
œ
œ
œ
œ
V
V7
I
Ton.
vi IV6 V7
œœ
I
D: IV V42
Harmonic function in D:
œ # œœ
œ (œ )
( )
I6
Pre-Dom.
YT: tVJy904MiIY
Figure 22.4.4 J.S. Bach, Christmas Oratorio, BWV 248, “Ermuntre dich,
mein schwacher Geist,” (Chorale) (1734)
The pivot chord in the first key, G, has tonic harmonic function, while in
the second key, D major, the G chord has pre-dominant function.
Observe the harmonic function of the pivot chords in the following examples
from Bach chorales.
83
vi IV6 V7
G: I
CHAPTER 22. MODULATION
Harmonic function in D:
&
####
œœ
œ
? #### œ
œœ œ œœ
œ
œ
D: IV V42
I6
œ œ œ
œ
œ
nœ
œ
œœ œœ
Ton.
V6
V7
I
A: V
Harmonic function in A:
V7
V
I
244
Pre-Dom.
œœ
Harmonic function in E:
E: I
I
œ œ œ œ œ
œ
J œ
J
j
œ œ
œœ n œ œ
œ
œ
¯VII6
IV6 viiø7 I
7
V
I
Dom.
YT: gl4FNanCrbc
Figure 22.4.5 J.S. Bach, Chorale 4, “Es ist das Heil uns kommen her”, BWV
9
84
b
& b b c œœ œœ œœ n œ œœ
? b b c œœ n œœ b œœ
b
U
jœ œ
j
œœ œ œ œœ. œ œ œ ˙
˙
J
œ œ œ œ œœ . œj œ œ œ œ b œ ˙
œ bœ œ œ bœ œ
œ œœ
œ
˙
U
j
.
œœ œ n œ œ œ œœ œœ ..
œ bœ
œ œ
u
Harmonic function in f:
f: i
Harmonic function in A¯:
b
&bb
iiø65
V7
i i
u
Ton.
i
A¯: vi viio64 I6 I
ii56
V
7
I
Ton-Prol.
YT: NE-uciPxYFE
Figure 22.4.6 J.S. Bach, Chorale 8, “Freuet euch, ihr Christen”, BWV 40
? bb
22.5 bHow to Recognize a Key After a Modulation
Look for the following cues when examining music containing modulations:
1. Look for recurring accidentals, then add them to the key signature to
determine the new key
(a) Lowered notes (like flats) usually create 4̂ (as do the flats in key
signatures)
(b) Raised notes (like sharps) often create 7̂ , the leading tone
CHAPTER 22. MODULATION
245
i. If there are multiple raised notes, look for the “sharpest of
sharps” (in key signature order) to determine which sharp is
acting as 7̂
2. If accidentals are canceled out, they indicate tonicizations or chromatic
non-chord tones
E¯ is lowered note acting as 4ˆ
bœ ˙
& b 43 œœœ. œ ˙˙
œ
? b 43 œ
F: I
œœ œœ ˙˙
œbœ ˙
˙
˙
V7/IV
œ
œ
˙
˙
IV
En cancels out E¯, which means
E¯ represented a tonicization
m
œ œœ œ œ œ
n œœ œ œœ œ œœ
œ œ
œœ œœ
œœ
œ œ
œ œ
V42
V24
I
I6
V7
œ
œ
I
Bn occurs 3 times and isn't canceled out, representing a modulation
m j
& b œœœ. œ n œ œ˙˙. œ
? b œ. bœ œ ˙
F: I
viio42/V
j
bœ
Bn is a raised note acting as 7̂
œ œ œ ˙˙˙
œ
n œ œ œ œ œ n œ (n œ ) œ ˙
œ œ œ œ œ œ œ œ ˙˙
( )
œ ˙
œœœœœ
œœ ˙
nœ œ œ. œ œ œ œ œ
œ
˙
V65/V
multiple secondary chords
destabilize F major
..
..
V6
C: I6 ii6
I64
V
I
cadential formula affirms new key
YT: 9WQbN91tpWI
Figure 22.5.1 J.S. Bach, English Suite No. 4 in F Major, BWV 809, Sarabande (ca. 1715)
22.6 Modulations with Chromatic Pivot Chords
You will sometimes encounter examples where the pivot chord is a chromatic
chord in at least one (and sometimes both) of the keys involved in the modulation.
22.6.1 Secondary Common Chord
Below is an example where the pivot chord is a secondary chord in both keys.
85
32
CHAPTER 22. MODULATION
b œ
&bb
308
Œ
246
Ó
∑
∑
œ œ
b
& b b œ œ œ œ œ œ œ œ œ œ œ œ œ œœ œœ
œœ œœ œœ
œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ
? bb j ‰ œ ‰ j ‰ œ ‰ j ‰ œ ‰ Œ
‰ œj ‰ j ‰ œ n œ
j
b œ J œ J œ J
œœ œ
œ œ nœ
308
311
311
E¯: I
b
&bb
∑
∑
314
∑
b
& b b œ œœ œ œœ œ œœ œ œœ œ œ œ œ œ œ œ n œ
œœ œœ œœ œœ
œ œœ œœ œœ œœ
? b b j ‰ œj ‰ j ‰ œ œ j ‰ œ ‰ j ‰ œ ‰ j ‰ œ ‰ Œ
b
œ J œ J œ J
œ
œ
E¯: V
314
ii6
b
&bb
A¯: IV
œœ
V7/ii
I
A¯: V7/vi
∑
œ œ
œ œ b œ œœ œœ œœ
œœ
œ
bœ œ
? b b j ‰ b œ ‰ j ‰ œœ œœ
b bœ
J
œ
b
&bb œ
œœœ œœœ
Ó
œœ
œœ
œ
J
I64
Œ
‰ œj œ
A - de!
bœ œ
œ œ œ œ œ œœ œ œ œœ
b œœ œœ œœ
‰ œJ ‰ œJ ‰ œJ ‰ œœœ ‰
J
V7
I64
V
I
YT: Wod-JellQ88
Figure 22.6.1 Schubert, Schwanegesang, D. 957, “Abschied” (1828)
22.6.2 Borrowed Common Chord
In modulation by borrowed common chord (or mode mixture), the pivot
chord will be a borrowed chord in one of the keys involved in the modulation.
In the following example, a borrowed chord, i6 in D2 minor, rewritten as a
4
C minor chord, is reinterpreted as vi6 in the second key, E major.
iiø65
f: i
CHAPTER 22. MODULATION
Harmonic function in A¯:
œ
b b 3 œ.
&bb 4
V7
i i
i
A¯: vi viio64 I6
I
ii56
V
7
I
247
Ton-Prol.
œ
J
œ
˙
dolce
b
& b b b 43 œ œœ œœ œœ œ œœ œœ œœ œ œœ œœ œœ œ b œœ œœ œœ œ œœ œœ œœ œ œœ œœ œœ
V43
D¯: I
&
bbbb
œ.
œ
œ
J
œ
œ.
œ
J
cresc.
#œ
œ.
œ
J
dim.
b
œœœ œœœ œœœ
& b b b b œ œœ œœ œœ œ œœ œœ œœ œ œœ œœ œœ œ œœ œœ œœ œ œœ œœ œœ œ œœ œœ œœ n œ # # œœ œœ œœ œ œœ œœ œœ œ œœ œœ œœ
D¯: V42
&
bbbb
#œ
I6
nœ.
œ
J
i6
E: vi6
œ
nn n n # # # # œ œ œ œ œ œ œ œ œ œ œ œ œ
π
p
j
b
n ##
& b b b # œ # n œœ œœ œœ œ œœ œœ œœ œ œœ œœ œœ n n n # # œ œœ œœ œœ œ œœ œœ œœ œ œœ œœ œœ œœœ ‰
E: V6
V56
I
YT: H3S8slvoHoU
Figure 22.6.2 Beethoven, Piano Sonata No. 31 in A2 major, Op.110, I, (1821)
22.6.3 Neapolitan Common Chord
A particularly adventurous and imaginative pivot is the Neapolitan, which can
bridge the gap between two foreign (or distantly related) keys.
34
330
CHAPTER 22. MODULATION
248
b œ nœ œ œ #œ œ œ ‰ œ b˙
& b 42
J
œ. œ bœ œ
J
b 2 œœœ ‰ n œœ œ ‰ œœ œ ‰# n œœ œ ‰ œœ ‰ œœ b ˙˙
b
& 4
œ œ
3
3
3
π
œœ n œœ
œœ # n œœ
œ
œ
b ˙˙
œ œ
œœ
? b b 42 œ
b ˙˙
˙
˙
i
V
fol - gen auf
luf - ti - ger Bahn.
3
330
d: i iio6
i46
V
Wo - hin?
∑
wo - hin?
3
b b ˙˙
˙˙
˙
˙
˙˙
N56
i
a¯: V56
b ∑ Schubert,
Figure
D.
(1828)
∑ Schwanegesang,
∑
∑ 957, “Frühlingssehnsucht”
∑
∑
∑
& b 22.6.3
YT: IvjZiYVZUIY
337
In the example above, Schubert bridges the tonal distance between D minor
and A2 minor with N65 (note the dominant-seventh quality of the Neapolitan in
337
this
instance), which acts as a V65 in A2 minor, a tritone away from D minor.
b
∑
∑
∑
∑
∑
∑
∑
? bb
∑
∑
∑
∑
∑
∑
∑
&b
22.6.4 Augmented Sixth Common Chord
In the next chapter, we will examine how Augmented Sixth chords are enharmonically reinterpreted in a process known as enharmonic modulation.
22.7 Modulations Without Pivot Chords
bb
∑
∑
&
• Direct Modulation
∑
∑
∑
∑
• Common-Tone Modulation
∑
∑
∑
∑
22.7.1
? b Direct Modulation
∑
∑
∑
∑
344
This section contains the following subsections below:
bb
∑ Modulation
∑
• Sequential
&
344
b
∑
∑
Direct modulation (also known as phrase modulation) is a type of modulation where a composer decides to move suddenly to a new key without using
pivot chords or preparing the new tonic with its dominant.
a¯: V5656
i
V
CHAPTER 22. MODULATION
# 2
& 4 œJ
337
337
brin
brin
--
r r
œ œ œj
ge
ge
Grü
Grü
œ œ
R R
--
sse
sse
des
des
œ
J
Fer
Fer
--
#œ œ œ
R R
nen
nen
ihr
ihr
zu.
zu.
#
œ
œ
œ
œ
œ
œ
& 42 œœ œœ œ œœ œœ œ œœ œœ œ œœ œœ œ œœ # œ œœ œ œœ œ œœ œ œœ œœ œ œœ œœ œ
337
337
≈ œ. œ. œ.
? # 42 œ
339
339
339
339
die
die
249
&
#
e: i
œœ
JJ
∑
All'
All'
œ
≈ œ. œ. œ.
o7/i ped
viio7
i
œœ œœ œjœj rnrœnrœr œ œœ œ œ œRœ œœ œ ‰ ‰ c
R R RJ J
œœ
RR RR
- reBluBlu- -men
men
- flegt,
ihih- re
im im GarGar- -ten ten
gepgep
-flegt,
# # œ œ œœ œ œœœ œ œœœœœœ œ œœœœ œ œ œœ œ œ œ œœ œ œœ œ œ œœ œ œœ œœœœ œ œ œ œ œ
œ œ œ œ œ œœœ œœœœœœœœ œœœœœ œœ œœœœœœ œœœ œ œ œ œœ œ œ œ œœ œœœ œœœ nœœnœœœ œœœ œœœœ œœ œœ œ œ œ œ œc
#œ œ
. .. .. .
. . . .
œœœœ
? # œœ .
‰‰
≈ ≈ œœ œœ œœ œœ œœ œœ œœ œœ
≈ ≈œœ œœ œœ œœ c
&
o7/i ped
e: viio7
i
C: I
V77/I ped
I
YT: uTWQRjGkprQ
Figure 22.7.1 Schubert, Schwanegesang, D. 957, “Liebesbotschaft” (1828)
In the example below from the second song of the same song cycle as the
example above, Schubert does not attempt to change gradually from C minor
to A2 major, but instead stops on a half cadence in C minor and begins on the
tonic in A2 major in the next bar.
? #### c ‰
˙
˙
CHAPTER 22.E:MODULATION
vi
346
346
b
& b b 43
b 3
& b b 4 œœœ ......
? b b 43
b œ ..
œ ..
c: i64
349
349
? bb c
b
Vsus4
∑
r j
œœ œœ ‰
œ œ
r j
œ œ ‰
œ œ
schneller.
bb b Etwas
& c Ó
? bb c
b
˙
˙
IVadd9 vi64
∑
œ ..
œ ..
V
Wie
U
c
c
c
˙.
˙.
V
j
œ
œ.
œ
hab'
A¯: vi250
?
˙˙ ..
n˙.
i
‰ œj œ
Œ
43
nœ
∑
U
r j
œœ œœœ ‰
œ
r œj ‰
œ œ
œ
œœ ....
n œ ..
bbbb
ich
oft
so
œœœœ œœœœœ œ œœœœ œœœœœ œ
œ
œ
œ
œ
3
œ
A¯: I
3
3
j
œ ‰
œ
3
3
j
œ ‰
œ
3
3
j
œ ‰
œ
3
j
œ ‰
YT: mLTyrvgKDUo
Figure 22.7.2 Schubert, Schwanegesang, D. 957, “Kriegers Ahnung” (1828)
Direct modulation is the most common type of “modulation” found in popular music. At the beginning of this chapter we defined this type of modulation
in popular music as “key change.”
251 35
CHAPTER 22. MODULATION
342
342
&
####
œ œ
c œ
#### c ‰
&
C˜m
b
& b bb
346
˙˙
˙
˙
E:
∑
Aadd9 C˜m/G˜
Bsus4
˙˙
˙
? #### c ‰
˙˙˙ ˙˙
˙
˙
˙
Vsus4
vi
∑
bœ
œ œ
œ œ œ œ œ œ œ . œ œ œ œ . œJ
bbbb
∑
˙
IVadd9 vi64
∑
YT: Siz-xBfIqpg
∑
∑
b b b b n b œœ
n b œœ
Fm
bbbb
nœ
∑
∑
A¯: vi
Figure 22.7.3 James Horner and Will Jennings, “My Heart Will Go On”
(1997)
346
b b b bdirect∑ modulation,
∑ composers
∑
∑do not ∑make any∑ attempt
∑ to connect
∑
With
&
two different keys through any pivot chords or common tones. In the next sec? bb b
b
∑
∑
∑
∑
∑
∑
∑
∑
tion, we examine how composers connect two keys through a common tone.
22.7.2 Common-Tone Modulation
In common-tone modulation, two chords are connected through a single
note
354 to bridge the distance between two keys.
In the following example, the note C4 acts as a hinge between a C4 major
chord ( V in F4 minor) and an A dominant seventh chord ( V7 in D major).
b
& b bb
∑
∑
∑
∑
∑
b
& b bb
∑
∑
∑
∑
∑
? bb b
b
∑
∑
∑
∑
∑
354
CHAPTER 22. MODULATION
90
90
SS r
SS r
r
r
œ
˙
œ
œ œœ ‰‰œ .. œœ ˙˙ œ
## # 4 œ # œ ‰‰œ .. œ ˙ œ
#œ
œ
œ
&
& # 44 ##!œœ ! !œ ##!œœ !œœ !œ !œœ !œœ !œœ ! !œ !œ !œœ !œ !œ !œœ
! !! ! !!!! !!!! !!!!
r
?
? ## ## 444 œœ ŒŒ ŒŒ ‰‰ .. œœr œœ ŒŒ ŒŒ ‰‰ .. œœR
R
f ˜: V
f ˜: V
## #
&
& #
?
? ## ##
f ˜:
f ˜:
r
œœ œ ‰ . œœr ˙˙
‰œ .œ œ œ
œ
œ œ œœ œ
!!œ !! !! !!œ !!œ !! !!œ !!œ
œœ Œ Œ ‰ . œœ
Œ Œ ‰ . RR
i
i
pœ
## # pœ ŒŒ ÓÓ
&
& # ww
pp
?
? ## ## ww
ww
pp
i
i
ƒ
r
œœ # œ ŒŒ ŒŒ ‰ .ƒœœr
# œ ## œœ œ # œ œœ ‰œ .œ
œ #œ œ œ
## œœ
!
!
!! !! ! ! !! !! !! !!
r
œœ ŒŒ ŒŒ ‰‰ .. œœr
ƒ
V
ƒ
V
5ˆˆ in f ˜
5 in f ˜
ww
ww
ww
7ˆˆ in D
7 in D
ww
pp cresc.
ww cresc.
w
ww
252
Sr
œœ ‰ .Sœœr ˙˙
# œ ‰œ .
œ
## œœ # œ œ ## œœ œœ œ œœ œœ
!! !! !! !! !! !! !! !!
œœ ŒŒ
V
V
r
ŒŒ ‰‰ .. œr
œ
r
r
œœ ‰ . œœr œœ ‰ . œœr
œœ # ‰œ .
œœ ‰œ .
## œœ # œ œœ œ œ œœ
!! !! !! !! !œ ! ! !
!!!!
ƒ
ƒ
r
r
œœ ‰‰ .. œœr œœ ‰‰ .. œœr
ww
ww
SS
ww
ww
A: V7
A: V77
œœ
œœ
pp
œœ
œœ
I
I
YT: bEiYmeeV6sI
Figure 22.7.4 Beethoven, Symphony No. 2 in D major, Op. 36, I. (1801–1802)
In the next example, the note A acts as a hinge between an A major chord ( V
in D minor) and an F major chord ( I in F major).
CHAPTER 22. MODULATION
bb c œœ ..
b
&
&b c
47
47
253
nnœœ œœ .. œœ œœ .. œœ œœ .. œœ œœ
p
bb b c #pœ . ?? ## œœ œœ .. œœ œœ .. œœ œœ .. œœ
&
& b c #œ.
pp
bb b c œ
&
& b c œ .. œœ ## œœ .. œœ œœ .. œœ œœ .. œœ
ppœ .
?
b
? bb b cc œ . nnnnœœœ œœ .. œœœœ œœ .. œœœœ œœ .. œœœœ
œ nnœœ œ œœ œ œœ
ÓÓ
ŒŒ
ÓÓ
ŒŒ
ÓÓ
## œœ
dim.
nnœœ b œ n œ œdim.
## œœ œœ ## œœ nnœœ œœ ## œœ œœ ## œœ
œ
b
œ
n
œ
œ
d:
d: V
V
bbbb
&
&
49
49
œœ
ŒŒ
∑∑
?
? bbbb
∑∑
∑∑
55ˆˆ in
in dd
&
&
ww
pp
jj ‰ Œ Ó
œ
œ
#
œ
‰Œ Ó
œ
#
œ
œ
n
œ
œœ œœ nnœœ œœ ## œœ œœ## œœ n œ œ # œ œ # œ
π
π
?
b
∑∑
∑∑
? bb b
bbbb
&
&
∑∑
3ˆ in F
œœ œœ.. œœ.. œœ.. ˙˙
∑∑
∑∑
3ˆ in F
π
π
∑∑
œœ
œœ
œ œœœ
œ œœœ
œœ œœ œ œ œœ œœ œœ œ œ œœ
π
π
ww
ww
F:
F: II
YT: qSRRbOvpaXg
Figure 22.7.5 Schubert, Piano Trio No. 1 in B-flat major, D. 898, I. (1828)
22.7.2.1
Chromatic Mediants
In a common-tone modulation, the two chords connecting the two keys are
typically in a chromatic mediant relationship. Chromatic mediants are
chords with roots a third apart that share only one common tone and have the
same quality (both are major or both are minor).
37
E
C
C˜
A
A
F
811
2
&4
812
824
&
&b
b
# n www
n www
• one common tone—A
• roots are a 3rd apart
• both chords are major
Figure 22.7.6 Chromatic mediant relationship in Figure 22.7.5
C˜
A
A
F
___ ___ ___ ___ ___ ___ ___
b b œ œ # n wwwœ
œ
œœ œ nœwww œ œ
&
œ
# 4
œ
œ
( ) œ
(œ) (œ)
( )
& 4 œ (œ) (œ)
(œ)
(œ) œ
(œ) (œ)
• one common tone—A( ) (œ)
787
LSS:
___ ___ ___
___ ___ ___
811
CHAPTER 22. MODULATION
254
Any major or minor triad will have four• chromatic
mediants,
roots are a 3rd
apart as shown in
RN:example
G: ___ below.
___ vi
___ ___ ___
vi
the
• both chords are major
812
795
D:___ ___ ___ ___ ___ ___ ___
Cm
E¯m
6 Dom Cm
____
DomCm
TonEmPD Cm
CadAm
Ton A¯m
4
www # ww www b ww www b b www www # www b www b ww b www n ww b www n www b www b b www
w
bw
w
& w___ ___b ___
LSS:
___ ___ ___
___ ___ ___ ___ ___ ___ ___
# 4 ϥ root
œ of second
n œ œis a third
œ
chord
# œ lowerœor #higher
œ œthan# œstarting
œ #chord
œ œ
& 4 • second chord is same quality
as starting chord
HF: C
RN:
E
C
Ton Dom
E
¯ C
____
A¯
PD
C
A
/V Dom
• the two chords within each bar share only one common tone
e: ___ ___ ___
N6 ___ ___
i
37
Figure
22.7.7 Chromatic mediants of the C major and C+6minor triads
820
b:___
E ___ ___ Fr ___
C ___ ___
Below are examples chromatic mediantsC˜that do not involve
modulation.
A64 Dom
HF:
Ton Dom Ton
___ /V Dom
____ Dom Ton ___ Cad
Ton
In fact, the progression in the following three
examples
are
found
in the last
A
F
bar of Figure
22.7.7, the progression from i to 2 vi (shown as Cm to A2m in
811
the example above).
42
&
803
812
G˜m
&b
Em
b
G ˜m
œœœ n œœœ # # ˙˙˙
œ
E¯ C A¯
# n www
n www
• one common tone—A
G ˜m
Em B (no 3rd)
• roots are a 3rd apart
• both chords are major
j
˙
œœ .. # œœ # ˙˙
˙
n œœ .. # œ # ˙
Cm Em œCm Am
˙ Cm˙˙ A¯m
b www b b www b www n www Jb www n www b www b b www
Em
œœœ n œœœ # # ˙˙˙
œ Cm E¯m
A
#˙
? 42C #E ˙˙ C
C
www # wwp www b ww www b b www www # www
bw
& w
• root of second chord is a third lower or higher than starting chord
• second chord is same quality as starting chord
• the two chords withinYT:
eachmeGuEnjERxc
bar share only one common tone
Figure 22.7.8 Richard Wagner, Das Rheingold, Scene 3 (1854)
Gm
820
? b b 44 œ˙˙ .
˙ ..
? bb
œ
œ
E¯m
œ.
b œœ
œ
Gm
œœ
n œœ
E¯m
œ.
b œœ
Gm
œ ˙
˙
n ˙˙
822
YT: AL2N4Bfl4Ec
Figure 22.7.9 John Williams, Star Wars: Return of the Jedi, “Main Title
(The Story Continues)” (1983)
CHAPTER 22. MODULATION
#
& 44 Œ
255
œ œ bœ nœ œ nœ bœ œ œ
Œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
# 4Choirœ œ ˙ .
œœ b œœ ˙˙ ..
w
ww
& 4 œ œ ˙.
w
J
Em
44
44
Cm
Trumpet
Horn
œœ œœ ˙˙ ..
?# 4
4
Kor - ah,
44
7
B
G
E
œ
œ
3
ww
3
D
B¯
G
œ ˙ ..
œ ˙
J
w
w
Syahd - ho,
91
B¯
(arrows show common tones)
G¯
(roots are a 3rd apart)
YT:
E¯ ZTg6hg1miFg
& ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
b
44
48
& b 43
∑ œ ∑ ∑ >œ ∑ b∑œ ∑ ∑ ∑n œ ∑ ∑>œ ∑ b ˙∑ ∑ ∑
& ∑ Sequential
22.7.3
Modulation
>
>
>
>
?
3
4
Modulation
a œsequential modulab 4 can also be accomplished by sequence.
48
4 œ areIn repeated
œ
œ
tion,
and
its
accompanying
harmonies
.
? ba∑ melody
b∑œ ∑ ∑ ∑ œ ∑ ∑œ ∑ bat˙∑ a new
∑ n œ ∑ ∑ œ to∑ a new
∑ pitch
∑
level to establish or lead
key. œIn the following >
example, the sequence
n
œ
b
œ
b
˙
.
>
> in the> new key.
>
of the original>idea occurs
>
48
Figure 22.7.10
Williams,
of the Fates”
Em JohnGm
E¯mThe Phantom Menace, “DuelE¯m
(1999)
63
&
∑
∑
3ˆ 4ˆ 2ˆ
∑
3ˆ 1ˆ 1ˆ
7ˆ 1ˆ ˆ2
∑
4ˆ ˆ3 3ˆ
b
& b b b 43 œ œœ œ Œ œ œ œ n œ œ œ œ œ œœ
& ∑ œ. ∑œ œ œ ∑œ œ œ œ ∑ ˙ .
p
63
œœ œœ œœ n œœ ˙˙ Œ
?
3
œ
b
b
Œ
Œ
Œ
Œ
Œ
? b b∑ 4
∑
∑
∑
63
f: i iiø42
i
V43 i V6
∑
∑
∑
same melodic pattern in A¯
4ˆ 2ˆ
3ˆ 1ˆ 1ˆ
7ˆ 1ˆ 2ˆ
4ˆ 3ˆ
œœŒ œœœ œ œœ œœ
œ∑œ œ œ ∑œ œ œ œ ∑ ˙
œœ œœ œœ œœ ˙˙
œ
Œ∑Œ œ Œ Œ ∑
∑
i A¯: I ii42
I
V43 I V6 I
same Roman numeral pattern in A¯
b
& b bb
YT: M9SzCHQCNGY
Figure 22.7.11 Beethoven, Piano Sonata Op. 2, No. 1, III. (1795)
? bb b
b
In the following example, an idea in C major is repeated up a step in D
major, then up another step in E minor before reaching an F4 ◦ chord, a chord
with dominant function in G major.
CHAPTER 22. MODULATION
14
14
14
Oboe
Oboe
Oboe
14
14
14
Violin I
Violin II
Violin
14
14
14
Violin II
Violin II
II
Violin
& 4242
&
2
& 424
&
2
2
&
4
&4
.
œœ œœ œ.œ. œ.œ. œœ œœ œœ. œœ
˙˙
256
3
33
same melodic pattern in D major
same melodic
melodic pattern
pattern in
in D
D major
major
same
. œ..
. œ.. .
.
. . œ œ. .
œœ œœ œ.œ. œ.œ œœ## œœ œ œœ. ## œœ œœ œ.œ## œ.œ. œœ œœ œ.œ œ ## œœ œœ œ.œ œœ. œœ œ œ. œ.œ
œœ œœ œ œœ ## œœ
œ
j
j
‰
œ
‰ œ
œœ œ
œœ œ œœ œœ
œœ # œ
œœ # œ ## œœ
˙˙
‰ œ
œœ ‰ JœJ
œœ ## œœ œ œ # œ
œ œ #œ
establishes F˜, destabilizes C major
establishes FF˜˜,, destabilizes
destabilizes C
C major
major
establishes
. .
.
œœ.. œœ œœ œ.œ œœ.. œœ œœ œœ. œ.œ œœ œœ ## œœ.. œœ.. œ œœ œ.. œœ.. œ.. œ. œ. .
œ œ œ œ. œ. œœ.
same melodic pattern in E minor
same melodic
melodic pattern
pattern in
in E
E minor
minor
same
..
œœ ## œœ œœ.. œ.. œœ œœ œœ. œœ. œœ ## œœ œœ..
œ
&
&
18
18
18
18
18
18
& ˙˙
&
& œ œœ œœ # œ
&
œ
#œ
18
18
18
œœ œœ ## œœ œœ
‰‰
œœ
E minor, affirms F˜ and movement
E minor,
minor, affirms
affirms FF˜˜ and
and movement
movement
E
away from C major
away from
from C
C major
major
away
22
22
22
22
22
22
22
22
22
œ œœ œ.œ.
&
œ
&
& œœ
&
& œœ
&
. œ
œ.œ œœ œ
ŒŒ
ŒŒ
arrival on G as tonic
arrival on
on G
G as
as tonic
tonic
arrival
. # œ..
œ.œ # œ
.
œ.œ
ŒŒ
ŒŒ
.
œœ.
œœ ## œœ ..
œœJ ˙˙
J
G: viioo
G: vii
viio
G:
.
œ.œ
.
œœ. œœ
œœ œœ ## œœ œœ
œœ œ
œ
œ
œœ œ
œœ ##œœ
V7
V77
V
dominant function in G major
dominant function
function in
in G
G major
major
dominant
Ÿ
œœŸ
ŸŸ
j
‰‰ œœj œœ
œœ
œœ
##œœ fœœ
f
‰‰ j
j œ #œ œ œ œ œ
œœ œ # œ œ œ œ ffœ
YT: jD9_dShQbN8
Figure 22.7.12 Mozart, Oboe Concerto in C major, K. 314, III. (1777)
In the next example, after a cadence in G minor, an idea in F minor is
repeated down a whole step in E2 minor to achieve the change of key to E2
major, which is the starting key of this aria, as can be seen in the key signature.
CHAPTER 22. MODULATION
36
36
351
351
bbbbb cc œœ ˙˙..
&
& b
g: i646
g: i4
bbbbb ÓÓ
&
& b
354
354
-
bbbbb ŒŒ
&
& b
V
V
va,
va,
ŒŒ
œœ œœ bb œœ œœ œœ bb œœ œœ œ
œ
ŒŒ ÓÓ
i
œœ
œ
i
pal pal -
œœ œœ
œ œ
-
-
-
œœ
œ
-
bb ˙˙
tan tan -
œœ
œ
-
œœ
œ
-
e¯: iioo
e¯: ii
œœ
œ
-
-
f: iioo
f: ii
same pattern down a whole step
same pattern down a whole step
œœ bb œœ œœ œœ b œ œ b œ
?
œ
b
bœ œ bœ
? b bb œ
bb
ŒŒ
ÓÓ
f: i
f: i
ŒŒ bb ˙˙
mi
mi
bbbbb cc ‰‰ œ œœ œ ‰‰ # œ n œ œ
&
& b
œ œ œ n #œ nœ œ
œ œ n œ œœ
?
? bbbbb cc œœ ŒŒ œœ
b
354
354
œœ
## œœ
cor
cor
351
351
257
-
œœ
ŒŒ
-
œœ
œ
V77
V
ŒŒ
œœ Œ œ Œ
Œ œ Œ
-
- pi
- pi
-
ŒŒ
œœ œœ œœ
œ œ œ
nn wœw
œ Œ Ó
Œ Ó
V77
V
U
U
œ
œ
œœ U
œ
U
œ œœ
-
ŒŒ
- do!
- do!
U
U
œœ
V566
V5
YT: VEmnmVXEqqM
Figure 22.7.13 Mozart, Don Giovanni, K. 527, “Mi tradi quell’alma ingrata”
(1787)
While this is by no means an exhaustive list of modulatory techniques, it
should give you a sense of some of the different means composers use to change
keys.
22.8 Practice Exercises
Day One
1. For each given key, list the five closely-related keys.
(a) d:
(b) D2:
(c) f:
36
36
785
&#
####
G major: G Am Bm C D
CHAPTER
22. MODULATION
#
& # # 2.
785
Em F˜o
258
For each progression,
analyze
the
Roman
numerals
with
D major:
DC7/B¯
EmF/A
F˜mDm
GC/EA Dm/F
Bm lead-sheet
C
˜o G 7 C
Fsecond
C/G ____
Lead-sheet
____
____key.
____ ____
____ ____ ____
____
symbols
andsymbols:
specify the
Lead-sheet symbols:
____
Roman numerals: F:
811
I
Roman numerals:
____
F:
I
V42
____
V42
bb
____
I6
I6
E
____
C
vi ˜
A
____
____
____
# n www
C
____
A
F
n www
vi
C : ii
___
I6
ii6
I46
V7
6
6
6
7
___ : ii
I
ii
I4
V
I
E
C
o
C˜ IV V
R. N.:
I
ii
iii
viA vii
• one common
tone—A
Lead-sheet symbols: ____ ____ ____ A
____ ____ ____ F ____ ____
a 3rdFapart
811
G major: G Am Bm C• roots
D are
Em
˜o
ww # ww
Day Two& w w
C E
C
812
3.
812
iv
nw
ww are major
iv6 • both chords
___ •: one
ii6 common
viiø7/V tone—A
I6
V7
I
4
GA¯ AC ABm
Care
˜oEa¯D
Em
• roots
3rd Cm
apart
Cm
m
Em F˜m
Cm Am
•
both
chords
are
major
b ww Vww ww vi b wwviiob wwI b wwiin ww iiib ww n ww
www R.b wwN.: www b IV
w w #w w
w
w w
C D major:
E¯ C
E
# n www
bw
bw
w
I
b www b b www
Cm A¯m
Borrowed
Chord
List w
the wclosely
related
keys to
ww chord
www # ww major
www bkey,
ww Modulation.
www b b wwwspecify
www # wwwisthe
wwand
www b bthe
bparallel
ww b blower
ww minor
b wwworn wwwhigher
n www itsstarting
bclosely
• root
of
second
chord
a third
than
starting
then
keyb w
w
w
b
w
&
E¯related keys.
• second chord is same quality as starting chord
# ###### # B
&&
F˜
787
787
b
&i b V6/iv
g:
Roman numerals:
&
37
D¯ c˜
C
E¯
A¯
C
C
A
Cm E¯m Cm Em
Cm A¯m
Cm Am
theoftwo
chords
each
barorshare
common
• •root
second
chordwithin
is a third
lower
higheronly
than one
starting
chord tone
• second chord is same quality as starting chord
• the two chords within each bar share only one common tone
E¯m
Gm
E¯m
Gm
Gm
D
Gm
E¯m
Gm
E¯m
Gm
œ ˙
to parallel œ
#
#
œ
œ
œ
œ
?
4
#
820 ## #
b
œ
œ
.
.
˙
œ
#
œ
œ
minor
.
#
&&
œ
? bbb 444 œ˙˙ ˙˙. .. œ
n ˙˙˙
œœ . b œœ œœœ n œœœœ . b œœ˙˙˙
˙ ..
bœ
nœ bœ
n˙
820
789
789
# # # ##4.
& ## #
809
809
&
817
778
&
####
& # ##
#
817
&
825
####
For each progression, analyze the Roman numerals with lead-sheet
symbols and specify the second key.
####
7/G Dm/F B¯7 Dm/A
A________
C
A A
A7
Lead-sheet
symbols:________
____
____ ____
____________
Lead-sheet symbols:
____ ____
____ ____
____
____ ____
Roman numerals:
Roman
numerals:A: A:I
Lead-sheet symbols:
___ : V42d
i6 Ger+66
___ : V42
i
____
____
___ 6
: I6
i
i
____
____
ii6 viio7/V
N6
A¯ : I6
___
____
____
7
i64VI V7
____
Fm
____
I64 viio7/vi vi
ii6 viio7/V
I64 viio7/vi vi
Determining Diatonic Common Chords. For each of the two keys in
each example, list the diatonic chords as lead-sheet symbols and as
Roman numerals then circle those diatonic to both keys
822
Roman
numerals:
?
bb
6.
____
6
i4 +6V
Ger
Gm i6 Gm/B¯
Eo7
Lead-sheet
symbols:
____
____ B¯m/D¯
____ ____ A¯/E¯
____ ____
Roman numerals:
g: i ____
N6 A¯/C
Roman numerals: g:
5.
VI24/IV V4/IV
2
Do7
825
&
####
Day
Three
&
I ¯III ¯IIII
d: ___
___ ___
___
___ ___
___
___ ___
___ ___
___
Lead-sheet symbols in Dm: ___
___
Lead-sheet symbols in F:
___
___ ___
___ ___
Roman numerals:
___
___ ___
___
F:
B¯
____
___
___
___ ___
___
Referring to the Harmonic Flowchart, fill in lead-sheet symbols, Roman numerals, and Harmonic Functions for the following example—be
sure to put some of the chords in first inversion for variety; create a
VI
37
LSS:
___ ___ ___
˙ ˙ w
( ˙) ( ˙ ) (w)
w
# 4
˙ ( ˙˙) (w)
&
4
CHAPTER 22. MODULATION
RN:
795
G: ___ ___
vi
˙ ˙ ˙˙ ˙ ˙ ˙ w
( ) ˙
( ) ( ˙ ) ( ˙)
( ˙ ) ( ˙)
( w) 259
___ ___ ___
___ ___ ___ ___ ___ ___ ___
___ ___ ___
vi
melody by adding embellishments (non-chord tones) and try to create
D:___ ___ ___ ___ ___ ___ ___
repeating motives and/or subphrases; LSS stands for lead-sheet symHF: RNTonstands
Dom ____
PD
/V Dom
Dom Ton PD Cad64 Dom Ton
bols,
for Roman
numerals,____
and
HF stands for Harmonic
Function
# ˙ ˙
& 44
LSS:
RN:
w
n˙ ˙
#w
___
N6 ___
___
___ ___ ___
e: ___ ___
˙ #˙
___ ___ ___
___ ___ ___ ___ ___ ___ ___
˙ #˙
˙ #˙
w
i
b:___ ___ ___ Fr+6 ___ ___ ___
HF:
Ton Dom
Ton
___ __/ V Dom
___ Cad64 Dom Ton
____ Dom Ton
Day Four
7. List the four chromatic mediants for each chord.
G ˜m
Em G˜m
Em
G ˜m
Em
(a) Fm:
803
(b)2
?
4
#˙
D#2: ˙˙
(c) G: p
(d) G4m:
i
Day Five
8.
œœœ
œ
n œœœ # # ˙˙˙
Em D˜o/F˜ Em/G
viio6
i6
œœœ
F/A A˜o7
viio7/V V
PD PD
œ.
n œœœ ...
œ
n œœœ # # ˙˙˙
j
# œœ
# œœ
J
B (no 3rd)
# ˙˙
# ˙˙
˙˙
˙˙
Em F˜7 Bm/D G7(¯5) Bm/F˜ F˜ Bm
B
iv V7
PD
i6
i6 V
PD
i
4
Analyze lead-sheet symbols, motives (with numbers, noting melodic
alteration when it occurs), Roman numerals, and harmonic function.
96
96
CHAPTER 22. MODULATION
LSS:
LSS:
Motives:
Motives:
260
___
___
___
___
& bb 433 œœ œœ œœ œœ œœ œœ ˙
& 4
˙
? b 43 Œ
? b 43 Œ
œ
œ
RN:
RN:
HF:
HF:
LSS:
___
LSS:
___
Motives:
Motives:
œ
& bb œ
&
?b œ
?b œ
RN:
RN:
HF:
HF:
___
___
___
___
œœ
œœ
œ
œ œœœ
œ
œœ
œœ
___
___
___
___
___
___
___
___
___
___
œ
œ
œ œœ œœ
œ
œœ
œœ
œœ
œœ
œ
œ
by G.K.B.
___ by G.K.B.
___
___
___
___
___
___
___
___
___
œ
œ œœ œœ œœ œœ œœ œœ œœ œœ œ
œ
œœ
œœ œ œœœœ œœœœ œ œœœœ œœœœ
œ
œ
___
___
œ œ ˙
œ œ ˙
nœ œ
œ n œœœœœ œœœœœ
œ
___
___
___
___
___
___
___
___
œœ
œ œœ œœœ
œ
___
___
___
___
___
___
___
___
___
___
___
___
œœ
œœ
œ
œœ
œœ
œ nœ ˙
œ nœ ˙
___
___
___
___
___
___
___
___
œ
œ
& bb
&
?
?b
b 22.8.1
Figure
Compose an eight-measure example using the motivic structure
and harmonic function in the example above. Create a new melody 97
with new motives but the same sequence of motives. You may use a
different time signature, mode, and accompanimental texture.
LSS:
___
___
___
___
RN:
___
___
___
___
HF:
___
___
___
___
Motives:
&b
?b
LSS:
___
___
___
___
___
___
RN:
___
___
___
___
___
___
HF:
___
___
___
___
___
___
Motives:
&b
?b
RN:
b
___
CHAPTER
HF: 22. MODULATION
___
LSS:
___
___
___
___
___
___
___
___
___
___
___
___
RN:
___
___
___
___
___
___
HF:
___
___
___
___
___
___
261
Motives:
&b
?b
Click here to download the first homework assignment for this chapter.
Click here to
the second homework assignment for this chapter.
b download
& to
Click here
download the third homework assignment for this chapter.
Click here to download the fourth homework assignment for this chapter.
Click here to download the fifth homework assignment for this chapter.
? to download the Unit 5 Practice Test.
Click here
b
PDF versions of the textbook, homework exercises, and practice exercises
can be found at musictheory.pugetsound.edu
Chapter 23
Enharmonic Modulation
23.1 Enharmonic Modulation
In an enharmonic modulation, the pivot chord is almost always misspelled
in one of the keys and therefore must be reconceptualized enharmonically by
the analyst. In this regard, an enharmonic modulation is a harmonic pun.
Here is a pun from Shakespeare’s Richard III, Act 1, Scene 1:
Now is the winter of our discontent
Made glorious summer by this sun of York
107
The “sun” of York is the son of York, King Edward IV.
Here is a simple enharmonic modulation:
œ
& 43 œœ
Dm/F
G7
? 43 œ
œ
œ
C: I
ii6
C
œœ
œ
Bm/F˜
œœ œ # œœ
œ (# œœ) œ
(œ)
V7
b: Ger+6
#œ
i46
F ˜7
#œ
# œœ
Bm
œ
V7
œ
œœ
œ
i
Figure 23.1.1 Enharmonic Modulation from C major to B minor
&
Like a verbal pun, this harmonic pun is effective because the third chord
( G7 ) has two “meanings”—in the context of C major, G7 is V7 and the root
wants to cadence down a fifth to C, but the G7 is a Ger+6 in the context of
B minor, where the root of the G7 wants to progress down a half step to a
chord of dominant function, i64 in the example above.
?
262
#
CHAPTER 23. ENHARMONIC MODULATION
872
&
P5↓
C: V7
resolves to
enharmonic
respelling
b
b
&
&
874
Figure 23.1.2
876
&
? ###
# www
w
m2↓
b: Ger+6
ww
w
41
I
# ww
#
# # ww
resolves to
V
respell top note: B¯ becomes A˜
b www
w
# www
w
Notice that the G7 can only be spelled correctly in one of the keys—either
as a dominant seventh chord on G (G–B–D–F) or as a Ger+6 on G (G–B–D–E4),
hence the term “enharmonic modulation.” The analyst must envision the other
spelling (the one not shown) to understand the double context, in the same
7
C: beVenvisioned
Ger+6
way “sun of York” must
as “son b:
of York.”
872 We will encounter two sonorities used in enharmonic modulations: the
bottom
three
notes respelled
dominant seventh sonority
and the
diminished
seventh sonority.
b b b wwww
# # #wwwwwww
&
P5↓
23.2 The&V7 andw Ger+6 as Pivot
ww Chords
w
878
˙˙
& # ˙˙
www
w
263
b: V7 modulation,B¯:
Ger+6
In this first type of enharmonic
the pivot to the new key will
7
V
I as a Ger+6 , or the Ger+6
consist of the V7 beingC:
enharmonically
reinterpreted
resolves
to
enharmonic
7
being enharmonically reinterpreted as V . Secondary dominants, like V7 IV ,
respelling
V7 Vrespelled
, etc., will also be reinterpreted harmonically as Ger+6 chords (and vice
enharmonically
874 versa) in enharmonic modulations.
m2↓
As we saw in the previous section,
the dominant seventh chord and the
Ger+6 chord have the same sound but are spelled differently. This involves a
fairly straightforward
b:enharmonic
Ger+6 respelling. MostVcommonly, the top note of
resolves
to the enharmonic alternative.
the chord is enharmonically respelled
to envision
o4
i
c: vii 2
i
876
˙
#˙
˙˙˙
# www
& ˙˙ w
˙
b ˙˙
#w
# # # www b ˙˙
˙
˙
a: viio7
respell top note: B¯ becomes A˜
enharmonically
respelled
enharmonically respelled
˙˙
b
˙
&b ˙
˙
878
e¯: viio43
b www
# www
w
w ˙
b
˙
b
˙
b
˙
˙
˙
b˙ ˙
b b ∫F:˙˙˙V7
e: Ger
b b+6b ˙˙˙
Figure 23.2.1
bottom three notes respelled
www5 a key based on itsb spelling:
Each
the
o6
b winww major,
i chord above
G¯:implies
I dominant seventh
#
#vii
chord occurs &
diatonically
only
on
the
5̂
scale
degree
while the Ger
b
w
# w
chord most commonly occurs with the lowest note on the lowered 6̂ scale degree.
&
+6
Less commonly, the b:
bottom
be respelled
and the upper+6
V7 three notes could
B¯: Ger
most note could be retained as a common tone.
˙˙˙
& #˙
enharmonically respelled
#˙
˙
˙˙˙
˙
b ˙˙˙
a: viio7
i
c: viio42
enharmonically
respelled
enharmonically respelled
b˙
˙
˙
b ˙˙˙
i
0
&
&
b ww
ww
&
# # # wwww
CHAPTER 23. ENHARMONIC
MODULATION
C: V7
b:
878
# www
w
Ger+6
264
b b b wwww
bottom three notes respelled
b: V7
B¯: Ger+6
Figure 23.2.2
Remember, you will not see this respelling in the music you are analyzing.
You must be able to visualize the enharmonic respelling in order to analyze
the enharmonic modulation correctly.
The examples below illustrate some of the ways this enharmonic modulation
occurs in pieces from the literature
In the first example from Tchaikovsky’s Nutcracker ballet, a D7 is spelled
on the staff as D–F4–A–B4 so that it sounds like a V7 IV in D major but is
spelled and resolves as a Ger+6 in the key of F4 minor.
CHAPTER 23. ENHARMONIC MODULATION
## #
&
& #
?
? ## ##
3
443
4433
D
D
œœœ
-- œ-œœ œœ œœ
œ œœ œœ
œœ
D: I
D: I
F˜m/C˜
F˜m/C˜
## # œ œ jj ‰
&
& # œœ œ ## œœ œ œœ ‰
Œ œ œ
?
? ## ## Œ˙˙ .. œœœ œœœ
f ˜: i664
f ˜: i 4
F ˜m
F ˜m
## # œœ ## œœ
&
& #
ŒŒ˙
?
#
? # ## ˙˙
˙
f ˜: i
f ˜: i
C˜o7
/D ped.
C˜o7/D ped.
œ
bb œœœ-œœ œœœ ......
- >>œ ..
bb œœ œœ
œ œ
œœ œ œ
r
œœr
œ
>>œ
265
D77
D
D
D
>
˙˙>
j
œj ˙
œ
viio7
/I ped.
viio7/I ped.
I
I
œœ
œœ
C˜77/B
C˜ /B
F˜m/A
F˜m/A
V442
V2
i66
i
œœ
œœ
D77
D
i442
i2
Ger+6
Ger+6
œœ œœ œœ ## œœ
## œœœ œœœ
œœ œœ
V77/IV (D-F˜-A-C)
V /IV (D-F˜-A-C)
f ˜: Ger+6
(D-F˜-A-B˜)
f ˜: Ger+6 (D-F˜-A-B˜)
ŒŒ ‹ œ # œ œ œœ œœ œœ ## œœ œœ œœ ‰‰
JJ
‹œ #œ œ
ŒŒ œœœ œœœ ŒŒ œœ œœ
˙˙ . ## œœ œœ ˙ . œœ œœ
˙.
.
F˜m77/E
F˜m /E
ŒŒ
pp
ŒŒ
˙˙ .
.
œœ
œ-œœ
œœ
C˜77/G˜
C˜ /G˜
ŒŒ ## œœ œœ ## œœ ## œœ
F
FŒŒ # n œœœœ œœœœ
#nœ œ
˙˙ .# # œ œ
.
F˜m/C˜
F˜m/C˜
V443
V3
C˜77
C˜
F ˜m
F ˜m
œœ # œ œ œ œœ # œ # œ œ œœ œ œœ œ œœ œ œœ # œ œ
œ œ # œ œJ
#œ œ œ #œ #œ œ œ
J
œœœ
œœœ ŒŒ # œœœ ŒŒ œœœ n œœœ œjj
n
œ
œ nœ
œœœ ˙˙ # œœ ˙˙ .. œ ## n œœ
œœ
nn œœ
œœ ˙
œœ
˙
˙
˙ ..
i664
i4
V77
V
i
i
YT: Kw0wLLVEMaA
Figure 23.2.3 Tchaikovsky, The Nutcracker“Waltz of the Flowers” (1892)
In the following example from the second movement of Beethoven’s Fifth
Symphony, the same pivot chords are used as in the example above— V7 IV
in A2 major is enharmonically respelled and resolves as a Ger+6 in C major.
99
99
102
CHAPTER 23. ENHARMONIC MODULATION
A¯
266
Ao7
œœ . œ b œœœ œœ . œ
J
J
πœ
nœ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
? b b b 38 œ œ œ œ œ œ œ
J
œ
‰
b
b 3
& b b b 8 œœ .. œœ œœ
3
3
œœ
œœ
œœ
3
3
3
3
A¯: I
b
& b bb
b œœœ
? bb b ‰
b
nœ
œ.
œ.
viio7/ii
A¯7
œ # œœœ ...
œ # œ.
ƒ
bœ.
bœ.
V7/IV
C: Ger+6
n œœœ ...
œ.
C/G
n œœœ
œ.
I64
œœ.
nœ
œœ.
œ
œœœ
œ.
.
n n œœœ
nœ
G7
œœ
œ.
V7
C
œ
n œœ ‰
J
œ
n œœœ œ
œ
I
YT: DdL2e4pE-uA
Figure 23.2.4 Beethoven, Symphony No. 5, Op. 67, II (1808)
In the following example from Les Miserables, a Ger+6 in E minor is spelled
as a V7 chord in F major and resolves to the I chord F major.
CHAPTER 23. ENHARMONIC MODULATION
356
#
& # c
E¯
bœ
#
& # c b œœ
bœ
And al
356
? ## c b œ
bœ
359
359
&
&
##
##
? ##
œ.
-
though
œ
n n œœ
nw
nw
˙.
œ
n œœ
˙
˙
e: iv7
œœ
œ
I know that he
œœ
œ
œœ
œ
is
œœ
œ
˙
˙
˙.
œ œ
blind
Still I
w
w
V
œ œ
œœ
œ
B
# œœœ œœœ œœœ œœœ
e: i
Am7
say
≈ œr œ œ œ œ
Em
œ
267
there's a
œœ
œ
C7
œ œ œ
way for
˙
b ˙˙
us
n˙
n˙
Œ
Ó
Ó
nœ nœ
I
love
F
b œ
him
b œ
œœ
œ
b œ
Ger+6
F: V7
I
YT: VjfmP7h3gBw
Figure 23.2.5 Music by Claude-Michel Schönberg, lyrics by Alain Boublil,
Herbert Kretzmer, John Caird, Trevor Nunn, and Jean-Marc Natel, Les Miserables, “On My Own” (1980)
In the next section we will examine how the fully diminished seventh chord
can be enharmonically reinterpreted.
23.3 The Fully Diminished Seventh as Pivot Chord
Each diminished seventh sonority implies four different keys. Play and sing
through the example below.
&
# # # wwww
b b b wwww
b: V7
CHAPTER 23. ENHARMONIC MODULATION
880
˙˙
& # ˙˙
enharmonically respelled
˙
#˙
˙˙
˙
˙
b ˙˙˙
B¯: Ger+6
a: viio7
i
c: viio42
enharmonically
respelled
enharmonically respelled
˙
& b b ˙˙˙
884
˙
b ˙ b b ˙˙˙
e¯: viio43
i
˙
˙
268
b ˙˙˙
i
b b ∫ ˙˙˙˙
˙
b˙
G¯: viio65
˙
b b b ˙˙˙
I
Figure 23.3.1 The Four Resolutions of a Diminished Seventh Sonority
In the example above, each note of the vii◦7 chord was treated in turn as
scale degree 7̂ and resolved up by half step. In the example below, each note
of the chord resolves as if it were the 7th of the chord, moving down by half
step to the root of a dominant seventh chord.
42
888
˙
& # ˙˙˙
˙
˙
& b b ˙˙˙
b˙
˙
b ˙˙˙
b˙
˙
b b ∫ ˙˙˙˙
∫˙
b ˙ b b ˙˙˙˙
enharmonically respelled
˙
˙
# ˙˙˙
a: viio7
V65
c: viio42
enharmonically
enharmonically respelled
respelled
892
e¯: viio43
b ˙ b ˙˙˙˙
V42
G¯: viio65
˙˙
˙˙
V7
V43
896
&
Figure 23.3.2 Resolutions of a Diminished Seventh Sonority to a Dominant
Seventh Sonority
This means that for any diminished seventh chord, you should be able to
imagine the other three respellings in the same way you can imagine other
spellings of words like two (i.e., to and too) or there (their and they’re).
In the following examples, a vii◦7 chord is enharmonically reinterpreted in
a new key.
4 .
In the first example, Beethoven enharmonically reinterprets F ◦7 C in G
4 .
minor ( vii◦43 ) as vii◦42 in E minor ( D ◦7 C ), which resolves to a V7 chord in
E minor.
ii6
ii6
V7
V7+6
b: Ger
i46
+6
b: Ger
i46
CHAPTER 23. ENHARMONIC MODULATION
C: I
C: I
Gm Gm/B¯ D/A Gm C˜o7 D
Gm Gm/B¯ D/A Gm C˜o7 D
b
& bb bb cc œœ
& b œœ
Íœœ
? bb c Í
? b bb c œ
b œ
g: i
g: i
b
& bb bb
& b
F˜o7/E¯
F˜o7/E¯
# nn œœœœ
#͜
͜
? bb œ
? b bb
b
g: viio42
g: viio42
œœ .. œœ # n œœœ ... œœœ n œœœ
œœ .. œœ # n œœ .. œœ n œœ
œœ ..
œ nœ. œ #œ
#œ
œ. œ nœ. œ
œ.
j
œœ j ‰
œœ ‰
œ
Jœ ≈ . œ
J ≈ . RÔœ
RÔ
œœœ ..
œœ ...
œ.
œ.
Em/B
Em/B
œœœ œœœ .. # œœœ œœœ n nn œœ
œœ œœ ... # œœ œœ n nn œœœ
p
œ œ . œ pœ n œ œ
œ œ . œ Jœ n œ Jœ
J
J
V
V
e:
e:
viio43
o4
viio4
3
vii
2
viio42
V7
V7
i46
i46
i
i
269
F˜o7/E¯
F˜o7/E¯
# nn œœœœ
#͜
͜
œ
i6 V64 i viio7/V V
i6 V64 i viio7/V V
D D˜o7/C
D D˜o7/C
V7
V7
D F˜o7/C Gm/B¯
D F˜o7/C Gm/B¯
œœœ .. œœœ œœœ .. œœœ œœœ
œœ ... œœ œœ ... œœ œœ
œ. œ œ. œ œ.
œ. œ œ. œ œ.
viio42
viio42
B7
B7
V viio43
V viio43
Em/B
Em/B
œœœ
œœ
i6
i6
B7(¯9) B7
B7(¯9) B7
# # nn œœœ n n n œœœ œœœ œ
# # œœ n n œ n œœœ # œœ
n œ n œ # œœ
cresc.
π
œ cresc.
π
Jœ n œ œ
J nœ œ nœ
nœ
V7
V7
i46
i46
≈. œ
≈ . RÔœ
RÔ
V7(¯9) V7
V7(¯9) V7
j
œj
œ
YT: mlxF5I1MfbM
Figure 23.3.3 Beethoven, Pathétique Sonata, Op. 13, I (1798)
In the next example from the second movement of Beethoven’s Fifth Symphony, Beethoven modulates from C major to A2 major by enharmonically
. 2
reinterpreting an E◦ 7 chord in C ( vii◦7 IV ) as vii◦42 in A2 ( G◦ 7 F ). Notice
the unusual resolution of the vii◦42 chord to a Ger+6 chord by leading all three
of the upper voices of the vii◦42 up by half step to the Ger+6 , which itself is
unusually spelled in the key of A2 major (E–A2–C2–D instead of F2–A2–C2–D).
100
100
CHAPTER 23. ENHARMONIC MODULATION
C
b
& b bb
b
& b bb
38
38
? b b b 38
b
? b b b 38
b C:
C:
n œœC^
œœ ..n œœ
œœ^
n œœ ..n œœœ
nœ
œ.
Sœ œ n œ
nœ. œ
œ
Sœr œ n œ œ n œ œ . œ
œœ .
œœr
n œ œœ . œœ
œI
œ. œ
I
n œœ ..
œ.
n œœ ..
Sœ .
Sœj ‰ ‰
j
œœ ‰ ‰
œ
œœ
bœ.œ
œœœ œJ
b œœ . œ
Ϲ
J
π
∑
∑
270
Eo7
b œœœ Eœœo7. œ œœœ œœ . œ œœœ ..
.
b œœœ œœJ . œ œœœ œœJ . œ œœœ ..
.
J
J
jœ
n œœj.
‰
‰
p‰ n œ ‰ n œ n œœ . œ
œ o7/IV (E-G-B
n œ ¯-D¯)
p n vii
o4
A¯: viio72 (G-B¯-D¯-F¯)
vii /IV (E-G-B¯-D¯)
A¯: viio42 (G-B¯-D¯-F¯)
E7 A¯m/E¯ Do7 Go7/D¯ A¯/C D¯
b b b b n œE7œœ. . Ab¯m/E
œœœ .. ¯ Dœœœo7..
b
.
. .
&
bb b b b n œpœœ. . b œœœ .. œœœ ..
. . .
&
.
. .
? b b b b œœp. b œœ . n œœ .
. .
b .
? b b b b œœ . b œœ . n œœ .
b
.. ¯ Aœ¯./C
E¯œ7/D
œ œœ..
œ.
œ. œ.
bœ. œ.
b œ .. œœ..
bœ. œ.
œD.¯
œ ..
œ
œ.
œ.
œœ..
œ.
A¯: Ger+6
i64 viio7/V viio43
I6
IV
A¯: Ger+6
i64 viio7/V V42
I6
IV
E¯
A¯
V
I
œE. ¯‰ ‰ œ ? œœAœ¯ œœ œ œ œ œ œ œ
œ.
Jœ ‰ ‰ œ ?Jœœ œ œœ œ œ œ‰œ œ œ
fœJ œ. f pJdolce ‰
fjœ. œ. ‰f ‰ œpj dolce
‰ œ
œ. œ. ‰ ‰ œ j œœ
‰ œœ
j
œ
œ
.
œ
œ
V.
Iœ
. œ
YT: DdL2e4pE-uA
Figure 23.3.4 Beethoven, Symphony No. 5, Op. 67, II (1808)
? bb b
b
4
In the final example of this section, Schubert reinterprets a G ◦7 in G
4
4
minor as an E ◦7 chord
in B minor ( vii◦65 V ). The G ◦7 chord in G minor
is analyzed as vii◦42 iv , meaning it could resolve to a C minor chord, but it
could also have been interpreted as vii◦43 VI , or as tonicizing an E2 major
chord. Because the chord never resolves in G minor, one cannot be certain of
the intended resolution. Remember that diminished triads are not tonicized,
4
so the G ◦7 would not be considered as tonicizing the note A (the root of the
ii◦ chord) or F4 (the root of the vii◦ chord).
? bb b
b
38
38
CHAPTER 23. ENHARMONIC MODULATION
b
& b 43 œ œ Œ
Gm
362
362
362
362
b
&b
43
tra - gen,
˙˙ .. ˙ .
B¯+/F˜
366
366
366
366
Œ ‰ œj œ . œj œj œj # œj. œr œ ‰ œj
Œ
Ich
œ œ œ œ ˙
# œœ œœ œœ œœ ˙˙
j
œ ‰œ
œ œ
III+64
b j r
œ
& b # œ . # œ n œJ # œR œR J
b
&b
o7
G˜o7
Gm
? b b 43
. œr
‰
œ œ
#œ
œ œ œ #œ
g: i
bre - chen will mir
mir das Herz
Herz
271
i
tra - ge Un - er - träg - li - ches, und
˙˙ .. ˙ .
j
œ. œ œ œ #œ . œ œ ‰ œ
œ. œ œ œ #œ. œ œ œ
cresc.
viio42/iv
b: viio65 /V
F˜sus4 F˜
#˙.
#œ
J
im
Lei
Lei --
--
Bm
nœ Œ Œ
--
--
--
∑
œœœœœœœ
œ
#œ œ œ œ ƒ
n ˙˙ # ˙ # œœ œ œœ œ œœ œ œœ œ
? b
#
#
œ
œ
b #œ. #œ nœ #œ
#˙.
#œ
#œ. #œ nœ #œ œ
# ˙.
n ˙˙
˙.
n n ˙˙ ..
-- be.
be.
˙
b: Vsus4 V
b
&b
369
369
∑
# ˙˙ .. n ˙ .
n˙.
n˙.
i
∑
∑
YT: 6PetvUTrUPY
Z
∑
Figure 23.3.5 Schubert, Schwanegesang, D. 957, “Der Atlas” (1828)
bb
∑
∑
∑
? bb
∑
∑
∑
∑ Exercises
& b Practice
23.4
369
369
Day One
1. Notate the specified chord, resolve it, then notate and resolve the
enharmonic respelling(s).
CHAPTER 23. ENHARMONIC MODULATION
&b
42
˙
& # ˙˙˙
888
b
˙
bb
&
272
˙˙_____
b˙
˙˙˙˙
g: ˙ Ger#+6
resolve b ˙˙
respell
a: viio7
V65
c: viio42
enharmonically
enharmonically respelled
respelled
892
826
2.
˙˙
& b b ˙˙
#
b˙
&
&
Roman numerals:
828
#
____
V7
b ˙ b b ˙˙˙˙
∫˙
____
____
iv
V
7
IV
V /V
___: Ger+6
__ : ____
i64
V42 viio7/iv
_____
resolve
bb
b& b b
b
b
____ ____ ____
____
____
& ____
7
f: V /VI
_____
b
œœ resolve
œ
b œœ
& b 44 œœœ # œœœrespellœœ
b œœ
œ
b b œ #œ
3. 830
Analyze with lead-sheet symbols and Roman numerals and label the
enharmonic
pivot chords in the examples below.
897
832
&bb
834
? b 4
b 4 œ
g: ____
# # # # 4 œœ
&
4&œ
œ
____
# # ____
œ
____
836
? #### 4 œ
4
&
##
E: ____
Figure
# 23.4.1
____
#
& #
_____
____V7____
____ ____ ____
G:
/IV ____
resolve _____
E¯: respell
I
¯VI
b
&bb
896
838
b ˙ b ˙˙˙˙ resolveb b ∫ ˙˙˙˙
__ : ____
˙
For the following Roman numeral progressions, label the chords with
e¯:symbols,
viio43
V42 key, and
G¯: notate
viio65
lead-sheet
specify the new
all of the chordsV43
in the appropriate inversion on the staff below. The enharmonic pivot
chord can be spelled correctly in only one of the two keys.
Lead-sheet symbols:
104
˙˙˙
˙
enharmonically respelled
# œœ
____
____
œœ
œ
____
____
#
& #
? ##
____
____
œ
_____
b˙
____
____
____
œœ
œ
____
œ
# œœ
____
____
____
œ
____
œœ
œ
nœ
#œ
resolve
____: ____
____
__
& # 44 œ
œœœ # œœœ
œœ
Day Two
? # # the
44 œspecified chord,
4. Notate
œ
œ
enharmonic
respelling(s).
b: ____
resolve
˙˙
˙
____
D: Ger+6
œ
œ
respell
____
œ
œ
__œ : ____
____
‹ # œœœ
_____
____
œ
˙˙
˙
˙
____
____
_________
____
____
resolve
n œœ
œ
n œœœ
œ
n˙
˙˙
n˙
resolve it, then notate and resolve the
____
____
____
____
39
CHAPTER 23. ENHARMONIC MODULATION
b
&bb
838
b
&bb
840
E¯: viio7
respell
b
&bb
842
844
&
273
bbb
_____
resolve
__ : ____
resolve
respell
__ : ____
resolve
respell
__ : ____
_____
_____
_____
resolve
5. Analyze with lead-sheet symbols and Roman numerals and label the
846enharmonic pivot chords in the examples below.
105
###
3 &
& b 4 œœ œœ œœ
œ œ œ
___ ___ ___
? b 43 œ # œ # # #œ
&
___ ___
b œœœ b œœœ b b œœœ
f ˜: viio7
respell
848
bœ
##
##
œœ #n œœ
& # 44 &
œ
œ
____ ____
? # # # 44
œ
852
&
# # #œ
œœœ
˙
___
resolve
____
b n n œœœ
___
respell
œ
____
____
œ
__ : ____
____
____
___
b œœœ
b b b ˙˙˙ ...
œ
b˙.
_____
___
_____
____
n b œœœ
__ : ____ resolve _____
A: ____ ____
Figure 23.4.2
b b ˙˙˙
œ bœ
____ ____
respell
œœ
œ
___
resolve
___
__ :___
_______
d: ___ ___ ___
850
___
bœ
œ
____
____
_____
____
___
____
n ˙˙
˙
n˙
____
b b b b b 44 œœ the first
œœ # œœ assignment
n œœœ homework
& download
n œœœ for
˙˙
Click here to
# n œœœthis chapter.
œ
œ
n
œ
˙ chapter.
Click here to download the second homework assignment
for this
____
____
____
resolve
Click here to download the Unit 6 Practice Test.
? b b b 44 œ
bb
b¯: ____
b
& b bbb
? bb b
bb
œ
œ
œ
____
____
____
nœ
____
œ
____
____
n˙
____
Chapter 24
Binary and Ternary Forms
24.1 Binary and Ternary Form
In this chapter we will compare the following:
Sectional versus Continuous
Binary versus Ternary
Rounded Binary versus Ternary
24.2 Sectional versus Continuous
39
39
We apply the descriptor “sectional” to a binary or ternary form when the
first section (the A section) ends on the tonic. (Note: We use lowercase letters
to refer to phrases and uppercase letters to refer to sections.)
Introduction
First Section
Introduction
First Section
Zart
bewegt
Phrase
1
Zart bewegt
Phrase 1
b 3
& bb bbb 43 ‰‰
& 4
369
369
b
& bb bbb
&
? b
? bb bb
b
369
369
374
374
374
374
378
378
∑
∑
3 j
43 œœœj
4 pœ
3 p‰
43 ‰
4
œœ œ œœ
œœ œœ œœ
œ
œ
œ
œ
œ
b œ
& bb bbb œ
&
œ ..
œ
? bb
? b bb œ
b œ
œ
œ œ
œ
b
& bb bbb
&
jœ
œœ j œœœ
œœ
Ro - sen
Ro - sen
œœ
œœ
b
& bb bbb œœ œœ œœ œœ
&
un - ter die
un - ter die
œ
Jœ
J
be
be
œœ
Jœœ
J
j
‰ œœ j
‰ œœ
œ
œ
Œ Œ œjj œjj œ .. œjj œ
Œ Œœ œ œ œ œ
œœ œ œœ
œœ œœ œœ
œ
œ
œ
œ
œ
j
œœ j
œœ
Gu - ten
Gu - ten
‰
‰
œ
œ
2
œ œ œPhrase
œ
œ œ œ œ œœ œœ œœ œœ
dacht,
mit
Näg - lein be dacht,
mit
œœ œœ œ j Nägj - lein be œJœœ œ œœœ œœœj œœœj œœœ œ œJœœ
J
œ œ œ œ J
œ
œ œ
œ œ
œ
œ
œ œ œ
œ
œ
œ
Phrase 2
-
j
j
œœ jœ
œœ j
œœ œœ œ œœ
œ œ
œ
œ œ
œ
œ
œ
A - bend, gut
A - bend, gut
Second274
Section
Second3Section
Phrase
Phrase 3˙
œŒ j j
œ Œ œj œj ˙
œ œ
Deck: mor - gen früh,
Deck: mor - gen
œ Œ œœ
œ Œ œœ
j
j
œœ jœ œœ j
œœ œœ œ œœ
œ œ
œ
œœ
œ
œ
œ
Nacht,
Nacht,
mit
mit
œ ŒŒ œ œ
œ
œ œ
steckt
schlupf
œœ
Jœœ
J
steckt
œœ
Jœœ
J
schlupf
œœ œ
œœ œ
œ
œ œ
œ œ œ
œ
œ œjj ˙ œjj j œ œ œ
Jœ œ ˙ œ œ j œ œ œ
J
œ
wenn Gott will, wirst due wie - der ge -
früh, wenn Gott will,
wirst due
wie - der ge -
œ J J
œ
? b
œ
œ
b b œ24. BINARY
œ AND
œ
CHAPTER
TERNARY
FORMS œ
œ
œ
378
Second Section
Phrase 3
b
& b b œœ œ œ
un - ter die
378
40
383
383
œ œj ˙
J
œŒ j j ˙
œ œ
Deck: mor - gen
œ
œ
œ
œ
J
275
j
œ œj œ œ œ
früh, wenn Gott will,
wirst due
wie - der ge -
œ œœ
b
œ œ œ.
j
& b b œœJ œœ œœ œJ œJ œ œœ b œœ œœ œ œ . œœJ œœ œœ œœ .. œœ œœ œ œœ œ œœ
œ œ œœ
J
œ
œ
œ
œ
? bb
œ œ
œ
œ
œ
b œ
œ
œ
œ
œ
œ
I = “Sectional”
bb
& b
b
&bb
? bb
b
b
&bb
j
œ
œ œj ˙
J
j j ˙
œ œ
Phrase 4
˙
- weckt, mor - gen
früh, wenn Gott will,
j
œ œj œ œ œ œ œ ˙
wirst due
‰ ..
wie - der ge - weckt.
œ œ œ.
j
˙
˙˙ ‰ b œœ œœ œ œ . œœ œœ œœ œœ .. œœ œœ œ œœ œ œœ œ ˙˙ ‰ ..
J
J
œ
œ
œ
œ
œœ ‰ .
œ
œ
œ
œ .
œ
œ
œ
œ
œ
œ
∑
∑
∑YT: 6kh51bIA2q8
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑ Section∑
b First
Phrase 1
∑
∑
∑
∑
∑
∑
388
Figure 24.2.1 Johannes Brahms, Fünf Lieder, Op. 49, No. 4 “Wiegenlied”
(1868)
b
&bb
388
The term “continuous” is used the first section of a binary or ternary form
does not end on the tonic chord. While this often means the first section ends
in a new key, it can also mean the first section ends on the dominant chord in
a half cadence.
112
? bb
& 42
œ œ œ. œ.
396
bb bp. .
&2
?
4 œ Œ
Andante
b
&bb
396
ten.
ten.
œ. œ. œ œ. œ. œ œ
. . œ. œ. œ
∑
∑
Œ œ Œ
œ Œ
œ
∑
Phrase 3
∑
&
? bœb j ‰ œ ∑œ œ œ œ œ œ
b œ
π
?
œ Œ
œ Œ
œ Œ
œœ
Phrase 2
j‰ œœ
œ. œ. œ œ œ # œ œ
œ
œ
œ. œ. . .
∑
Œ œ Œ œj ‰ œ ‰
J
œ
∑
ten.
ten.
œ∑ œ œ œ œ œ
œ
Œ
œ
œ
Œ
Second Section
Phrase 5 (contrasting material)
≈
≈
Phrase 4
∑œ œ œ œ
œ
Œ
? 242 œœ ŒŒ
?
44 œ Œ
ŒŒ
œ ŒŒ
œœ Œ œœ Œ
œ
œœ ŒŒŒ
œ
ŒŒ
Œ
œ
œœ
CHAPTER 24. BINARY AND TERNARY FORMS
&
& œœœ
&
?
?œ
?
œœ
jj ‰‰
œœj ‰
œ
Œ
ŒŒ
Phrase 3
Phrase 3
Phrase 3
œœ œœ
œ œ
π
π
π
œ
œœ
&
œœ œœ œ œœœ œœœ ## œœ œœ
&
& œ œ œœ
#œ œ
?
? œœ ŒŒ œjjj ‰‰ œœ ‰‰
?
œ Œ œœ ‰ œJJJ ‰
&
&
&
?
?
?
œœ
œœ
œ
œœ
œœ
œœ
œ
œœ
œœ .. ## œœ
œœ .. # œ
j
œœjj ‰‰‰
œ
œœ œœ œœ œœ œœ
œ œ œœœ
Œ
œ Œ
ŒŒ œœ ŒŒ
ten.
ten.
ten.
276
Phrase 4
Phrase 4
Phrase 4
ten.
ten.
ten.
œœœœ
œœ œœ œœ œœ œœœ œœœ œœ
œ
ŒŒ
œœ ŒŒŒ
œœ Œ
œ
œ
œœ œœ œœ œœ
œ œ œ œ
œœ ŒŒ
œ Œ
Second Section
Second Section
Phrase 5Section
(contrasting material)
Second
Phrase 5 (contrasting material)
jj‰ œœ Phrase
material)
≈≈
œœj‰ œœ nn œœ ≈≈ œœ5 (contrasting
œœ œœœ œœœ œœœ œœ œœ
œ
œ
œ
œ
œ
‰
≈
≈
œ
œ
œ
œ œœ n œœ œœ œœ œœ œ. œ. œ œœ œœ œ œ œœ œ œœ œœ œœ œœ œœ
pp œ œ œ.. œ.. œ
œ œ œ œ
ƒ
ƒ
jj‰‰ ƒ pœ œ
jj ‰‰
ŒŒ
œœj‰ œœ œ œœ
œœ œœ œœj ‰ œœ
Œ
œ œ œ
œœœ
œ
V
Vtonic” = “Continuous”
“notV
“not tonic” = “Continuous”
“not tonic” = “Continuous”
Phrase 6
Phrase 6
Phrase 6
œœ
œœ...
œ
œœ
œ ŒŒ œj ‰‰ œœ ‰‰
œœ Œ œœj ‰ œJJ ‰
J
œœ
œœ...
œ
œœ
œœ
œœ...
œ
œœ
œœ
œœ
œœ
œœ..
.
œ œ œ
œœ œœ œœ œœ
œ
œ
œœœ..
.
œ
œœœ..
.
ten.
ten.
ten.
œœ
œœ
œœ œœrr œ
œœ œœœr œœ
œ œ œœ
œœ œœ
œœ œœ
œœ
œ œ œœ œœ
œœ œœ œ œ
œœ
œœ
œ
œœ
œœ
œ
œœ ‰‰
œœ ‰
œ
‰‰
j
‰
œ œ œj
œœ œœ œœ
YT: lLjwkamp3lI
Figure 24.2.2 Joseph Haydn, Symphony No. 94 in G major, Hob. I:94, II
(1791)
In naming any binary or ternary form, use the terms sectional or continuous
before binary or ternary, for example “sectional binary,” “continuous binary,”
“sectional ternary,” or “continuous ternary.”
Other descriptors include “two-reprise,” which means both the first section
(the A section) and second section (the A’ or B section) are repeated, and
“rounded,” used in conjunction with binary (“rounded binary”) to specify that
the opening material returns after the contrasting section.
In the following sections we will discuss three types of binary forms:
1. Balanced Binary
2. Rounded Binary
3. “Simple” Binary (usually called “binary”)
24.3 Balanced Binary
A balanced binary form, according to Douglass Green in his book, Form in
Tonal Music, features a binary form with a first section (the A section) ending
in a new key, and the second section ending with essentially the same cadence,
now transposed to the original key, as in the following piece by Bach.
CHAPTER 24. BINARY AND TERNARY FORMS
First
First Section
Section
First Section
3
b
‰‰ œ œœ œ œœœ œ œœœ œœœ œœœ œœ œœœ œœœ œœ œœ œœ œœ œ
3
&
4
3
b
œ œ œ œ œ œœ
& b 44 ‰ œœ œ œœ œœ
&
?
33
œœ œœœ œœ œœœ œœ
∑
‰
?
b
4
∑
‰
? bb 434
œ
œ
∑
‰ œ
œœ
œ
œœ
œ
277 113
113
113
œ
œœ œœœ œœ œœ œœœ
œ
œ
œœ œ œ œ œ œ œ œ œ
œ œœ œœ œœ œœ œœ œ œœ œ œœ
œ œœ
œœ œœœ œœœ œœœ œœ œœœ œœœ œœœ œœ œœœ œœœ œœœ
œ
œ
œ
œœ
œœ œœœ œœœ œœœ œ œœœ
œ
These
bars
major
These 9
bars modulating
modulating from
from F
major to
to C
C major
major are
are transposed
transposed in
in the
the last
last 999 bars.
bars.
These
99 bars
modulating
from
FF major
to
C
major
are
transposed
in
the
last
bars.
œœœ œœœ œœœ
bb œœœ œœ œœ œœ œœœ œœ œœ œœ œœœ œœ œœ œœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ nnœœ œ œœœ œœ œœœ œœœ
&
&
b
n œ œœ œ
&
?
b œœœ œœœ œœœ
?
&
?
& bb œœœ œœ œœ œœ œœœ œœ œœ œœ œœœ œœ œœ œœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœœ œœ œœœ œœ œœœ œœ œœœ œœ œœœ œœ œœœ œœ œœœ ?
&
œ œ œ œ œ œ
œ œ nœ œ œ
b
&
& bb œœœ œœ œœ nnœœ œœ œœ œœœ œœœ œœœ œœœ œœœ
&
œœ œœ œœ œ œ œ œ œ n œ œ œ
œ œ œ œœ œœ œœ œœ œœ n œ œœ œ œœ
?
nœ œ œ
? bb
?
b
œ
bb ‰‰ œœ œœœ œœœ œœ œœœ
&
œ
&b ‰
&
œ nœ œ œ
?
? b œœ nnœœ œœ œœœ œœ œœœ œœœ œœœ œœœ œœœ œœ
?
œ
bb
œ
bb œœ œœœ bbbœœœ œœœ œœœ œœœ œœ œœ œœ œœ œœ
&
œœœœœ
&
&b
œ
œ
?
? b œ œœœ œœ œœœ œœ œœœ
?
bb œœ
œ œ œœ œœ œœ œœ œœ
bb œœ œœœ œœ œ œœ œ œœœ œ œœœ œ œœ œ
&
œ
œ
&
&b
œ
?
? bb œœ œœœ œœœ œœœ œ œœœ
?
œœ
b
114
œ œ
œœ œœœ œœ œœ œ œœ nnnœœœ œœ œœ
œ œ œ œœ
œ
œ
n
œ
œ
œ
œ
œœ œœ nn œœ œœ œœ œœ œœ œœ œœ œœ œ
œ
œ œ œ œ œœ
œœ œœœ œ œœœ œ nnnœœœ
œ
œœ
œœ
œœ œœœ œœ œœ œœœ œœœ œœœ œœœ œœœ
œœ
œ œœ
œ
Second
Second Section
Section
Second
Section
œœ
œ
ŒŒ
Œ
ŒŒ
Œ
‰‰ œœ œœœ œœ œœœ œœ
‰ œ œ œ
Cadence in C major
Cadence
Cadence in
in C
C major
major
œœ nnœœ œ œ œ œ œ œ
œ n œ œœ œœ œœ œœ œœ œœ œœ œœ œœ œ b œ œ œœœ œ œœœ œ œœœ œ œœœ œ œœœ
œ œ œ œœ bb œœ œœ œœ œœ œœ œœ
bœ
œ
œ
œœ œ œœœ œœ bbœœ ##œœ œœ œœ œœ œœ
œ
œœ œœ œ œœ
œ
#œ
œ
œ
œ
œœ
œ
œœ
œ
œœ œœœ œœ œœ œ œœ œ œ œ
œ œ œ œœ œ œœ œœ œœ œœ œœ bbœœ
œ œ bœ
œ
nn œœ œ œœ œ œœœ œœœ
n œ œœ œœ
œœ
œ
œ
œ # œ œœ œ œœ œ
## œœ
œœ
œœ
œœ œ œœ œ œœœ œ
œ œœ œ œœ
œœ
œœ nnœœ b œ œ œ œ
œ n œ bb œœ œœ œœ œœ œœ œ œœ œ œœ
œ œœ œ œœ œ
œœ œ œœœ œœ œœœ œœœ
œ œœ
œ
œœ œœ œ bbœœ œ œ œ œ œ
nœ œ œ œ œ
œ œ œœ b œ œœ œœ œœ œœ œœ œœ œœ œ œœ nnœœ œœ œœ œ œœ œœ œœ œ œœ œ œ œ œœœ œ œœœ œ œœœ œ œœœ œ œœœ
œ œ œœ œ œ œœ œ œœ œœ œœ œœ œœ œœ œœ œœ
œœ œœœ
œ
œ
œœ œœ œœœ
œ
œœ œ œœ œœœ n œ œœœ # œ œœœ œ œœœ œ œœœ œ œ œ œœœ œœœ n œ œœœ # œ œœœ œœœ œœ œ b œ œ
œ
œ œœ œ nnœœ ## œœ œœ œœ œœ œœ œœ œœ nnœœ ## œœ œœ œ œœ bœœ œœ œ œœ
b
œ
œ
œœ
œœ œ œ œ
œ
œœ n œ œœ œ œœ œ œœ œ œœ œ œœ
œ œœ œœ œœ nnœœ œœœ œœ œœœ ## œœ œœœ œ œœ
#œ
nœ
œœ œ œœœ œ nn œœ œ œœ œ œœ œ œœ œ œœ œ
These 9 bars are modulating from B¯ major to F major.
œ œ œ b œ œ œ bœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ
œ œ
&b
œ œ œ œ œ œ œ œ œ œ œ œ
œ œ bœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ
? b œœœ œ œ œ œ œ œ œ œ œ œ
œ
œ œ œ œ
& b œ œ œ œ œ œ œ œ œ œ œ bœ œ œ œ œ œ œ œ œ œ œ
œ œ œ œ œ œ œœœ œ œ œ œ œ œ œ
? b œ œ œ œ œ œ œ œ œœ œœ œœ œ œ œ œ œ œ œ œ œœ œœ œ œ
œ œœœœœœœœœ
œ
œœ Œ Œ
œ
œ
Cadence in F major
&b
Œ Œ
œ
œ
œ
œ
œ
œ
œ
b
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ œ œ
œ œœ œœ œœœ œœ œœ
? b œœœ œ œ œ œ œ œ œ œ œ œ
œœ
œ
œ
œ
CHAPTER 24. BINARY AND TERNARY FORMS
278
& b œ œ œ œ œ œ œ œ œ œ œ bœ œ œ œ œ œ œ œ œ
œ œ œ œ œ œ œ œ œœœ œ œ œ œ œ œ œ
œ
? b œ œ œ œ œ œ œ œœ œœ œœ œ œ œ œ œ œ œ œ œœ œœ œ œ
œ œœœœœœœœœ
œ
œœ Œ Œ
œ
œ
Œ Œ
Cadence in F major
&b
?b
These 9 bars are modulating from B¯ major to F major.
œ œ œ b œ œ œbœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ
œ œ
&b
œ œ œ œ œ œ œ œ œ œ œ
œ
YouTube: https://www.youtube.com/watch?v=HFeLqgVLxBM
œ
œ
œ
œ
œ
œ
b
œ
œ
œ
œ
œ
œ
œ œ œ œ œ œ œ œ œ œ œ œ œœœœ œ œœ œœ œœ
œ
œ
?
œœ œ œ œœ œœ œ œ œ œ œ œ
œ Invention No. 8 in F major, BWV 779
Figure 24.3.1 b J.S.
œ œBach,
114
Because the first section These
of a9 bars
balanced
binary
ends
in a new key, it is
are modulating
from B¯ major
to F major.
a continuous
binary
form.
œ
& bb œœ œœœ œœ œ œ œ œbœœœ bœ œ œœbœ œœœœœœœœœ œœœœœ œœ œ œ œ œ œ œ œ œ œ œœ œœ œœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ Œ Œœ œ
œ œ œ œ œinœ œ movements
œ
œ Baroque era,
œ œ œ from
œ œ œœ the
Balanced &
binary form
can be œfound
œ
œ
œ
œ
œ
œ
œ
œ
œ
b
œ
œ
œ
œby
œ œ œ œ œ œHandel,
œœ œ œ œ œand
œœ œ œothers.
œ œ œ œ œ œ œ œ œ œThe
œ œ œ œ œ œmovement
?
œ
œ
œ
œ
including dance
suites
Bach,
below
œ
œ
œ
œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ Œ œ œ Œœ œ œ œ
? bb œœœ œ œ œœ œ œ œ œ œ œ œ
œœ
shows the endingsœ ofœ œthe
first and section sections of theœ Courante from J.S.
Bach’s French Suite No. 6 in E major, BWV 817.Cadence in F major
114
inherently
œ
Œ Œ
& b # œ# œ œ œ œ œ œ œ œ œ bœ œ œ œ œ œ œ œ œ
œ œ œ œœœ œ œ œ œ œ œ jœ œ œ œ œ œ œ œœœ j .
#
3
œ
œ
#
œ
j
œ
œ
œ
œ
‰
≈
œ
#
œ
&
4 œ œ
œ œ œ œœ. .
? b œ œ œ œœ œ œ œ œœœ œ œ œ œ œ œ œ œœ œ œ œ œ œ œ œ œ œ œ
œ œ œ œ œ œ œ œ œ œ J œ JŒ Œ
œ
..
œ in F major œ .
Cadence
? # # # # 43 œ œ œ œ œ
≈œœœ
J ..
œ
j
j
##
& # # 43 œ œ œ œ œ œ œ œ œ œ œ # œ œ ‰ ≈ œ œ œœœ.j.. ..
œ
# # # # œ œ œ œ œ œ œ œ œ œ ‰ ≈ J œ œœJjj.. .
œ
œ
& # œ
J
œ œ œJ œJœ.. .
? # # # 43 œ œ œ YT:œ jrHP6Fp1yUY
œ
≈œœœ
J ..
œ 6 in E, BWV,
. Courante, bars
œ
œ
Figure 24.3.2 J.S. Bach, French
Suite
No
817
œ œ œ
œ œ
? #### œ œ
J
œ
..
≈
15–16
œ
j
# ##
œ œ œ œ œ œ œ œ œ œ œ ‰ ≈
œ j.
& # œ œ
J
œ œJ œ œJœ. . ..
œ.
œ œ œ
œ œ
œ
? #### œ œ
J ..
œ
≈
œ
YT: jrHP6Fp1yUY
Figure 24.3.3 J.S. Bach, French Suite No 6 in E, BWV, 817 Courante, bars
31–32
24.4 Rounded Binary
In a rounded binary form, the material at the beginning of the first section
returns, often shortened, after a contrasting phrase at the beginning of the
& #
œ œJ œ œJœ. .
CHAPTER 24. BINARY AND TERNARY FORMS
œ
œ279.
œ
œ
œ
œ
? #### œ œ
J
≈ œ œ
œ
œ œ
œ
œ
J
second section. A generic phrase diagram of rounded binary form is shown
below.
First Section
a
b
a
(opening melody
returns)
Below is an example of a rounded binary form.
First Section
First
Section
PhraseSection
1
First
Phrase 1
CC œ œœ
C œœ œ
pp
CC pÓÓ &
C Ó &
&
## #
&
##
&
& #
## #
&
# ##
&
&
œœ
œ
Phrase 1˙
˙
œœ˙
œ˙˙
˙˙
œ œ
œœ œœ œœ œœœ œœ œœ œœ œœ œœ œœ œœ œ
œ œœœœœ
œœœ
œ
œœ œ œœ œ œœ œ œœ œ
œ œœ œ œœ œ œœ œ œœ
œ œ
œ œ
œœ œœ œœ œœ œ œœ œœ œœ œ œœ œ œœ œ œœœ œœ œœœ œœ œœ œœ œœ œ œœ œ œœ
œ œ œœ œ œ œ œœ œ œœ œ œœ œ œ œ œœ œ œœ œ
Phrase 2
2
œœ œ œ œ œ œ œ œ œœœ œœ ## œœ œœ œ œœ œœ œ œ œ œ œ œ .
œœ Phrase
Phrase˙2
œ œœ œœ œœ œœ œœ œœ œœ œ # œ œ œœ œ œ œœ œœ œœ œœ œœ œœ œœœ ..
œ œœ.. œœ.. ˙˙
œœ œœ œ .
ffœ. œ.
œ
f ? œ œœ œ œœ œœ œ œœ œœ # œ œœ œ œœ œœ œœ œœ œœ œ # œ ˙
Ó ? œ œ œ œ œ œ œ œ œ œ # œ œ œ œ œ œ œœ œœ œœ ## œœ ˙˙ ..
œœ ÓÓ ? œ œ œœ œ œœ # œ œ
œ œ œ ˙˙ ..
œ
Second Section
Second Section
(contrasting material and texture)
Phrase 3Section
Second
Phrase 3 (contrasting material and texture)
Phrase 3
œ œ œ #texture)
Phrase
œ # œ œ œ 3 (contrasting
œ œœ # œ n œ œmaterial
œ œ œ œœ n œ œ œ
œ œ and
j
œ œ œœ ## œœ œœ nn œœ œœ œ œœœ œœœ œœ œœ ˙˙˙ . œœjj ‰‰‰ Œ
œ œ œ œ ## œ ˙ . œ ŒŒ
#œ ˙.
ff
pp
‰‰
f
p
œœ œ œ œ œ œ ˙ œ
jj ‰ ŒŒ
œ
œ
˙
œ
œ
œ
˙
œ
œ
œ
œ
œ
œ
œ
œ œ œ œ œ œ œ œ ˙œ œ œ œœ ˙ . œj Œ
œ œ œ œ œ œ ˙˙ . œ
.
Phrase 4 (opening melody returns)
4 (opening melody returns)
œœ œœœ œœ œ œ œœ œ œ œ œ
œ
œ
Phrase ˙4 (openingœ melody
returns)
## # Ó Phrase
œ
œ
œ
œ
œ
œ
œ
œœ œ œ œœ œ œ œ œ œ œœ œ œ œ œ œœ œœ œ œœ œœ œœ œœ ..
œ
œ
˙
#
&
#
Ó
œ
œ
&
œœ œœ œ ...
œ œ œ œ œ œ œ œœ œœ
& # Ó fœ œ ˙
œ
œ
f
œ
˙
œ
f
## #
? œœœ œœ œœ ˙˙
∑
œ
œ
&
œ
œ
#
##
œ œ ˙˙ ....
œœ œ œ œœ œ œœ œ œ œ œ œ œ œœ ?
∑∑
œ
œ
?
œ
&
œœ œ œ œ œ œ œœ œ œœ œœ œ œœ œœ œ œœ œ œœœ
.
&
œ
œ
œ
œ
## #
&
# ##
&
&
?
## #
?
? # ##
.. œœ ## œœ œœ œœ
..
pp
.. pÓÓ
.. Ó
..
Second Section
a
## #
&
##
&
& #
?
#
?
? ## ###
..
œœ œœ # œ œœn œ œœ œ œ
# œ œn œ œ œœ
## œœ œœ œœ nn œœ
# œœ œœ œœ nn œœ &
œ nœ &
&
115
115
115
j
j..
œ
œ
œ
œ
œ
280
œ J J.
œ
œ.
œ
J
≈ œ œ
####
œ œ œ œ œ œ œ œ œ œ œ ‰
œ
&
œ24. BINARY AND TERNARY FORMS
J
CHAPTER
? #### œ
œ
œ
œ
œYT: zHtXRBi91dA
œ
≈
Figure 24.4.1 Mozart, Piano Sonata in D major, K. 284, III.
/:
First Section
:/:
A: PAC
a
D:
Second Section
a'
HC
b
a''
D: HC
PAC
:/
Because both the first section (the A section) and second section (the B
section) repeat in the example above, this form would be called “two-reprise
continuous rounded binary form.”
Another example
of a rounded
a
a binary formbis below.
a
116
116
First
First Section
Section
.
343 œœ . œœ œœ œœ
œ œ
4
pp
? b 433 ŒŒ
?
b 4
œœ œœ
&
& bb
Phrase
Phrase 1
1
œœœ
œœ
(opening melody
returns)
Phrase
Phrase 22
œœ˙˙ œœ œœ œœœ œœœ œœœ œœœ ... # nn œœ œœœ ... œœ ˙˙˙
#œ œ
˙˙
œœ œœ œœ œœ œœ œœ n œ
œœ œœ œ n œœ
& b œœ˙˙
œ
?
? bb ˙˙
œœ œœ œœ œ
œ
œœ œœ œœ .. ## œœ œ .. œœ ˙
b
&
œœ
Œ
œœ Œ
Second
Second Section
Section
œœ .. œ œœ œœ œœ
... ...
Phrase
Phrase 33
˙˙
˙˙
œœ
œœ .. œœ
œœ
œœ
.
&
& ..
œœœ œœœ œœœ
œ œœ
œœ œ .. œ
œœ œ œœ œœ
(melodically
(melodically related
related to
to first
first phrase)
phrase)
... œ .. œ
œœ œœ
œ œ œœ œœ œœ ˙˙
œ
œ
œ
˙
(different accompanimental texture and register)
(different accompanimental
accompanimental texture
texture and
and register)
register)
(different
Phrase
(opening melody
melody returns)
returns)
Phrase 44 (opening
?
?
&
& bb œœ œœœ .. ## œœ œœ .. œœ œœœ œœ Œ
&b
œœ œœ
œœ
œœ .. œœ
œœœ œœœ œœœ œœ˙˙ œœ œœ œœœ œœœ œœœ œœœ ... œœ œœ œ
œ œ œœ ˙˙
˙˙
œœ œ œ œœœ
œ
œ
œ œ
œœ œœ
œœ
œœ
...
...
YT: 2vs-CrxwOmE
Figure 24.4.2 Schubert, 20 Minuets, D. 41, No. 18 in F major
?b
• “Two-reprise” means both the first and second sections repeat
This form of the example above would be called “two-reprise continuous
rounded binary form” because:
• “Continuous” means the first section does not end on the tonic chord
• In a rounded binary form the opening melody returns after contrasting
material
..
..
CHAPTER 24. BINARY AND TERNARY FORMS
281
Rounded binary form is often encountered in compositions during the Classical
era (1750–1825) in music by Haydn, Mozart, and Beethoven, especially as the
form of a theme from a theme and variations, and as the minuet and/or trio
section in a Minuet and Trio.
24.5 Simple Binary
“Simple” binary is a term used to describe a binary form that does not have
features like the similar endings of a balanced binary or the return of opening
material like the rounded binary. You will encounter this type of binary form
in music especially throughout the Baroque era, as well as in the early Classical
117
117
era.
117
First Section
Section
First
First
Section
œ
œ œ œ
œ
˙
œ
œœ œ
bb bb CC œ œ œ œ œ œœ œ ## œœ œœ ˙
œ
&
&
œœ œœ œœ œœ œ œ œ
œœ œœ œœ
œœœ
œ
b
?
œ
? bbb CC œ œœ
œ
(starts in G
G minor)
(starts
(starts in
in G minor)
minor)
b œœ œœ œ œœ ## œœ œ
bb b
œ
œ
&
&
œ œœ œœ
?
œ
œ
b
œ
? bb b
& bb bb
&
? b
?
bb b
œœ ..
nn œœ
JJ
œœ œœ œœ œœ
œœ
œœ
œœ
1.
1.
1.jj
j
œœœj
œœ œ œ œ
œ œ œ
...
˙˙
œœ œœ œœ œœ ...
(ends in B
B¯ major)
(ends
(ends in
in B¯¯ major)
major)
2.
2.
2.jj
j
œœœj
˙˙
œœœ
œœ œ œ œ
(develops melody and
and motives from
from first section)
section)
Second
Second Section
Section (develops
(develops melody
melody
and motives
motives from first
first section)
œœ œœ œœ œœ œœ œœ nn œœ œ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ nn œœ œœ
... œœ œœ œœ œœ œœ œ œœ œœ œ ˙˙
œ
œ
œ
.
œ œ
œœ œœ œœ œœ
œœ œœ œœ œœ œœ œ
nœœ œ œ œœ œœ œœ œœ œœ œœ
.. œ œ
œ
n
œ œ
.
(begins in B
B¯ major)
(begins
(begins in
in B¯¯ major)
major)
b œ nœ œ œ œ œ œ œ nœ œ
bb b œ n œ ##œœ œœ œ œ œ œ œ œ n œ œœ œ
&
&
œœ
?
? bb bb nn œœ œ nn œœ ## œœ œœ
œ
œœ
bbb ˙
&
&b ˙
?
? bb bb
œœ
œœ œœ œœ œœ œ œ œœ œœ œœ œœ œœ
œœ œœ œ œ œ
œ œ œ
œ œœ
œœ œ œ œ œ œ
œœ
œ œ œ œ
œœ œ œ œœ œ œœ œ
œœ œœ œ œ œœ œ œ # œ
œ œ œ œ # œ œœ
œœ
mwmw
œœ œœ œœ œœ œœ œœ œœ œœ nnœœ œœ # œ œœ œœ œœ œœ œœ
#œ
œœ nnœœ œœ œ nnœœ # œ ˙
œœ œ œœ
œ œœ # œ œœ ˙
œœ œœ
œ
œœ
œœ
œ
bb œœ œ
œ
œ bœ œ
œœ œ b œ œ œœ nnœœ œ œœ œ œœ œœ œ
MM m
M
mww
Mœœ
˙˙
œœ bbœœ œœ Mœœ Mœœ
œœ
b bb œ œ œ œ œ œ
&
& b œ œ œœ œ œ œ œœ œ œœ nnœœ ## œœ œœ œ œ œœ
? b œœ œœ œœ œœ œœ ##œœ œœ œ
?
bb b
œ œœ œœ œœ
œ
œœ œœ œœ œœ œ œ
œ
M
M
Mœœ ˙˙
Mœœ
œ
œœ œœ œœ œœ # œ œ œœ œœ
#œ
œœ
˙˙
œœ œœ œœ œœ
(back in G
G minor)
(back
(back in
in G minor)
minor)
œœ œ œœ œ œ œ œ œ
œ œ œ œ œ œœ œ œ œœ œœ œœ œœ ## œœ œœ œ nn œœ nn œœ œœ œ
œ
œ
œ
œ
œ
## œœ œ œœ œ
œœ œ œ œ
œœ œ œ œ
œœ
(opening melody does
does not return
return—not
not rounded binary)
binary)
(opening
(opening melody
melody does not
not return—
—not rounded
rounded binary)
ŒŒ n œ
nœ
ŒŒ
? bb
œ
MM
œ bœ œ œ œ
mw
Mœ Mœ
˙
Mœ œ
˙
˙
CHAPTER 24. BINARY AND TERNARY FORMS
b
& b œ œ œ œ œ œ œ œ œ nœ #œ œ œ œ œ
? b œ œ œ œ œ #œ œ
b
118
œ œ œ œ
œ œ œ
? bb # œ
&b
œ
œ nœ #œ œ œ œ œ
œ
b
&b
b
Œ
#œ
œ œ œ
282
(back in G minor)
œ œ œ œ œ œ œ #œ œ œ nœ nœ œ œ
œœœ œ
œ
œ
Œ
(opening melody does not return—not rounded binary)
b
&b œ œ œ œ œ œ œ œ
? b
b œ
œœœœœœœ
œœœœ
nœ
Œ
œ nœ œ
nœ bœ œ
œ
œ
Œ
œ
Œ
œ
œ œ œ œ œ œ œ
#
œ
œ
#œ
œ
œ
œ
œ
#œ œ œ
œ
œ œ œ
œ œ œ
œ œ œ m
œ œ œ œ
œ
œ
Œ
nœ
œ
œ
œ
˙
˙
..
..
(different ending than first section—not balanced binary)
? bb
YouTube: https://www.youtube.com/watch?v=KMrJxhYj3tc
b
Figure 24.5.1 J.S. Bach, English Suite No 3 in G minor, BWV 808, Gavotte
I.
Notice in the example above that the first section and second section can
begin similarly in a binary form, resulting in the large-scale form AA’. The
second section often features development of the primary idea from the first
section. We will discuss development in the next chapter.
&b
? bb
24.6 Binary Principle
Binary principle, as defined by Peter Spencer and Peter Temko in their
book A Practical Approach to the Study of Form in Music, states that the
first section of a binary form modulates to a new key and the second section
modulates back to the first key. We find this principal exemplified in a high
percentage of binary forms in the Baroque era, and diagrammed in the example
below.
&b
b
? bb
/:
:/:
A: PAC
a
a'
D:
HC
b
a''
D: HC
CHAPTER 24.
a BINARY AND
a TERNARY bFORMS
First Section
PAC
:/
283
a (opening melody
returns)
Second Section
Major: I modulation V
V
modulation I
Minor: i modulation III (or v) III or (v) modulation i
Original key
New key
Original key
Figure 24.6.1 Diagram illustrating Binary Principle
24.7 Ternary Form
b
& bbb
& bbb
&
? bbb
bbb
?
& bb b b
? bb
bb
? b
bbb
& bbb
& bbb
& bbb
?
bbb
?
& bb b bb
? b
bb
? b
bbb
& bbb
& bbb
&
? b bb b
b
?
& bb b bb
? bb
bb
? bb
bb
& bbb
& bbb
&
? bb bb b
& b b bb
?
? bb b b
bb
?
& bb b b
b
? bb
b
œ
24 œ . œ œ œ œ . œ œ œ œ . b œ œ œ œ œ œ œ œ œ œ œ
œ
24 œ . œ œ œ œ . œ œ œ œ . b œ œ œ œ œ œ œ œ œ œ œ œ
œ œ œ œ . b œ œœ œ œ œ œ œ œœ œ œ
F œœ
œ
œ œ œ nœ
œœ
422 Fœœœ . œœ œ œœ . œœ
œ
œ
œ
œ
œ
œ
œ
42 œ . œ œœ œ œ . œœ œ œœ . b œ œ
œ nœ œ œ œ œ œ
œ
442 Fœ œ
œ
œ
œœ œœ
œ
œ nœ œ
œ
2 œœ œœ
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œ
œ
œœ œœ
œ
œ nœ œ
œ
2 œœ œœ
4 œœ œ
œ œ œ œ. bœ œ œ œ œ œ œ œ œ
œ.
œ.
œ
. œ œ œ œ . œœ œœ œ œ . b œ œ œ œœ œœ œ œ œ œ
œ
p . œ œœ œ œ . œ œ œ . b œ œœ
œœœœœ
œ
œ
œ
œ
œ
œ
p œ œœ œ œ œ œœ œ œœ . b œ œœ œ œ œœ œ œ œ œœ
œœ
œ. œ
œ
œœ
pœœ . œœ
œ
œ
œ
œœ
œ
œ
œ
œ
œ
œ
œœ
p
œ
œ
œ
œ
œœ
œ
œ
œ
œ
œ œ œ œ œ œ œ œ œ œ œœ œœœœ œ
œ
œ œ œ œ œ œ œ
œ œ œ œœ œœ
fœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ
œ
œœœ
œ œ œ œœ œ
œ
fœ œ œœ
œ
œ œ œ œ œ œ œ œ œ œ œ œ œ œœ œ œ
fœ
œ
œ
œ œ œ œ œ
œ œ œ œ œ
f
œ
œ
œ
œ œ œ œ œ
œ œ œ
œ
œ œ œ œ œ œ œ
œ œ œ œœ œœœ U
œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ Uœ
œ
pœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ U
U
œ
œ
œ
œ
œ
œ
œ
œ
œœ
œ œ œ œ
pœ œ œ
œ
œ
œ
œ
U
œ
œ
œ
œ
œ
œ
œ œ œU
œ
œ œ œ
p
œ
œ
œ
U
œ
œ
œ œ œ œ œ
œ œ
p
œ œ
œ. œ œœ œ œ. œœœ œœ œ œ . œb œ œ œœ œœ œ œœ œ œ œ œUœ œ
œ
œ
œ
œ
œ
œœ
f
œœ œœ
œ nœ œ
œœ œœ
œ
119
Ternary form is usually diagrammed as ABA and is described as “statement, 119
digression, restatement.”Green, Douglass M. Form in Tonal Music: an Intro- 119
duction to Analysis. 2d ed., Holt, Rinehart and Winston, 1979, p. 84 A piece
119
in a rather simple and straightforward ternary is shown below.
120
b
œ œ œ œ. œ œ œ
& b b œ.
p
œ
œ
œ
œ . b œ œ œ œ œ œ œ œ Uœ
œ
œ
œ
œ
poco rit.
U
120
? b œœ
bb
œœ
œœ
p
? b b œœ
b
œœ
œœ
œœ
œ
œ
œ
œ nœ
bb œ . œ œ œ œ . œ œ œ œ . b œ œ œ œ œ œ œ œ œ œ œ œ
b
& 24. BINARY AND TERNARY FORMS
CHAPTER
284
œ
œ
f
?b b bœ . œœœ œ œœœ œ . œœœ œ œœœ œ . œb œ œ œ œ œ œ œœ œnUœœ œ
& bb b
œ
œ
œœ
œ
œ
œ
U
poco rit.
œ
œ . b œ œ œ œ œ œ œ œ Uœ
b
œ œ œ œ. œ œ œ
& b b œ.
œ
œ
p
œœ
œœ
œœYT: BJviMnAB_jg
œ
œ
œ
b
?
&
b
œ
Figure 24.7.1
b b Mozart, Andante in E-flat major, K. 15mm
bb
œ
poco rit.
Below is a diagram of K. 15mm by Mozart.
? bb
b
E¯:
A
B
a
a'
HC
b
PAC
œ
A
b
HC
U
a
HC
a'
HC
PAC
bbb
&Character
pieces from the Romantic era with titles such as “Nocturne,”
Figure 24.7.2 Diagram illustrating Binary Principle
“Intermezzo,” and “Song Without Words,” among others, by composers such
as Schubert, Chopin, Mendelssohn, Schumann, and Brahms, are often in a
larger ternary form where each section might be longer than eight bars.
Below are examples from a larger ternary piece, Rachmaninov’s Prelude in
C-sharp minor, Op.3 No.2.
121
? bb
b
# # # # Lento
c
&
œ
>
ƒ
? #### c
œ
œ
>
&
####
? ####
œ
>
œ
œ
>
w
>
w
w
>
‰ j‰
œœ œœ # œœ n n œœ # œj
œ- œ- œ- n œ n œ- œ # œœ˙ ∏
.
.
-œ œ- ‹ œ- # œ- # œ‰ œ œœ # œ ‰ # œ ‰
œ ‹ œ n œ # œJ # œœ
œ J
˙
n œ.
œ.
˙
‰
‰
œœ
œ˙
‰ œœ
œ
˙
˙
œœ œ ‰ n œj ‰ # œj
œ- # œœ- n n œœ- # œœ
nœ
œ .
.
œ- ‹ œ- ‰ # œ- ‰ # œœœ # ‹ œœ # # œœ œ
n œ J œ # œJ
n œ.
œ.
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Figure 24.7.3 Sergei Rachmaninoff, Prelude in C-sharp minor, Op. 3 No. 2,
First A section bars 1–13
&
####
? ####
&
####
‰ œ œœ # œ ‰ # œ ‰
‰ œ œœ # œ ‰ # œ
? #### c
‹ œ # œ # œœ
œ
œ ‹ œ n œ # œJ
œ œ
n
œ
J
œ
J
œ œ w ˙ - - - n œ. - œ. - ˙ - - - n œ. CHAPTER 24.> BINARY
> w AND˙ TERNARY FORMS ˙
>
#### - - &
œ œ œ œnœ #œ œ
œ ‹œ #œ
œœ
3
F 3 3
-3
? #### Œ - #œ nœ
œ
w
w
Agitato
&
####
‰
œ
œ # œJ
œ. -285
- - œ œœ œœ œœ œ
œ œ œ œnœ # œ œ
œ ‹œ #œ œ œ œ œ œ œ
-3 -3 œ #œ nœ
w
3
-3
œ
3
3
cresc.
3
3
œ œ œ œ
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Figure 24.7.4 Rachmaninov, Prelude in C-sharp minor, Op.3 No.2, B section
bars 14–42
? ####
>œ >œœ # >œœ # n >œœ
œœœ œœ ‹ œœ # n œœ
‰
‰ J
&
# # # # Ï pesante
& ####
nœ
&
˙˙
nœ
˙˙
>
? #### >
>œœ >œœ ‹ >œœ n # >œœ
? # # # # ‰ œœ œœ # ‹ œœ ‰ # # œœ
J
Ï pesante
? ####
nœ
˙˙
nœ
˙˙
>
>
55
##
& ## ∑ ∑ ∑ ∑ ∑
Tempo primo
53
####
>œ >œœ # >œœ # n >œœ
# >œœ
œ œ
‰ # # œœ ‰ œœ œ ‹ œœ ‰ # n œœJ
J
sÎ
nœ
œ
˙
nœ
œ
˙˙˙
>
>
>
>œœ >œœ ‹ >œœ n # >œœ
# >œœ
œ
# œ
‰ # œœ ‰ œœ œ # ‹ œœ ‰ # œJ
J
sÎ
nœ
œ
˙
nœ
œ
˙˙
>
˙
>
>
∑ ∑ ∑ ∑ ∑ ∑ ∑
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# >œœ
‰ # # œœ
J
œ
œ
>
# >œœ
‰ # œœ
J
œ
œ
>
∑ ∑
#### ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
&
Figure 24.7.5 Rachmaninov, Prelude in C-sharp minor, Op.3 No.2, Second A
section bars 45–61
? #### ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
24.7.1 Compound Ternary
A compound ternary is a ternary form in which one of the sections (the A
or the B) is itself a binary or ternary form. Examples can be found in the
minuet and trio as well as the da capo aria.
? #### ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
In the next section, we will examine the differences between rounded binary
and ternary.
CHAPTER 24. BINARY AND TERNARY FORMS
286
24.8 Distinguishing between Rounded Binary and
Ternary
In homework and on the test, you will encounter pieces that are five or six
phrases long that could be rounded binary or ternary. While other authors
have their own means to differentiate rounded binary from ternary, this text
offers the following criteria to consider:
1. Proportion: consider the proportion of the contrasting section to the
other sections. If the contrasting section is too small to stand alone, the
form is more likely to be rounded binary.
2. Nature: consider the nature of the contrasting section.
(a) If the melody is built from motives from the first section, the form is
likely to be a rounded binary. Ternary form will have a contrasting
melody in the contrasting section.
(b) If the harmony consists mostly of a dominant pedal, or a V chord
alternating with a I or I 64 chord, the form is likely to be a rounded
binary.
3. Era: consider the era when the piece was written. A piece by a Baroque
composer (J.S. Bach, Handel, Scarlatti, Couperin) or Classical composer
(Haydn, Mozart, and Beethoven) is more likely to be in rounded binary
form, whereas a piece by a Romantic era composer (Schubert, Schumann,
Chopin, Mendelssohn, and Brahms, among others) is more likely to be
in ternary form. Note that these are generalities. Baroque and Classical
composers wrote compositions in ternary form and Romantic composers
wrote pieces in rounded binary form.
Consider the following piece by Beethoven:
122
122
Vivace moderato.
& 433 ‰ œ œ
&4 ‰ œ œ œ
pœ .
œœ
?3
.
? 43 œ. œœ
4 œ.
Moderato
œ œ
œ œ
œœ.
œœ.
œ.
œ.
œ.
œ
.
#
œ
‰ œœ œ # œ œ ‰
‰
‰
F
F . .
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œ. # œ œ œ.
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n ˙˙ ..
p
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œ
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..
.
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œ œ
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poco rit.
U
U
œ
œœœ
.
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.
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˙
nn ˙˙˙ ..
.
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.
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.
œ
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p
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123
Œ
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..
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Œ
..
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Figure 24.8.1 Beethoven, Eleven Bagatelles, Op. 119, No. 9
?
In terms of proportion, bars 9–12 contain contrasting material to bars 1–8.
Because the contrasting material lasts for half as long as the open section, we
consider the proportion as pointing toward rounded binary.
In terms of the nature of the contrasting section, the melody is built from
the contour of the first four notes of the first measure, and the harmony alternates between V and I 64 . Both the harmony and melody point us in the
direction of rounded binary.
Finally, consider the era in which Beethoven lived. Is he considered a Classical or Romantic composer? This is a difficult question to answer, as Beethoven
is a unique figure who is a bridge between the Classical and Romantic eras.
However, it’s generally safe to consider Beethoven as belonging to the Classical
era, and therefore as likely to write a rounded binary form.
You will encounter examples on homework and the test where these three
criteria are not unanimous and you will have to weigh the evidence to come to
a conclusion.
&
?
&
?
CHAPTER 24. BINARY AND TERNARY FORMS
288
24.8.1 Written-Out Repeats
Occasionally you will encounter an example where the repeats are written out.
When you encounter such a piece, put the repeats in your diagram even though
there are not in the score.
24.9 Practice Exercises
134
134
134
134
134
Day One
1. For Handel’s Gavotte, HWV 491, please fill in the blanks below the
staves and diagram the form. Also, name the form. You will need
to determine which notes are non-chord tones in order to determine
Allegretto
RomanAllegretto
numerals.
œœ œ œ œ œ œ œ
## Allegretto
44 œ œ œ œœ œœ œœ ˙˙˙ ..
Allegretto
œ œ œ œ œ œ œ œ œ ˙.
œ
&
&#
&
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___
œœ œ œ œ œ œ œ œ
œœœœ
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œ
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___
___
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___
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œœ œ ...
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œ
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pp
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b œ n œ œ. 289
œ TERNARY
œ
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CHAPTER 24. BINARY
FORMS
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Circle all of the terms that apply to the name of the form:
TWO-REPRISE SECTIONAL
2.
CONTINUOUS
ROUNDED BALANCED
BINARY
TERNARY
For the theme from first movement of Mozart’s Piano Sonata in A
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A
a
/TWO-REPRISE
:
B
:/:
a'
SECTIONAL
CONTINUOUS
bROUNDED BALANCED
c
BINARY d TERNARY
:/
Day Two
3. Menuetto
For this diagram:
Polonaise in F major by Mozart, please fill in the blanks below
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150
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24.9.3
Mozart,
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A
a
/TWO-REPRISE
:
B
a'
SECTIONAL
:/:
CONTINUOUS
bROUNDED BALANCED
c
BINARY d TERNARY
:/
Menuetto diagram:
Trio diagram:
G: HC
m. 4
D: PAC
m. 8
e: PAC
m. 12
G: HC
m. 16
PAC
m. 20
123
..
..
CHAPTER 24. BINARY AND TERNARY FORMS
4.
25
25
25
25
For this Allegro in B-flat major (K. 3) by Mozart, please fill in the
blanksAllegro
below the staves and diagram the form. Also, name the form.
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œ nœ
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j
œœœ œœœ œœœ nn œœ nn œœ ‰‰ œœjjj
œ œ nn œœ nn œœ ‰‰ œ
œ
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∑
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____
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œœ ‰‰ œJJœJ œœ œœ œœœ œœœ
‰ J
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œœj œœ nn œœ œœ œœ œœ ‰‰ œœJ
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‰ JJœ
nœ
œ ‰ JJœ
J
J
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‰‰‰ œœJœJ œœœ œœ œœ ‰‰‰ œœJœJ
J
JJ
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____
‰
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127
127
127
127
____
œ œ œ b œ___
___œ___
___
œ
esc.
(œ)
œ nn œœ œœ œœ œœesc.
.
esc.
(œ) b œ
œœœ____
nn œœ œœ œœ œœ ((œœ)) bbb œœœ ...
____
œ.
œœœ ... ____
esc.
œ
œœJœJ œœœ...
JJ œ .
V
___
V ___
V
V ___
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œ œ œ œ œ œ ˙ ___
˙
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b
& bbbbb
&
NCTs:
&
b
&
œ t5R0ORjKloE
bœ œ œ œ œ œ œ œ œ œ œ œ œ œ
? b b œ œ œ œ œ œ œ œ œ œ œYT:
œ
œ
˙
? bbb
?
___ ___
..
...
.
...
.
?
? bb
bb b 24.9.4 Mozart, Allegro in B-flat major
Figure
RN:
HF:
____
____
____ section
On
scratch
paper,____
create a____
diagram____
of the ____
form. Include
____
____
____
____
____
____
____
labels
bbb using uppercase letters, phrase labels using lowercase letters,
&
b
b
b
& bbcadences
and
using the abbreviations PAC, IAC, HC, DC, PC.
&
&
Circle all of the terms that apply to the name of the form:
? b
?
?
? bbbbbb
b
TWO-REPRISE
SECTIONAL
CONTINUOUS
ROUNDED BALANCED
BINARY
TERNARY
Day Three
5. Please fill in the blanks below the staves and diagram the form of “After the Ball” from Alexander Gretchaninoff’s Children’s Book, Op.98.
Also, name the form.
#
œ
œ
˙
œ
˙
& # 43 œ˙ .˙ # œ˙ .˙
œ.#œ œ. J œ œ
œ˙ .
œ. #œ œ. J ˙.
# œ˙ .
F
˙
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œ ˙ œ #˙
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4
œ
Tempo di Mazurka
__________
________
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#
j
j
j
j
j
œ œ œ. j
& # .. œ œ . œ œ . œ œ œ œ . œ ˙
œ œ. œ œ œ œ. œ ˙.
p œ.
f . œ.
œ.
.
œ # ˙˙ ..
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.œ œ. Œ œ œ.
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.
.
.
_________ _____
#
& # œ˙ .˙
˙
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œ
œ
˙
œ.#œ œ. J œ œ
œ˙ .
______
˙
# œ˙ .
___
œ
œ. #œ œ. J ˙.
rall.
..
129
? ## 3
4
F
˙
œ
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œ #˙
˙
œ ˙
œ
˙
˙
œ #˙
˙
œ
CHAPTER 24. BINARY AND TERNARY FORMS
150
LSS:
Motives:# #
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##
____
˙
LSS:
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Motives:
œ
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j
j
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˙
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œ ______
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.
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rall.
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.
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in B¯:
.
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p
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292
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j
j
j
j
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.
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œ
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b œœ œœœœ
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____
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˙
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YT: 3AeFVFC1zy0
NCTs:
œœœ œœœ
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œ
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œ
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?
#
? bb # œ œ œ œ œ œ
œ
œ œ œ bœ œ œ
œœœœ˙
Figure 24.9.5 Gretchaninoff, Children’s Book, Op.98, No. 13, “After
the Ball”
RN: On
____
scratch
paper,____
create a____
diagram____
of the ____
form.
# ____
HF: & #____
____
____
____
____
____
____ section
Include
____
labels using uppercase letters, phrase labels using lowercase letters,
and cadences using the abbreviations PAC, IAC, HC, DC, PC.
?Circle
##
all of the terms that apply to the name of the form:
TWO-REPRISE SECTIONAL
6.
138
138
CONTINUOUS
ROUNDED BALANCED
BINARY
TERNARY
For the theme from Brahms’s Variations on a Theme of Haydn Op.
56a (the theme is also known as “St. Anthony’s Chorale”), please fill
in the blanks below the staves and diagram the form. Also, name the
form.
& b b 42 œœ ..
œ.
p
? b 2 œ
b 4 œ
b
&b
œœ œ œ œœ œ
œ œœ œœ œ œœ
> >
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œ œ
œ œœ œ œœ œ
œœ œ
j
œ.
nœ
œ
nœ
œ #œ nœ œ.
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œ œ
œ œ
œ œ
œ
œ
b
&b
? bb
˙ œ œœ
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f
œ˙ . œ b œ œ
œ Œ
œ œ
œ
___
___
œœœ ..
œ.
f
œ
œ
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œ œœ œœ œ œœœ
> >
œ
œ
___
___
œ œœ
œ
œj ‰ .. .. œ œ œ
œ œ œ œ b œ˙ . œ œ œ œœ œœœ œœœ
œœ
˙˙ . œ b n ˙˙˙ .
˙
œ
œœœ
p
œ
˙
˙
˙
.
.
œœœ
œ œ œœ œ œœ . . ˙
˙
˙
œœœ
œ œ
___
___
œœ .. œœ œ œ
œ œœ
π
? b b œ œœ œœ
œ
œœ œ œ œœ
œ
œ œœ œ œ
œœ .. œœ œœ œœ œœœœ
œ œœ
? bb œ # œ œ n œ œ
œ #œ œ nœ œ
b
&b
œœ
œ
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œ œœ œœ
œ
___
___
œ
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œ
œ
œ œ n œœ
œ
___
___
œœ
œ
œœ
œ
‰ œJ œ
˙œ . œ œ œ ˙ œ œ œ
˙ œ œ œœ. œ œ
___
___
œœ .. œœœ œœ
œœ .. œ œœ
f
œ
œ œ
œ
˙œ . œ œ œ
˙ œ œ
œ. œ œ œ œ œ œ. œ bœ œ œ. œ œ œ œ œ
˙
˙
˙
___ (tonic
(tonic prolongation
prolongation follows
follows cadence)
cadence)
___
œœ
œœ
œ.
œœ
œœ.
>œ
œœ
œ
___
___
>œ >œ >
œœ œ œ œœœ
œ œ œ
œ œœ
œ
œ.
œœ
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___
___
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dim.
dim. smorz.
smorz.
œ #œ
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˙
˙˙
π
˙˙
1.
1.
œœ. œ œ œ
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œ nœ œ
œ nœ œ
2.
2.
œ
œœ
___
___
U
›
›
›
›
π
U
.. ›
›
..
œ œ œ œ œœ œfœ œ ˙ œ œ œ œ
J œœ n œœ J ‰Jœ J
œ #œ œ nœ œ ˙ œ
œ
J œ œ œ œ œ œ #œ œ nœ œ œ œ
œ
œœ œ œ œ
NCTs:
œ
œ
œ
œ
œ œ œ293
CHAPTER 24. BINARY AND
TERNARY
FORMS
œ
___
___
œ
œ
œœ
? bb c œ œ œ œ œ œ œ
œ œ œ œ œ œ œ œ œ ___
œ
œœ œœœ œœœ œ
Jœ
b π œ
&?b b b cœœ œJ œœ œœ
b ˙œœ.____
œ œœ œœ
RN in bB¯:
&
HF:
____
f
? b b œ˙ . œ b œ œ
LSS:
____
Motives:
˙œ œ œ ˙ œ œ œ ˙œ œ œ œ. œ.
. œ œ œ ____
œœ. œ œ ____
œ œœ œœ
˙____
˙ . œ œ ____
œ. œ.
œœ œœ
˙
˙˙____ ..
____
____
____
____
____
dim. smorz.
π
œ . œ œ œ œ œ œ . œ b œ œ œ . œ œ œ œ œ œ. œ. œ. œ. ˙ .
˙
˙
œ œ ˙ ____.
____
____˙
____
____œ œ ____
b œœ œœœœ
& b bJ J
b
1.
œ œ œ bœ œ
œ
U
›
›
›
π
2.
U
›
›
œœ œœœœ ˙
˙
J J
&
NCTs:
œ 3EbkqX94ng8
bœ œ œ œ œ œ œ œ œ œ œ œ œ œ
??b b œ œ œ œ œ œ œ œ œ œ œYT:
œ
œ
˙
bb
___ (tonic prolongation follows cadence)
Figure 24.9.6 Brahms, Variations on a Theme of Haydn, Op. 56a
RN:
HF:
____
____
____ section
On
scratch
paper,____
create a____
diagram____
of the ____
form. Include
____
____
____
____
____
____
____
labels using uppercase letters, phrase labels using lowercase letters,
and cadences using the abbreviations PAC, IAC, HC, DC, PC.
Circle all of the terms that apply to the name of the form:
TWO-REPRISE SECTIONAL
CONTINUOUS
ROUNDED BALANCED
BINARY
TERNARY
Click here to download the first homework assignment for this chapter.
Click here to download the second homework assignment for this chapter.
Click here to download the third homework assignment for this chapter.
Click here to download the review sheet for material studied prior to this
chapter.
PDF versions of the textbook, homework exercises, and practice exercises
can be found at musictheory.pugetsound.edu
Chapter 25
Sonata and Rondo Forms
# 3
œ
& 4 .. œ œ œ ˙ .
œ œœ
œ œ
25.1 Sonata
? # 43 .. œ œForm
œ œ œ
139
œ œ œ œ œ œ ˙.
m.1
..
..
Sonata form,G:also
knownV6as “first-movement
form,”
is vi“[t]he most important
I
V7
I
I
principle of musical form, or formal type, from the Classical
period
7 I into
D: ii
I64
Vwell
the 20th century,” according to the Grove Music Online. The purpose of this
mm. 7-8 in aspects
G major
mm. 9-10 and harmonic
chapter is to serve as an introduction to formal, thematic,
# . œ We will œfocus on sonata form as it existed during the height.
of sonata form.
œ ˙
.
& . ˙
of the Classical era. Further and more detailed study of sonata form occurs in
higher-level music theory courses.
? # ..
6
G: V5
IV
I
25.1.1 Diagram
ofI Sonata
Form
V7
I6
vi
4
V7
..
I
Below is a generalized diagram of sonata form, which serves as our starting
point. Real-world examples will contain differences and elaborations.
EXPOSITION
PT transition
DEVELOPMENT
RECAPITULATION
ST (CT)
Fragmentation &
sequencing
Retransition
PT transition
ST (CT)
In major:
I
modulating
V
V
V modulations
V pedal
I
tonicizations
I
I
In minor:
i
modulating
III
III
III modulations
V pedal
i
tonicizations
i
i
PT = Primary Theme
ST = SecondaryTheme
CT = ClosingTheme
It is fairly common for a piece in sonata form to have multiple secondary
themes (ST 1 , ST 2 ). In some sonatas, the development section features new
material. Some sonatas will not have a closing theme. As we work with real
world examples, you will see the ways in which composers realize sonata form.
While the diagram above designates three large sections (exposition, development, recapitulation), repeat signs in sonatas from the classical era designate
the sonata as a two-reprise form—the exposition repeats, then the development
and recapitulation repeat as a single unit. Douglass Green, in his book Form
in Tonal Music, notes the sonata’s evolution from and synthesis of rounded
binary and balanced binary:
294
CHAPTER 25. SONATA AND RONDO FORMS
295
The typical sonata form, as it appeared in the 18th century, is
a combination of rounded and balanced binary. It begins the
return with a restatement of the opening of part one, as in the
rounded binary, and it closes with a restatement of the final
sections (second and closing themes) of part one transposed to
the tonic, as in the balanced binary.
25.1.2 Sonatina Form
While “sonatina” is sometimes understood to mean a short sonata or an easy
sonata for beginners, in terms of form, sonatina form is sonata form without the development section. Sonatina form is sometimes encountered in the
second, slow movement of a larger work like a symphony, as well as in overtures. A familiar piece in sonatina form is the “Miniature Overture” from The
Nutcracker by Tchaikovsky.
YouTube: https://www.youtube.com/watch?v=JRXIDEpquCg
Figure 25.1.1 Tchaikovsky, The Nutcracker, “Miniature Overture” (1892)
Exposition
PT
0:00
ST
0:49
CT
1:28
Recapitulation
PT
1:40
ST
2:30
CT
3:09
25.1.3 Sonata Principle
Important to sonata form is sonata principle, which Charles Rosen discusses
in his book Sonata Forms.
The exposition of a sonata form presents the thematic material and
articulates the movement from tonic to dominant in various ways so
that it takes on the character of a polarization or opposition. The
essential character of this opposition may be defined as a largescale dissonance: the material played outside the tonic (i.e., in the
second group) is dissonant with respect to the center of stability, or
tonic. Sonata style did not invent this concept of dissonant section,
but it was the first style to make it the generating force of an entire
movement.1
Rosen continues:
The dominant is conceived as a dissonant tonality in the exposition....The polarization, in fact, leads to the concept of a dissonant
section, which raises the dissonant interval or chord to a higher
power: that is, a simple reintroduction of the tonic key will no
longer serve as a resolution, but the section outside the tonic needs
to be resolved as a whole.2
1 Sonata
2 Sonata
Forms, Revised Edition, 1988, p. 229
Forms, Revised Edition, 1988, p. 244
CHAPTER 25. SONATA AND RONDO FORMS
296
25.1.4 The Monothematic Sonata
Haydn was especially fond of restating the Primary Theme in the dominant
where the Secondary Theme would normally occur. This reinforces the idea
that the tonal design of a sonata was as important as thematic design.
25.2 The Four Structural Functions in Music
In the “Structural Functions” chapter of A Practical Approach to the Study
of Form in Music, Peter Temko and Peter Spencer enumerate four structural
functions.
1. Expository function
2. Transitional function
3. Developmental function
4. Terminative function
25.2.1 Expository Function
Music expressing expository function maintains a stable tonal center and
clear melodies, usually with well-defined phrases. The vast majority of the
music we encountered in binary and ternary form in the last chapter was expository in nature. Additionally, the primary and secondary themes in a sonata
form are usually have expository function. Below is the secondary theme from
the first movement of Mozart’s Piano Sonata, K. 333.
632
632
632
636
636
636
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&
&
& b c œœœ ...
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?
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IAC in
in B
B¯¯
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œœ œœœ œœ œœ œœœœ œ œœ œ œ œœ œœ œœ œœœ œœ œœœ œœœ œœœ œœ œœ œœ œœ œœ œ œ ŸŸŸ œ
œ œ œ œ œ œœ œ œ œœ œ œ œ œ
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PAC
PAC in
in B
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47
47
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CHAPTER 25. SONATA AND RONDO FORMS
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____ ____
Mozart, Piano Sonata, K. 333, I, Secondary Theme
Notice the perfect authentic cadence that closes off
four-phrase par____this
____
allel double period within the larger sonata form. Cadences are important
demarcations within a form.
____ ____
25.2.2 Transitional Function
____ ____
Music of transitional function moves from one tonal center to another and
often features a contrasting accompanimental texture more rhythmically active
than preceding expository material. Tonicizations may also occur within a
transition. Transitions are sometimes called bridges. Mozart and Haydn often
ended their sonata form transitions with a half cadence followed by a rest to
signal that the secondary theme was about to commence. Again, notice the
importance of cadences to demarcate the form.
Allegro con brio
Allegro
con
brio
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con
brio
Primary
Theme
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(Primary Theme repeats with triplet accompaniment)
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Theme repeats
repeats with
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(Primary
œœ œ..
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F
F
3
3
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.
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(PAC)
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.. œ .. œ. œ .. œ . transition
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.
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transition
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nœ œ
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5
pp 3 3 3 5553
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prolongation after
after cadence)
cadence)
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33
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and is
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&
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CHAPTER
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& œœ.. Œ Ó 25. œœSONATA
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pp 3 3 3 553
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w
(tonic prolongation after
cadence)
(rhythmic motionœresumes and is unceasing) œ
(tonic prolongation after cadence)
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####
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Secondary Theme
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œœ.. œ.œ. œ.œ.
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(half cadence followed by rest)
D major, the dominant of C
G major)
major)
(ST in G
œ
Closing Theme (tonic andYT:
dominant
harmonies emphasized)
Lfq9P-zT_0I
œ Hob.œ XVI:35,
œ I.
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ΠHaydn,
ΠPiano
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Figure
& 25.2.2
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‹œ
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10
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CHAPTER
FORMS
J
œœ 25. SONATA AND RONDO
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legato
legato
legato
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(cadence from
from V
V to
to II closes
closes PT)
PT)
(cadence from
from V
V to
to I closes
closes PT)
PT)
(cadence
(cadence from
V to IIactivity)
closes PT)
(increased
rhythmic
(increased rhythmic activity)
(increased rhythmic
rhythmic activity)
(increased
(increased rhythmic activity)
activity)
. œœ œ
œœœ.. œœ œœ œœœ œœœ œœ œœœ œœœ œœœ
œœ œœ œœ œœ œœ œœ œœ œœ
### œœœ œ œœœ œ œœœ œ œœœ œ œœœ œ œœœ œ œœœ œ œœœ œ
œ œ œ œ œ œ œ œ
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œ œ
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Secondary
Theme
Secondary Theme
I
Secondary Theme
Theme
Secondary
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œ œ œ œ Œ Secondary
œ œœœ ## œœ œœœTheme
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transition
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Figure 25.2.3 Mozart, Piano Sonata, K. 284, I.
25.2.3 Developmental Function
Music with developmental function often contains sequences and fragmentation of earlier melodies. In addition, developmental music modulates through
multiple keys. Phrase lengths may be irregular and elisions may be used by
the composer to keep the listener off balance.
It can sometimes be difficult to distinguish between transitional and developmental music. A development section is typically longer than a transition
and therefore will contain more sections of a varying nature and as well as a
greater number of modulations.
CHAPTER 25. SONATA AND RONDO FORMS
300
Examples from a development section can be found in Section 11.1 of this
text. Note the fragmentation and sequencing of melodic ideas as well as the
different keys expressed in the examples throughout that section.
25.2.4 Terminative Function
Terminative function is typically expressed through a rather emphatic alternation of tonic and dominant harmonies, usually to affirm a tonal center.
The closing theme of a sonata has terminative function.
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Figure 25.2.4 Mozart, Symphony No. 41, K. 551, I., Closing Theme
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in an earlier chapter, has ABACA form or ABABA form. The 7-part
typically has ABACABA form, although other designs exist. A diagram for
7-part Classical form is shown below.
Major:
A
I
Minor:
i
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The refrain (the A section) is always in tonic. The first episode (the B
section) was typically in a closely related key—the dominant (V) if in major
or the mediant (III) if in minor. There was greater variety of keys used for
the second episode (the C section), including tonic minor in a major sonata or
the submediant (vi or VI). A retransition in this case is defined as a transition
returning to material previously heard.
Note that the B section being first stated in the dominant then later in
tonic is an example of sonata principle, a principle which occurred in many
Classical era pieces (see Charles Rosen’s Sonata Forms for more on sonata
principle).
An example of Classical seven-part rondo form is found below in the third
and final movement of Beethoven’s Pathétique Sonata, Op. 13.
148
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b 25. SONATA AND RONDO FORMS
CHAPTER
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13,
œ First˙ œ.EpisodeŒ
Œ œ œ œ. œ œ œ œ . œ œ œ œ œ. œ œ œ . œ œ œ III,
œ œ
b
œœ first episode
œ œ ofœ aœ parallel
?The
œ ≈of œthe
œ is≈œ clearly
œ in ≈theœ form
œ≈ melody
œ
œ
œœ
œ
œ
œ
≈
œ
≈
b b b final
œ
&
œ.
œnœ
œ
œ
œ
œ
œ
period.
œnœ ˙
œœ . ?
bb b ‰ Œ
&
˙
bb
˙ ˙ . b‰œ œ œ œ ‰˙œ Œn ˙ Œ ‰œ˙œ. œ ˙ œb‰œœ
?
˙
b
˙
‰
‰
b
œ
&bb
œ ˙
œ œ œ œ
˙˙n..œ œ
œ p œ.œ n œœ. œ. œœ. œ ˙ . œ œ œ .̇ œ œ ˙.
.
? b b œ. œ œ ˙pœ. b ˙œ. œ. œ˙. œ˙. œ. ˙œ ˙ œ œ. b œ n œ.̇ œ bœ.˙. b ˙ ˙
. ˙ ˙
˙
˙ ..
œ
? b b b pœŒ œ œ œ œ
œ
Œ
b
bb b ‰≈ Œ œ œ. ≈ œ œ.
œ. ≈ œ œ œ. Œ≈ Œ ˙
?
?
œ
b
≈
œ
œ
& b b œnœ
œ. œ ≈ œ œ˙œ œb. œ
œ
˙ ˙ œ ˙ ˙ œ˙ b œ œ œ œ œ &
œ œnœ
œ
YT: 05Xyc2FHHRI
p
?
Figure
Op.
III, Conclusion
of First
‰ b ˙ ˙ ‰Pathétique
‰œ 13,
‰œ
‰œ œ
? bb bb b 25.3.4
œ ˙ ‰Sonata,
n
œ
œ ˙Beethoven,
œ
b
œ
n
b
˙
œ
œ
˙
œ
˙
œ
Episode
œœ
œœ œ ˙
b œ
.˙
œ nœ œ
œœ
œ
œ
œ
p
.
.
.
.
.
A retransition follows and leads to a half cadence on a G major chord. The
? b b ≈ n œ œ œ.
b œ
.
≈œ œœ œ
refrain follows in C minor.
? bb
Figure
b
.
≈œœœœ
.
≈œ œ œ œ
œ.
œ.
&
≈
œ
œnœ œ .
25.3.5 ‰Beethoven,‰ Pathétique‰ Sonata, ‰Op. 13,
œœ
œœ
œœ
Second Refrain œ n œ
œ.
œ.
YT: 05Xyc2FHHRI
œ.
≈
œœ
œœ .
‰ œto
œ
III, ‰œ
Retransition
nœœ
.
w
œ
b
. .
& bb b b
œ œ˙˙ ..œ œ œ œœœ œ œ ˙.̇œ œ œ n œ˙˙. ˙œ œ œ˙˙˙ œ... œ œ œœ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
˙
œ
œ
œ œ303
. . . AND
. RONDO FORMS
& b œ. 25. SONATA
CHAPTER
p
dolce .
b œ˙.
œ œœ.œ œœ. œœ. œ ˙˙ .. œ œ œ .̇
˙ œ.
œ
œ
?The
bb b second
episode
(the
C
section)
follows
immediately
after
the
Œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ refrain.
œŒ œ
œ
œ
œminor.
? second
bb œ episode is in Aœ2 major,œ the submediant
œ
œ
œ
The
(VI)
of
C
b
b
Œ Œ ˙ œ. œ ˙
& bb b bb ‰ Œ
˙
.
˙
˙
œ
˙˙ .
œb œ
b
œ
˙
˙
œ
&
˙ œœ ˙ .
œ œ œ n ˙˙˙
œ
œ
œ
œ
œ
œ
œ
˙
.
.̇
.
œ p. . . .
p
˙
? b b œ œ œœ. b ˙œœ. œœ˙. œœ˙. ˙œ . ˙ œ b œ n œ.̇ œ b ˙. b ˙ ˙ .
˙.
œ
? b b b œŒ
˙ ˙Œ
œ ˙
b p
.
.
.
.
b
?
& bb b bb ‰≈ Œœ n œ œ œ ˙ ≈ œ œ œ œ ˙ ≈ œ œ œbœœ ≈ œ œ œ œ & Œ≈ Œ ˙ œ œ ≈ œ ˙œ œb œ
˙
œ œ œ œ
˙ YT:˙05Xyc2FHHRI
œnœ œ .
œœ .
p
Figure
Op. 13, III, Second Episode
˙‰Beethoven,
? b b 25.3.6
˙ ‰Pathétique
œ ˙ ‰Sonata,
‰œ œ
œ
b
˙
b
œ
n‰œ œ on a˙ half
b‰œ
˙ cadence
n œ œ ˙ ˙on
œ
˙
œ
b œ
A retransition
follows
the
second
episode,
ending
G
œ
œ
œ
.
œ nœ
œ
œ œ
œ œœ
œ.
œ
major. pœ.
.
.
.
? b b ≈ n œ œ œ.
b œ
? bb
b
œ.
‰
.
≈œœœ œ
œ nœ œ
.
‰
.
≈œœœœ
œœ
œ.
‰
.
≈œ œœ œ
œœ
œ.
‰
&
œœ
≈
œ.
œœ
œnœ .
≈
œœ
œœ .
‰œ n œ œ
‰œ œ
.
YT: 05Xyc2FHHRI
Figure 25.3.7 Beethoven, Pathétique Sonata, Op. 13, III, Retransition to
Third Refrain
An abbreviated version of the refrain follows, leading directly to a restatement of the second episode (the B section), this time in tonic major (C major).
YT: 05Xyc2FHHRI
Figure 25.3.8 Beethoven, Pathétique Sonata, Op. 13, III, Third Refrain and
Second Episode restated in tonic
Following the Second Episode is brief retransition that develops final motives of that episode through sequences.
YT: 05Xyc2FHHRI
Figure 25.3.9 Beethoven, Pathétique Sonata, Op. 13, III, Retransition to
Final Refrain
After one last statement of the refrain in C minor, the Coda begins immediately after the cadence closing the refrain.
CHAPTER 25. SONATA AND RONDO FORMS
304
YT: 05Xyc2FHHRI
Figure 25.3.10 Beethoven, Pathétique Sonata, Op. 13, III, Final Refrain
.
œ œ nœ œ œ œ
.
œ œ nœ œ œ œ
.
œ œ nœ œ œ œ
œ.
#
œœ
bb œ Œ ‰
b
œ
Œ ‰
Œ ‰
& b
3
3
3
3
3
3
S
S
p
ƒ
cresc.
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
.
n
œ
b
œ
œ
œ
œ
œ
œ
œœ.
œ
œ
œ
? bb œ
œ
œ
œœ
b
b
&bb
œœ. n œœ.
œœ n œœ
œœœ œœ
œ. n œœ.
YT: 05Xyc2FHHRI
Figure 25.3.11 Beethoven, Pathétique Sonata, Op. 13, III, Coda
?Tob review a simple, five-part rondo form, see the section on the second
b b of Eine kleine nachtmusik in the chapter on Creating Contrast Bemovement
tween Sections.
25.3.1
b b Sonata Rondo Form
& b
Sonata rondo form is a rondo in which the second episode (the C section) is
replaced by a development section, resulting in a design of A-B-A-Dev.-A-BA.? b b b
25.4 Rondo Character
Rondo
b b bcharacter is characterized by quick tempo in duple meter with
&
character, typically achieved through the use of staccato articulation.
light
This
duple meter could be either simple ( 24 ) or compound ( 68 ). During the Classical?era,
the final movement of a multi-movement composition, e.g. a sonata,
b b b or symphony, was often in rondo character. Not all pieces in rondo
quartet,
form are in rondo character.
Listen to the following six examples to develop familiarity with rondo character.
b
1.
&bb
? bb
b
YT: kmiuh_OL2Zg
Figure 25.4.1 Joseph Bologne, Chevalier de Saint-Georges, Violin Concerto No. 9 in G major, Op. 8, III.
2.
YT: ysB5SeaJp6s
Figure 25.4.2 Haydn, Piano Sonata in D major, H. XVI:37, III.
149
CHAPTER 25. SONATA AND RONDO FORMS
305
3.
YT: QYUANirkakg
Figure 25.4.3 Haydn, Symphony No. 104 in D major, Hob. I:104, IV.
4.
YT: YhGkLPqWjBc
Figure 25.4.4 Haydn, String Quartet in E-flat major, Op. 33, No. 2,
IV.
5.
YT: hwxNp-LzDYo
Figure 25.4.5 Mozart, Symphony No. 36 in C major, K.425, IV.
6.
YT: H0x_dCrKd4w
Figure 25.4.6 Mozart, Symphony No. 39 in E-flat major, K.543, IV.
7.
YT: zuMs8kD5Des
Figure 25.4.7 Mozart, String Quartet No. 19 in C major, K.465, IV.
25.5 Standard Forms in a Multimovement Classical Piece
Below are the forms commonly encountered in the various movements of Classical symphonies, string quartets, and sonatas.
1. First movement: Sonata form
2. Second movement: Ternary form (ABA), sonatina form, or five-part
rondo
3. Third movement: Minuet and Trio (Compound Ternary)
4. Fourth movement: Rondo form, sonata form, or sonata rondo form
25.6 Practice Exercises
1.
Identify the structural function of each excerpt below as expository,
transitional, developmental, or terminative. Aurally identify the tonic
CHAPTER 25. SONATA AND RONDO FORMS
306
and determine if the key is maintained or if other keys occur. Listen
for cadences to demarcate the form.
(a) Haydn, Piano Sonata No. 59 in E-flat major, Hob. XVI:49, I.
YT: je74Fhokrxg
(b) Beethoven, Symphony No. 5 in C Minor, Op. 67, I.
YT: W2qW6fOtAMY
(c) Mozart, Piano Sonata No. 18 in D major, K.576, I.
YT: rUgMSF49YE4
(d) Mozart, Symphony No. 40 in G Minor, K. 550, I.
YT: kWBCjaxVaeE
(e) Mozart, Piano Sonata No. 7 in C major, K. 309, I.
YT: ZbWsNTiaebY
(f) Haydn, Symphony No. 104 In D major, Hob. I:104, I.
YT: 21o-aldOI08
(g) Mozart, Piano Sonata No. 7 in C major, K. 309, I.
YT: V_i_FMMPKPc
(h) Mozart, Piano Sonata No. 18 in D major, K.576, I.
YT: rUgMSF49YE4
(i) Mozart, Piano Sonata No. 8 in A minor, K. 310, I.
YT: U4K2mz_rPcs
(j) Haydn, Piano Sonata No. 60 in C major, Op. 79, Hob. XVI:50,
I.
YT: EhJ-G0Lp8bI
(k) Mozart, Piano Sonata No. 14 in C Minor, K. 457, I.
PT = Primary Theme
ST = SecondaryTheme
CT = ClosingTheme
CHAPTER 25. SONATA AND RONDO FORMS
EXPOSITION
DEVELOPMENT
transition ST1
PT
307
RECAPITULATION
ST2YT:CT
sBYfP1gbTkE
Retransition
PT
transition
0:00
(l) Mozart,
Symphony No. 40 in G Minor, K. 550, IV.
ST2
CT
4:45
5:12
139
# 3
œ œ œ œ œ œ ˙. .
œ
.
& 4 .. œ œ œ ˙ .
YT: B5fqVYXVDwU
œ œœ
œœ œœ 1:27 3:13
3:48 4:19
3:37 Cadences
œ œ 0:48
Listen to ?the
pieces
below
and fill in the diagrams.
and
# 0:30
œ 1:01
..
43 ..
textural1:36
changes
will
designate
the
form—listen
carefully
for
these.
2:07
2:24 2:37 3:04
m.1
(2nd time)
2.
ST1
V6
G: I
V7
EXPOSITION
transition ST
? # ..
(2nd time)
G:
0:51
V65
I
vi
D:RECAPITULATION
ii
I64
V7 I
DEVELOPMENT
#
& .. œ ˙
0:00
PT
I
œœ˙
CT
I
0:08
0:22
0:58
1:12
V7
I
mm. 7-8 in G
major CT
transition
ST
..
I6
4
vi
0:45
1:35
EXPOSITION
PT transition
mm. 9-10
PT
IV
V7
..
I
2:03
1:40
DEVELOPMENT
2:11
RECAPITULATION
ST (CT)
Fragmentation &
sequencing
Retransition
PT transition
ST (CT)
In major:
I
modulating
V
V
V modulations
V pedal
I
tonicizations
I
I
In minor:
i
modulating
III
III
III modulations
V pedal
i
tonicizations
i
i
PT = Primary Theme
YouTube:
https://www.youtube.com/watch?v=Rxsrsp7dLCg
ST = SecondaryTheme
CT = ClosingTheme
Figure 25.6.1 Mozart, Piano Sonata K. 545, I.
EXPOSITION
PT
DEVELOPMENT
transition ST1
ST2
CT
RECAPITULATION
Retransition
PT
transition
ST1
ST2
CT
3:48
4:19
4:32
4:45
5:12
0:00
(2nd time)
1:36
0:30
0:48
1:01
2:07
2:24
2:37
1:27
3:04
3:13
4:32
3:37
YouTube: https://www.youtube.com/watch?v=wPKFdj5V3Bw
Figure 25.6.2 Mozart, Eine kleine nachtmusik, K. 525, I.
Examples for Assignment 36, Section 1
3. For each excerpt below, identify the structural function as either expository, transitional, developmental, or terminative.
(a) Haydn, Piano Sonata No. 59 in E-flat major, Hob. XVI:49, I.
YT: je74Fhokrxg
2:31
2:54
CHAPTER 25. SONATA AND RONDO FORMS
(b) Mozart, Piano Sonata No. 7 in C major, K. 309, I.
YT: ZbWsNTiaebY
(c) Beethoven, Symphony No. 5 in C Minor, Op. 67, IV.
YT: fOk8Tm815lE
(d) Mozart, Piano Sonata No. 8 in A Minor, K. 310, I.
YT: U4K2mz_rPcs
(e) Mozart, Piano Sonata No. 14 in C Minor, K. 457, I.
YT: sBYfP1gbTkE
(f) Haydn, Symphony No. 104 in D major, Hob.I:104, IV.
YT: QYUANirkakg
(g) Mozart, String Quartet No. 17 In B-flat, K.458, IV.
YT: nHtaGz8sqTw
(h) Mozart, Piano Sonata No. 18 in D major, K.576, I.
YT: rUgMSF49YE4
(i) Mozart, Piano Sonata No. 8 in A minor, K. 310, I.
YT: U4K2mz_rPcs
(j) Haydn, Piano Sonata No. 60 in C major, Hob. XVI:50, I.
YT: EhJ-G0Lp8bI
(k) Mozart, String Quartet No. 17 In B-flat, K.458, IV.
YT: nHtaGz8sqTw
(l) Mozart, Piano Sonata No. 14 in C Minor, K. 457, I.
YT: sBYfP1gbTkE
308
CHAPTER 25. SONATA AND RONDO FORMS
309
Click here to download the first homework assignment for this chapter.
Click here to download the second homework assignment for this chapter.
Click here to download the Unit 7 Practice Test.
Chapter 26
Voice Leading Triads
26.1 Voice Leading
Voice leading, also known as part writing, refers to rules about melodic
motions of voices involved in harmonic progressions. The primary concerns
behind voice leading rules are independence of parts, voicing of chords, and
economy of melodic motion for the sake of singable parts.
“SATB” voice leading refers to four-part chords scored for soprano (S), alto
(A), tenor (T), and bass (B) voices. Three-part chords are often specified as
SAB (soprano, alto, bass) but could be scored for any combination of the three
voice types. SATB voice leading will also be referred to as “chorale-style” voice
leading.
152
Soprano
Alto
& c ˙˙
152
?c ˙
& c ˙˙
?c
&c
˙
˙
˙˙
˙
˙
˙
˙
˙
˙
Tenor
Soprano
Bass
Alto
˙˙
˙
Soprano
Bass
Alto
Tenor
˙
˙
˙˙
˙
Figure 26.1.1 Soprano, Alto, Tenor, and Bass voices on the grand staff in
Tenor
“chorale-style” voice leading
Bass
Soprano
“Piano-style” voice leading means the three upper
parts are in the upper
staff (the right hand part) and the bass is the only Alto
voice in bass clef (the left
Tenor
hand part).
?c
&c
˙
˙˙
?c ˙
&
˙
Bass
?
26.2 Types of&Motion
Figure 26.1.2 “Piano-style” voice leading
?
Definitions must be set out regarding types of motion between two parts.
310
CHAPTER
LEADING
TRIADS
˙
Soprano
c ˙ 26. VOICE
152
&
˙
˙
311
Alto
• Contrary motion occurs when the two voices move in opposite direc? ction˙˙ to each˙ other by Tenor
step or leap.
˙
Bass
• Oblique motion occurs when one voice stays the same and the other
voice moves up or down by step or leap.
152
• Similar motion occurs when both voices move in the same (or “simiSoprano
˙˙ direction—both
˙˙
up
(by step or leap) or both down (by step or leap);
& clar”)
Alto
˙ motion
˙ is also Tenor
similar
called “direct” motion
˙
˙
Soprano
• c
Parallel
a specific type of similar motion and occurs when
&
?
˙˙ voicesmotion
˙˙ move inis the
Alto
cboth
Basssame direction by the same interval—both up
by step, or both down by a third.
˙
Tenor
? c ˙˙
Bass motion
˙
contrary motion
oblique
similar motion
parallel motion
˙
˙
˙
˙
˙
˙
˙
&
˙
?
& c˙ ˙˙˙
?
same note
˙ ˙˙˙
˙
Soprano
Alto
Tenor
˙
˙
up (by 3rd)
˙
up (by 2nd)
up (by 6th)
c 26.2.1
˙
Figure
The
˙ four types
Bassof motion
˙
˙
up (by 2nd)
43
&
917 oblique motion
motion
parallel motion
26.3contrary
Objectionable
Parallels
# # # ww similar˙nmotion
˙
w
˙
˙
w
˙
˙
˙
˙&
˙
n ˙ ˙n b b ˙˙˙ n n ˙˙˙ ˙ n ww
n
˙
&
˙
? writing in three or four parts, avoid having any two voices move in parWhen
I
¯VI ¯VII up (by 2nd)twelfths
C: V
allel fifths or parallel octaves (and theirA:
octave
equivalents—parallel
˙
˙
and
unisons).
In˙the Renaissance,
Baroque,
Classical,
G: I ˙ and
¯VIRomantic
?parallel
˙ ¯VII I
˙
˙
˙ objectional
eras, these
parallels
were
thought
to
destroy
the
independence
of
921
(by 6th)
n wwupconsidered
# # # were
n
˙
up (by 2nd) Parallel
the voices. Parallel 3rds, 4ths, and 6ths
acceptable.
b
˙
w
n w n b ˙˙ b ˙˙ n n ˙˙˙ n ˙˙˙ ww
&
2nds and 7ths generally were not used.
same note
˙
& ˙˙
˙
par. 5ths ˙
˙
? ˙ ____ ˙
up (by 3rd)
˙
˙
˙
˙
par. 5ths
˙˙ ____
˙
____˙
n ww
# n ww
b b b b ww
w
˙˙
˙
˙
¯VI ¯VII par. 8ves
IV
˙˙ A: ¯VI˙˙ ¯VII
par. 5ths
˙
˙ ____ ˙ par. 5ths____
˙
˙
˙
˙# # ˙
b
w
b
w
# # ww
b b b ww
& b b wwww
w
Figure 26.3.1 Objectionable parallel fifths and parallel octaves # w
925
1. F: ____
2. e: ____
& Voice Ranges
26.4
____
____
930
prac test
C: I
3. E¯: ____
4. A¯: ____
____
I
5. A: ____
____
____
For
??the purpose of music theory class, we will set out restrictions for voice
ranges that are likely more limited than those found among vocalists in the
class. These voice ranges are based on those most commonly found in J.S.
ø4
Bach’s1.371
B¯: iiChorales.
2. E: viio42/V
3. f˜: Ger+6
4. b: V56/VI
5. F: EnGer+6
3
Soprano
935
&˙
#˙
Alto
&
˙
#˙ ? b˙
Tenor
#˙
?
Bass
˙
Figure 26.4.1 Voice ranges for soprano, alto, tenor, and bass voices
939
&
˙
¯VI ¯VII
A: I
¯VI ¯VII
G: I
# # n ww
& # nw
I
n b b ˙˙˙ b n ˙˙˙ n n ˙˙˙ n ˙˙˙ www
CHAPTER 26. VOICE
LEADING TRIADS
921
26.5 Rules of Melody
C: V
¯VI ¯VII
C: I
312
IV
Rules of melody have been included in books on composing, writing counter¯VII
point, and music theory for centuries. The purpose of the rulesA:of¯VI
melody
asI
described in this text are to aid in the construction of singable melodies and to
____
____
reflect a____
summary of____
melodic practice____
in music. (Remember
that each
part in
an SATB composition is considered na w
melody.) Because these rules
of
melody
#
# n wwon the bmelodies
b b b wwwfound inb b bJ.S.
www 371# #Chorales,
b b Bach’s
are
based
b b wwstylistically
# www you
w
w
&
w
w
will no doubt
w be familiar with exceptions that have occurred in music#composed
152
since1. Bach’s
in____
1750.
F: ____ death
2. e:
3. E¯: ____
4. A¯: ____
5. A: ____
925
&c ˙
930
prac test
˙
Soprano
˙
Bass
˙ resolve:
˙ 7̂ goesAlto
1. Tendency tones should
to 8̂ and, to a lesser extent, 4̂
goes____
to 3̂ (other tendency
tones are
6̂ and 2̂ , both
of which should
resolve
____
____
____
____
˙
Tenor
down by step) ? c ˙˙
?
2. Avoid augmented intervals
3. 1.
Leaps
larger than
a o4
4th
of +6diminished
should
change
6/VI
+6
B¯: iiø4
2. E: vii
/V and leaps
3. f˜: Ger
4. b: Vintervals
5. F: EnGer
3
2
5
direction after the leap
Soprano
Tenor
& c ˙˙˙ Alto ˙˙˙
Alto
Consecutive
# ˙ leaps should outline a triadTenor
Soprano
935
&
4.
#˙
#˙ ? b˙
&
?
Bass
˙
The ˙following example
how difficult a melody can
˙ be to sing
? demonstrates
c˙
˙
Bass
when these rules are broken˙
939
& œ
+5
#œ
Figure 26.5.1
941
&
contrary
motion
7ˆ not
resolving
&œ ˙ ?
œ˙
large leap
?˙
˙
consec. leaps not outlining triad
oblique motion
œ
˙
˙
œ
˙
? note
same
˙
œ˙
˙
œ˙
similar motion
˙
up (by 3rd)
up (by 6th)
˙
˙
˙
parallel motion
up (by 2nd)
˙
up (by 2nd)
26.6 Rules of Spacing
par. 8ves
˙
˙
˙
˙ (soprano,
˙ and tenor)
˙˙
& ˙˙ voice parts
˙
˙
Generally, the upper three
alto,
are
kept
close
˙
˙
˙
˙
˙
together. The general rule par.
is to keep
the distance between
5ths soprano par. 5ths
5ths ˙
5ths
˙˙ of spacing
˙˙ within ˙anpar.octave
˙
˙˙ par.
and alto as well as the?distance
between
alto
to tenor
˙
˙ of each ˙
other. Allowing a distance greater than an octave between ˙soprano˙and alto ˙
˙
(or between alto and tenor) is considered spacing error. The distance from
the bass to the tenor can be greater than an octave.
&
?
w
w
w
w
Soprano
Spacing
an 8ve or less
Alto
Tenor
an 8ve or less
more than an 8ve okay
Bass
Figure 26.6.1
In terms of spacing chords, one should consider the spacing that occurs in
the overtone series.
CHAPTER 26. VOICE LEADING TRIADS
&
?
&
œ
˙œ œ
œ œ œb œ
(
313
œ
( bœ )
œ
œ
œ
)
153
œ
? 26.6.2
Figure
œ Overtone series starting on C2
˙ spaces between notes occur lower in the overtone series. Consider the
Larger
voicings of the following chords. Some “ring” or resonate better than others.
Notice that all of the notes fall within the voice ranges specified above.
&
w
w
ww
?
&c
?c
w
w
ww
ww
ww
w
w
ww
w
w
ww
w
w
w
w
Figure 26.6.3
26.7
& Voice Leading Root Position Triads in Four
& Parts œ œ œ ( b œ ) œ
?
We?are writingœin four parts but triads have three notes. We will double the
œ
root of every root position chord. (The root is in the bass when a triad is in
˙
root position, so we are doubling the bass note in an upper part.)
Principle 26.7.1 Doubling rule for root position triads. Always double
the root in root position triads.
&
w
To move from one chord to the
the interval
that occurs
w next, consider
& w in the bassw line between
ww chord andwsubsequentwwone.
w
melodically
the
current
w
?
?
26.7.1
w
w
w
w
w
w
wBass
w
w
w of a 3rd
w or 6thw
movement
ofwthe interval
In the upper three parts (soprano, alto, and tenor): retain the two common
tones and move the other voice by step
&
&
?
?
˙˙
Root
˙˙ 5th
3rd
Root
Bass moves by 3rd
C: I
˙˙
˙˙
iii
Root
5th
3rd
Root
˙˙
˙
˙
5th
3rd
Root
Root
˙˙
˙˙
Root
5th
3rd
Root
Bass moves by 6th
C: I
&
vi
Figure 26.7.2
?
26.7.2 Bass movement of the interval of a 4th or 5th
In the upper three parts, do one of the following:
&
?
153
˙ Root
Root
? ˙˙˙ 5th
5th
?
˙ Root
˙
˙
˙˙
˙˙
˙˙
5th
5th
3rd
3rd
Root
Root
3rd
3rd
Root
Root
Root
Root
Root
CHAPTER 26.
LEADING TRIADS Bass moves by 6th
BassVOICE
moves by
by 3rd
3rd
Bass moves by 6th
Bass
moves
C: II
C:
iii
iii
C: II
C:
˙˙˙
5th
5th
3rd
3rd
Root
Root
314
vi
vi
1. Retain the common tone and move the other two voices by step
&
&
?
?
˙˙˙
˙
˙˙
˙˙
˙˙˙
˙
˙˙˙
3rd
3rd
5th
5th
Root
Root
Root
Root
Bass moves by 5th
Bass moves by 5th
C: I
C: I
˙˙˙
˙
˙˙˙˙
3rd
˙˙˙ 3rd
˙ 5th
5th
˙˙ Root
Root
Root
˙˙ Root
5th
5th
Root
Root
3rd
3rd
Root
Root
Root
Root
3rd
3rd
5th
5th
Root
Root
Bass moves by 4th
Bass moves by 4th
C: I
IV
C: I
IV
V
V
2. Move all of the upper voices in the same direction (each upper voice will
move by a 2nd or 3rd to the nearest chord member in the second chord)
154
&
& ˙˙
?
˙
˙?
Root˙
˙˙
˙˙
5th
3rd
& ˙ 5th Root
˙˙
Bass moves by 5th
˙ 3rd
˙ Root
V
? ˙ C: I
˙
Root
Root
Root
˙˙
˙
˙
3rd
Root
5th
5th Root
3rd
˙˙
˙
˙
Root
5th
3rd
Root
Bass moves by 4th
C: I
3rd
Root
5th
Root
IV
26.7.3Bass
Bass
of the interval of a 2nd
movesmovement
by 2nd
C: I
ii
Move
the three upper parts
in contrary motion to the bass line.
154
& ˙˙
?˙
˙
& ˙˙
˙ ˙3rd
3rd
?˙ ˙3rd
Root
* exception: 3rd of V resolves up by step;
Root3rd
results in doubled
* 5th
3rd
5th
˙
˙
Root
˙˙
˙
˙
5th
3rd
Root
Root
Bass moves by 2nd
5th
C: I Root
ii
Root
Bass moves by 2nd
C: V 26.7.3
vi
Figure
Exception:
the
bass
by the interval of a 2nd in the deceptive
3rd of V chordWhen
is not in&
melody,
canmoves
resolve down
progression in the minor mode (V–VI in C minor), always move the 3rd of
& ˙ Root up by step˙˙while
the V˙chord
the other notes (the 5th and the doubled root)
? 5th
5th
3rd
move in contrary motion to
the bass. In this situation, two voices move in an
˙ Root
3rd
upward
and two
voices move in a downward direction. This results
? ˙ direction
in a doubled
˙ Root 3rd in the˙VIRootchord. In the major mode, use this voice-leading
solution if 7̂ is in the soprano voice (because it is a tendency tone).
C: V
vi
b
& b b n ˙˙
? bb
˙
b ˙
˙
˙
3rd
5th
˙˙
Root
Root
c: V
bad
n˙
˙
3rd
3rd
˙
˙
5th
Root
VI
c: V
aug. 2nd
˙
˙
˙˙
VI
˙ 3rd to deal with
Roottwo possible˙ways
two examples
&The˙˙ following
˙˙ 5th demonstrate˙˙ the
3rd
5th
Figure 26.7.4 Voice leading the deceptive progression in minor
the deceptive
the major mode.3rd
Root
Root progression in
? ˙˙
5th
Root
˙˙
3rd
Root
˙˙
5th
Root
˙
˙
Root
Root
repeated root: change chord member while maintaing correct doubling (Root, Root, 3rd, 5th)
C: I
I
I
I
˙ 3rd
˙ Root
Root
?˙ ˙˙˙Root
˙˙ 5th
&
Root
3rd
5th
Root
˙ Root
Bass
moves
by
2nd
˙
˙
3rd
Root
CHAPTER
26. VOICE
LEADING
TRIADS
Bass moves
by 2nd
?
C: I
ii
˙
˙
Root
C: I
ii Root
˙ 3rd
? ˙
Root
& ˙˙
315
Bass
moves 3rd
by 2nd
* exception:
of V resolves up by step;
results iniidoubled 3rd
* exception: 3rd of V
up by step;
C:resolves
I
*
results in doubled 3rd
3rd
* *3rd
exception:
3rd
of
V
resolves up by step;
5th
3rd
3rd
3rd
˙
˙
results in doubled 3rd
˙˙* 3rd
5th
˙ 3rd
Root
&˙ ˙˙
˙
3rd
?
Root
& ˙˙ 3rd
5th
˙
˙
Root
? Root
˙ 5th
Bass
˙
˙ Root
Root
˙ Rootmoves by 2nd vi˙ 5th
C:
V
?
Bass moves by 2nd ˙
˙ Root
C: V
vi
3rd ofRoot
V chord is not in melody, can resolve down
5th
& ˙˙
˙˙
& ˙˙ Root
˙ ˙5th
˙ Root
5th
?
Root
&˙ ˙˙3rd3rd
˙˙ 5th
˙ Root
5th
Root
3rd
˙
˙
Root
? 3rd
˙
˙ Root
C:
vi
3rd
?˙VRoot
˙ Root
˙ Root
aug. 2nd
˙ Root
bad
C: V
vi b
C: V
vi ˙ 3rd
n˙
& b b n ˙˙ 3rd
˙ aug. 2nd ˙˙
˙bad3rd aug. 2nd bad
5th
b n ˙ 7̂ in an inner
˙ ˙voice in the deceptive
Figure
n˙˙ 3rd progression
& b b 26.7.6
n ˙˙˙ in major ˙
? bb bb b˙ n3rd
Root
3rd
˙
&
5th
˙ 3rd
˙
5th
˙˙ 5th
˙˙
b 3rd
˙ Root
˙
Root
3rd
26.7.4
bass note
˙ Root ? ofb ˙c:the
? b b Repetition
˙ Root
˙
V
VI
c: V
VI
5th
˙˙ 5th
˙
b
b
˙
˙
b
˙
˙
˙
˙
Root
˙
˙
Root
Root
Root
Repeat the upper three notes or arpeggiate the upper notes to different chord
˙VI3rd
members while maintaining the voicing of a doubled the root,
one 3rd and one
˙ VI
c:
VRoot
c: V
V
& ˙˙VIc:3rdV
˙˙c:VI
˙ 5th
5th
5th.
˙
3rd
Root
Root
˙ Root
3rd
˙˙5th
3rd
Root
˙
?˙ ˙˙ 5th
3rd
Root
&
˙
˙˙ Root
5th
˙
3rd
& ˙˙ 3rd
˙
5th
˙
Root
5th
Root
5th
˙
˙
˙
Root
3rd
Root
˙repeated
Root
3rd
Root
Root
root: change chord member while maintaing correct doubling (Root,
3rd, 5th)
˙I Root,
Root
˙
I˙ ˙ 3rd
I ˙5th
?C: I˙˙ 5th
Root
5th
˙ 5th
˙
˙
˙
Figure 26.7.5 7̂ in the soprano
voice
in the deceptive progression in major
Bass moves
by 2nd
C: V
vi
3rd of V chord is not in melody,Root
can resolve down 5th
5th
3rd can resolve down
3rd of V chord is not in melody,
? ˙
Root
˙˙
3rd
Root
Root
˙ Root
Root
˙Root
Root
I
I
Root
repeated root: change chord member while maintaing correct doubling (Root, Root, 3rd, 5th)
repeated root: change chord
correct doubling (Root,
C: I member while maintaing
I
I Root, 3rd, 5th) I
C: I
I
Figure 26.7.7 Repeated notes in the bass line
26.8 Voice Leading First-Inversion Triads
Instead of focusing on the intervallic distance the bass part travels between
roots of chords, voice leading first inversion triads requires focusing on the
doubling or voicing of the chord itself. When approaching or leaving a first
inversion chord, move as smoothly as possible while avoiding objectionable
parallels, spacing errors, and melodic errors.
26.8.1 Voicing a First Inversion Chord
In contrast to the doubling rule for root position chords (i.e., “double the
bass”), do not double the bass note for first inversion triads. Instead, double
the root or fifth, depending on which can be approached and left most smoothly.
? # ### #c
& # cw www
w
CHAPTER 26. VOICE LEADING TRIADS
A: ____
____
w
w
w
w
____
____
____
316
____
? # # # B¯c
F/A Gm wC/E Fw
w5th
w
3
˙
œ
b
œ˙ œ 5thRt œœ
& 4 ˙A: ____ œ____
Rt
____
____
œœ GmœCm/E¯
5th
œ F/A
Rt œ
? b 43 ˙œ B¯œ œ 3rd
œ 3rd œ F
b
œœ 5th œ˙ œ Rt œœ
& b 43 ˙˙
5th
Rt
w
____
œœ œ Rt œ
5th
œ
˙
œ
œ
? b b 43D œ Bm D/F
œ œ
3rd˜ G
# # c YT:œ8ZKxI8d4VbM œ 3rd
œœ I œ Vœœ 5th viœ ii V
&
Figure 26.8.1 J.S. Bach,B¯:
Chorale
237, “GottRtlebel noch”, BWV 320
5th ˜œ Gœ
? # # c œœ D œœ Bmœ œ D/F
## c
œ
œœ œœ œ 3rdœœ 5th œœ
&
Rt
D: I
vi
I
IV
? # # c œœ œœ œ œ 5th œ œ
B¯
E¯ œ 3rd Aœ/C
B¯
F: IV
I6
ii
V6
6
w
____
I
6
6
o
F/A
œ
b c D:œœ I vi œ I IV
3rd
( œ)
œ
œ
b
œ
œ
&
œ
Rt
œ
## œ
œ
œ 5th œ
œ
&
? b b c œ YT: 3B9KD9CJ3tA
œ (œ) œ 3rd œ
œ
Figure 26.8.2 J.S. Bach, Chorale 153, “Alle Menschen müssen sterben”, BWV
262
? # inversion
If the 3rd of a first#B¯:
is doubled,
I
IV it will beviiin one ofI the following
V
6
o6
6
situations:
1. Diminished triads in first inversion—always double the third (the bass),
not the root or fifth
w
w
____
1.
____
w
____
w
.. w
..
____
2
____
.. w
__
œœ œ œ 5th œ œ
œ 3rd œ
? # # c œœ
D: ILEADING
vi
I6
IV
CHAPTER 26. VOICE
TRIADS
B¯
E¯
b
& b c œœ
œ
? b c
b
œ
œœ
œ
œ
B¯: I
317
Ao/C
œœ
œ
œ
( œ)
IV
B¯
Rt
5th
3rd
viio6
œ
œ
œ
œ
œ
œœ
œ
œ
3rd
F/A
( )
I
V6
YT: Lul-S82JIeM
Figure 26.8.3 J.S. Bach, Chorale 103, “Nun ruhen alle Wälder”, BWV
392
2. Consecutive first inversion chords—alternate between doubling the third
and not doubling the third
E/G˜
##
& # c œœ
œ
? ### c œ
œœ
A
158
5th
œ
œ
Rt
3rd
V6
A: I
158
Rt
D/F˜
œœ
œ
œ
C˜m/E
œ Rt
œ 3rd
Rt
œœ 5th
œ 3rd
œ 3rd
iii6
ii6
Rt
5th
3rd
3rd
IV6
Bm/D
œœ 5th
Rt
E/G˜consecutive
D/F˜ 1st
C˜m/E
inversionBm/D
triads
##
& # c œœ
# ### œœ
?
#
&# c
œœ
A
œœ Rt œ Rt
œ 5th
5th
œ Rt œ 3rd œ Rt
œ 3rd
œ 3rd œ 3rd
YT: QSv7SkXmhFI
Rt
œœ 5th
œ 3rd
œ 3rd
Rt
5th
Figure 26.8.4 J.S. Bach, 6Chorale6 106, “Jesu
Leiden,
Pein und Tod”,
A: I
V
IV
iii6
ii6
BWV 245
#
? ##
consecutive 1st inversion triads
3. Approached in opposite direction in both parts
& b c œœ
œ
?b c œ
F: ii
&b
œœ . 3rd œ œ
J
œœ
œ 3rd ˙
œ
˙
˙
œœ œ œ 3rd ˙
œ
I6
ii6
I6
viio6
œœ
œœ
3rd
IV
ii7
YT: 7OQrWJvezT4
Figure 26.8.5 Palestrina, Missa Aeterna Christi Munera, Sanctus
?
b never double the third of the V chord because it is the
Note that you should
leading tone (7̂ ).
œ.
œ
?b c œ
œ œ
J
œ
œœ
œœ
3rd
CHAPTER 26. VOICE LEADING TRIADS
œ
˙
œœ œ ˙œ
˙
3rd
œ
318
26.9 Voice Leading Second Inversion Triads
F: ii
I6
IV
ii6
I6
ii7
viio6
When a triad is in second inversion, double the fifth (the bass note).
b
&b c
B¯
E¯
D
Gm
œœ œ œœ 3rd œœ
5th
˙.
˙.
˙˙ ..
œ
œ Rt # œ
œ œ œ 5th œ
œœ
? b c œ
b
œ
g: III
&b
Gm/D
VI
b
i64
V
i
YT: ivm4RACsrBU
? bb
Figure 26.9.1 J.S. Bach, Chorale 204, “Wer weiß, wie nahe mir”, BWV 166
26.10 Special Situations
Avoid parallel fifths when the roots of triads are a second apart, as in the
following examples:
1. ii6 to I64 (see the first measure in the examples below)
2. I to vii◦6 (see the second measure the in examples below)
&
&
?
?
˙
˙
5th ˙
˙
Root ˙
˙
Root ˙
˙
5th
|| 5ths
|| 5ths
C: ii6
C:
˙˙ 5th
˙˙ 5th
˙˙ Root
˙˙ Root
I64
ii6
I64
˙˙
5th ˙
˙
Root ˙
Root ˙
˙
5th
|| 5ths
|| 5ths
˙˙
˙˙
˙
˙˙
˙
5th
5th
Root
Root
C: I
viio6
C: I
viio6
Figure 26.10.1 Parallel fifths when roots are a 2nd apart
&
&
?
?
˙˙
˙˙
˙
˙˙
˙
C: ii6
˙˙
˙˙
˙
˙˙
˙
ii6
I64
Root
5th
Root
5th
C:
|| 4ths
|| 4ths
I64
Root
Root
5th
Root
5th
Root
5th
5th
˙˙
˙˙
˙
˙˙
˙
|| 4ths
|| 4ths
˙˙
˙˙
˙
˙
˙
C: I
viio6
C: I
viio6
Root
5th
Root
5th
& 26.10.2 Parallel fourths as a corrective when roots are a 2nd apart
Figure
&
In any such situation where the roots are a second apart (even if the chords
are?inverted), revoice each chord so the 5th of the chord is below the root of
the?chord in the upper voices
&
&
?
?
165
165
œ
?b c œ
œœ
œœ
3rd
˙
œœ œ œ 3rd ˙
œ
ii6
viio6
CHAPTER 26. VOICE LEADING TRIADS
I6
F: ii
IV
I6
ii7
319
26.11 Types of Six-Four Chords
When you are harmonizing
melodies and writing music, there are three situabb c
&
œ use a œœ64 Rtchord.
˙˙ ..
# œœ
tions where it is appropriate
to
œœ
œ œ
B¯
E¯
Gm/D
D
Gm
œœ œ œœ 3rd œœ
5th
V
˙.
˙.
typically occurs in the patterns
I–IV 64 –I
5th
1. Pedal
6
4
6
2. Passing ?
4
3. Cadential
The pedal
6
4
œ
bb c œ
6
4
g: III
i64
VI
& œœœ
œœ
œ
œœœ
C: I
IV64
I
? œ
œ
œœ
œ
œ
œ
C: V
i
œœ
œ
or V–I 64 –V.
œ
œœ
œ
œ
I64
V
Figure 26.11.1 Examples with the Pedal Six-Four
The passing 64 typically occurs in the patterns I–V 64 –I 6 (or its retrograde)
and IV–I 64 –IV 6 (or its retrograde).
& œœœ
œœ
œ
œœ
œ
C: I
V64
I6
?œ
œ
œœ
œ
œ
œ
C: IV
œœ
œ
œœ
œ
I64
IV6
œ
œ
Figure 26.11.2 Examples with the Passing Six-Four
In an earlier section we discussed the Cadential
that section to review the cadential 64 chord.
6
4
chord. Please refer to
&
26.12 Summary of Doubling Rules for Triads
?
To generalize, here are the doubling rules for voice leading triads in root position, first inversion, and second inversion:
• Root Position Chords: DOUBLE THE BASS
• First-Inversion Chords: DO NOT DOUBLE THE BASS
◦ Exception: vii◦6 and ii◦6 : DOUBLE THE BASS
◦ Exception: Consecutive first inversion chords—alternate between
DOUBLE THE BASS and DO NOT DOUBLE THE BASS
• Second-Inversion Chords: DOUBLE THE BASS
26.13 Practice Exercises
Day One
159
? bb c œ
b
œ
Rt
œ
œ
# c
œ
œ
E¯: I
vi
IV TRIADS
ii
CHAPTER 26. VOICE
LEADING
1.
156
HW
e: III
5th
Rt
œ
œ
œ
iv
V
VI
320
For bass movement of a 3rd or 6th, in the upper voices hold two
common tones and move the other voice
For bass movement
# # cbyœ step.
5th
Rt
b c œœmove
of&
a 2nd,
the upper voices in contrary
motion
to the bass with
œ
3rd
5th
the exception of the deceptive progression, which has special rules.
œ Rt doubling by specifying whichœ voice
3rd
Keep track of
has the
œ root,œ third,
?
#
œ
c
c
œ
#
or fifth
for
each
chord.
œ
Rt
œ
cb œ Rt œ
& b œ œ 5thRt5th
# c œ 3rd
b b c œœœ 3rd
&
œ
HW
d:œ III3rd Rt iv
V
VI
D: I Rt iii
IV
ii
156 PRAC EXER
?c
œ
˙
œ
Rt
œ
œ
œ
5th
œ
Rt
&
? #b b# # œc 5th
#
5th
œœ RtRt œ œ
œ
œœœ 3rd
c
b
œ ____ œ ____ b b cc œ____
œ ____ œ
&
œ
Bass moves by: ____
____
Rt
HW
5th
Rt
œ
3rd
III
VIœ
iv
VI
? ca: i œ VII
˙
œe: III Vœiv
œIV
HW
E¯: Rt
I 3rdœ vi
ii
V
VI
œ
U
œ
? # # #3 c œRt œ
œ
œ
œ
b
œ
c
œ and
b œhold
For
bass
of
tone
Rt
Bass
____
____œeither
____(1)œ
____ one common
____
Bach chorale #2222.
&moves
4by:movement
œœ ____
œœ a 4th,
˙˙
œ
5th
( nRtœ )
move a:the
by III
step, orVI(2) moveivthe upper
Nun preiset alle ???
i two voices
VII
V voices
VI in the same
A: iii
IV
V
vi
B¯: V
vi
IV
ii
direction. Keep track of doubling
by
specifying
which
voice has the
U
#
œ
œ
˙
3rd
œ
#
5th
œœ each chord. # cœ œ Rt
c3 œœ or
root,
?
œ) for
& #bthird,
Bach chorale #222
&
4 œœ 5thRtRt3rd (fifth
œœ
œ
# œœc (5thn3rdœ ) ˙˙
3rd
b
b
Nun preiset alle ???
b
c
œ
œœœ 3rdRt œ u œ
b
œ
Rt
&
œ
HW
HW
œ 5th
Bass moves by:
____
____
____
œ
œ
? b c œœ œ3rdRt ____
#
œ ˙ œ
œ
œ
c
œ
#
œ
? # G:
3 ____ (œ)œ ____
____
____ Rt
____
œœ
œ
PRAC EXER
? b 4b cœ RtRt
# œc œœ 5th u˙ œ
œ
bb
Rt
œ IV
œ
HW
œ Rtiv œ V____ VI œ ____ D: I ____
iii
ii
Bass movesd:by:III
bb œ f:Rt i ____
˙
III œ
G: vi
ii ____ V
I
œœ ____
& # #G:œ____
˙ iv ____ VII
5th
œ b____
5th
Rt
#
œ
œ
c
b
c
œœ 3rd
& œ 3rdœ ˙
œ (œ) œ̇ #
Rt
Day Two ? b œ Rt( ) 5th5th ˙
œ
#
œœ œ œ
c œœœ
œœRtœ 3rd3rd˙˙ œ
œ
œ
b cœœ 5th
œ
HW 3.
&
œ
œbass b symbols,
Given
the bass line and figured
the Roman
5th analyze
#
œ
?
#
œ
œ
œ
œ
HW
c
œ
c
#
œ
œ in
b
numerals
alto, and tenor parts
Bass moves by:
____ add soprano,
œ____RtRt ˙the____staffœ and
3rd
œœ below
(œ )
œ̇
œ
Rt
˙
?
œ
#
“chorale-style,”
following
good# voice
Choose
the becA: œRt(iii) Rt ____
cB¯:œV leading.
œ
œrulesviof____
œV____
B¯:
IV
vi
IV
iiœ
Rt œ
b b ____
ginning register for each upper part carefully, considering the number
c œœ
b b bcb____
&B¯:
œ
# c 3rd
œœ Rt œ
# œ c œœ 5thœ
Rt
œ
of
the
a 2nd.VII
iii
V interval of
b: iv
Basstimes
movesB¯:
by:the
____bassvimoves
____ ii by ____
PRAC EXER
4.
HW
? b b cb cœ
& b
œ
3rd
____
Rt
5th
____
œœ
œœ
œ
œ
____
____
Rt
____
œ
œ
˜
III
œ
œœ
VI
œ
œœ
f: i
iv
VII
III
G: vi
V
I
œ ii ____
œ
œ
œ
____
____
____
____
____
____
? d:c ____
œ
œ
œ
œ
b
# # cnumerals
Givenb b the
bass
line,
Roman
below the staff and
5th
œ the
c œœ
œ analyze
˜ œœ
œ
&
œ 5th œ (allœ threeœ upper
3rd
add soprano, alto, and tenor parts in “keyboard-style”
d: ____
____
____
____
____
____
____
____
voices in the
clef), following rules of good voice leading. Choose
œ treble
Rt
œ
?beginning
the
for
considering
the
b c œ Rt register
c œcarefully,
œ
œ eachœ upper# #part
b
Rt œ
œ
direction of the bass line.
#
vi
ii
V
b: iv
VII
III
VI
& cB¯: iii
?# c
œ
G: ____
œ
œ
œ
____
____
____
˙
____
Day Three
5. Analyze the Roman numerals in the blanks below the staff and the
doublings of the chords in the squares—specifying Root, 3rd, or 5th—for
J.S. Bach’s Chorale 367, Befiehl du deine Wege.
155
? # # c œœ
PRAC EX
œ
5
œœ
R
œœ
5
R TRIADS
3
CHAPTER 26. VOICER LEADING
#
& b # c œœ
b c
I
D: ____
160
&
PRAC EX
6.
HW
œœ
7.
R
3
R
œ
œ
R
R
321
viio6
ii ____ ____
I
____
____
œœ
œœ
œœœ
œœ
œœœ
œ œœ
? # #g: ____
HW
œ
œ
œ
œ
œ
œ
œ
œ
wœœ
œ
œ
œ
6
6
˜
œ
g: ____
____
____
____
œœ____œ ____
? #b# cD:œœ ____ œ ____
œœ
œ____ ____ ____
œ
& b c œœ
œœ
w
#
œ
#
œ
œ
œ)
w(analyze
Givenb b the
bass
the Roman nuœœ line andœfigured œbass symbols,
œ
c
& D:and
œ œ____
œ tenor
œ
œadd soprano,
merals
and
parts
in
chorale
style. Review
œ
____
____ alto,
____
____
____
œœ
ww
? b b# c rule for doubling œin diminished
the special
triads
in
first
inversion.
You
œ œ
œœ
#
œ
(œ ) alterations.
œ
œ
may
wish
to
review
figured
bass
with
chromatic
œ
&
? b c #œ
6
6
˜
bb
i
viio6
i6
V
VI
____
____
____
____
& b g:c ____
?
?#b b## #c cœ
&
œ
160
IV
____
I6
5
____
____
____
? bb c œ
œœ
œœ
œœ
www
& b œ
b
c
& b
(one of several
6
œ6
œ˜
ww
possible solutions)
œ
œ
? b b g:c ____
____
____
____
____
œ
œ
œ
˙
œ
˙
? bb c œ
œ sureœ your progression follows the Harn œ 6 making
b I the melody
Harmonize
V
I
ii6
V
b ____
____
____
____
____
monic
(analyze
the harmonic
function
of each chord, ab6
6
Ω
& b B¯:Flowchart
Ton.
Dom.
Ton.
Pre-dom.
Dom.
HF:
____then____
____
____
____bass parts
breviated
as “HF”),
add alto,
tenor,____
and
c: ____
____
____
____
____ in chorale
style following rules of good voice leading. Use first-inversion chords
? b a smoother bass line.
to make
b#
& b# c œ
&b c
?#
? b b# cc
PRAC EX
œœ
œ
œ
œ
˙
œ
˙
w
D: ____
____
____
____
____
____
B¯:
HF: ____
____
____
____
____
____
____
____
____
____
# ____
#HF:
& # c œ
œ
œ____ œ
œ
œ
____
____
____
œ
œ
œ
____
œ
Day Four
? # # # cthe figured bass symbols to specify Roman numerals with
8. Analyze
inversion symbols below the staff. Add soprano, alto, and tenor parts
6
A: Istyle. VSpecify
I root, third,
IV6
V6 fifth for
I every
V chord.
vi Addiin keyboard
and
tionally, specify the six-four chord type (pedal, passing, or cadential).
#
& # c
? ## c œ
b: ____
6 chord
4
9.
type:
6
4
____
œ
6
4
˜
˙
____
____
____
œ
œ
6
6
____
____
____
For the given Roman
numeral
progression,
provide soprano, alto,
i
V64
i6
iio6
i6
V
i
tenor, and bass voices
in chorale style. Be4 careful not to exceed any
cadential
passing root, third, and fifth
voice’s range. Specify
for every chord. Additionally, specify the six-four chord type.
161
4
e: ____
6
4
____
____
____
chord type:
____
____
____
____
CHAPTER 26. VOICE LEADING TRIADS
322
b
&bb c
? bb c
b
c: i
6
4
chord type:
b
iv
i64
____
iv6
iio6
i64
V
VI
____
b c
Click here &
to download
the first homework assignment for this chapter.
Click here to download the second homework assignment for this chapter.
Click here
? to
b download the third homework assignment for this chapter.
Click here btocdownload the fourth homework assignment for this chapter.
PDF versions of the textbook, homework exercises, and practice exercises
can be found at musictheory.pugetsound.edu
&b
b
? bb
Chapter 27
Voice Leading Seventh Chords
27.1 Voice Leading Seventh Chords
There is one general rule for voice leading any seventh chord: resolve the 7th of
the chord down by step. All other voices should move smoothly to the nearest
chord tone in a voicing containing the appropriate doubling.
Principle 27.1.1 7th chords. Resolve the 7th of a 7th chord down by step.
? bb bb
?
bb bb
? bb bb
?
bb bb
œ
œ
242 œœ œœ œœ œœ œœ œœ œœ œœ
4
pp
242 œ
œœ
4 œ
Textural reduction:
reduction:
Textural
? bb bb 22 œœœœ
?
bb bb 44
A¯
A¯
? b bb 2 œ
b 4
A¯: II
A¯:
œœ
œœœœ
œ
E¯77/D¯
/D¯
E¯
A¯/C
A¯/C
œœœœ
œ
œœœœ.. œœ œœ
œœ œœ œœ
œ
7th
7th
resolves down
down by
by step
step
resolves
6
V442
V
II6
2
323
œœ
œœ œœ
œœ
œœ
œœœ
œœ
E¯/G
E¯/G
œ
V66
V
YT: SrcOcKYQX3c
bbb b
&
Figure 27.1.2 Beethoven, Pathétique Sonata, Op. 13, II.
? b b bb
j
œœœj
7th
œœœ 7th
œœ
E¯77/G
/G
E¯
V656
V
5
œœœ
œ
A¯
A¯
œ
II
163
163
?
? ###### ww
ww
ww
CHAPTER 27. VOICE LEADING SEVENTH CHORDS
401
401
401
401
### ##
&
& #
### ##
&
& #
?
? ######
### ##
&
& #
686 jj
œ œ
8 œœ œœ .. œœ œœ œ œJJ
Ich träum - te von bun - ten
Ich träum - te von bun - ten
686 ‰
8 ‰ œœ
p
686 ‰ pœJœ
8 ‰ J
Textural
Textural reduction:
reduction:
406
406
406
406
j
œj
œ
œœ œœ œ œœ œœ
œ
‰‰ ‰‰ œJœJ ‰‰ ‰‰
Blu - men,
Blu - men,
so wie sie wohl blü - hen im Mai;
so wie sie wohl blü - hen im Mai;
jj
œœ œœœ ŒŒ
Bm7/D
/D
A
EEœ7 (œ ) œ A
j Bm
.
j
œ
(
)
œ
.
œ
œ
.
j
œœ ‰
œœœ œœ . (œ( œ)) œœ œœ
œœ ‰
œ
œœ œœ œ
? b b 2 œœœ A:
b b 4 A:
œœœ
II
? bb 2
bb 4 œ
œ
7th
œœ œ œœ œœ œ œœ œœ
œ
œ
j
‰‰ œJœJ ‰‰ ‰‰ œœj ‰‰ ‰‰
œ
œœ œœ œ œœ œœ
œœJ ‰‰ ‰‰ œœJ ‰‰ ‰‰ œœ ‰‰
J J
JJ
686 jj
œ œ
8 œœœœ œœ.œ. œœ œœ œœ œ œJJ œ
? bb 2
b b 4 Ich œträum - te œvon bunœ- ten œBlu - men, œ so
träum - te von bun - ten
Blu - men, so
### ## 6 Ich
p
‰
œ.
&
œœœœœ..... œ œœœœœ.....
?
& b b b#b 42868 œ‰ œœœœœœ......
œ œœœ ...
œ. œ.
pp
œ.
Textural
œœ..
?
? ##reduction:
œœ.. A¯/Cœœ..
#### 6868 A¯‰‰ œ .
E¯ /D¯
7
324
j j
œ (œ) œ
œœ œœj ŒŒ œœj œœ .. ((œœ)) œœ œ .. (œ) œ œœ ‰‰
F˜˜m
m
F
jœj
œ
œ.
A
A
.
.. ww
œœ
œ vivi
œœ
œ
œ
œ
7
7
œ
œ
œ
œ
wie sie wohl blü - hen im Mai;
wie sie wohl blü - hen im Mai;
œœœœ ... 7th7th œœœœœ.. ... œœ ..œœœ ...
. œ
.7th œœ .
..
œœE¯/G
7th
œ 7th
6œ
iiii655œ
œœ. .
E¯7/G
œœ 7
œV7
V
œ .œ .
A¯
II
œ
YT: 2GGPY3mhqLc
resolves down by step
A¯: I Schubert, Winterreise,
V42
I6
V6
V56
I
Figure 27.1.3
D. 911,
“Frühlingstraum”
(1823)
The one exception to this is in the progression I – V43 – I6 , which closes the
theme of the first movement of Mozart’s Piano Sonata K. 331.
### 6 œ
& 8 œœ
f
? # # # 68 œ
œ
j
œœ
œ
J
œ
œ
J
œ œœ
œœ
œ
œ
œ
œ
œ
J
E7/B
A/C˜
V43
I6
œ
œ
œ
œœ œ œ
J
œ
œœ
œ
J
‰
‰
### 3 œ
œœ 7th œœ YT: vp_h649sZ9A
& 4 œ
Figure 27.1.4 Mozart, Piano Sonata K. 331, I
œ
œ
œ
#
example below, one can see that the 7th resolves up by step.
?In#the
3
# 4 œ
œ
œ
A
##
& #
? ###
A: I
..
..
163
J
J
œ
œ
œ
œ
œ
œ
œ
œ
œ œ
J
J
J LEADING SEVENTH
CHAPTER 27. VOICE
CHORDS
f
? # # # 68 œ
œ
##
& # 43 œœ
œ
? ### 3
4 œ
A
E7/B
A/C˜
V43
I6
..
‰
325
œœ
œ
œ
œœ 7th
œ
œ
A: I
œœ
Figure
# # 27.1.5 The I – V43 – I6 progression with acceptable parallel fifths
#
&Notice
that parallel fifths occur in this progression because of the upward
resolution of the 7th. These parallel fifths may have been deemed less objectionable
? # # because they consist of unequal fifths (where one of the fifths is in
a case #of parallel fifths is diminished).
27.2 Voice Leading Successive Seventh Chords
Sometimes you will encounter a situation where there are successive seventh
chords. This is especially the case in circle of fifth progressions. When voice
leading a circle of fifths progression with root position seventh chords in four
parts (SATB), alternate between incomplete seventh chords (without the fifth
of the chord) and complete seventh chords, as can be seen in the example below
from Vivaldi’s Concerto for Two Violins and Cello in D minor, RV 565.
32
32
32
32
32
32
String
String
Orch.
Orch.
Cello
Cello
solo
solo
34
34
String
String
Orch.
Orch.
34
34
34
34
Cello
Cello
solo
solo
& bb
&
?b
?b
?b
?b
& bb
&
?b
?
b
44
4
44
4
Dm
Dm3rd
œ
œœ
œœ
œ
œ
3rd
5th
5th
3rd
3rd
Rt
Rt
Gm7
7
Gm7th
œœ
œœ
œ
œ
œ
Œ
Œ
Œ
Œ
7th
3rd
3rd
Rt
Rt
Rt
Rt
C7
C7
œœ
œœ
œ
Œ
Œ
Œ
Œ
3rd
3rd
7th
œ
œ
7th
5th
5th
Rt
Rt
Œ
Œ
Œ
Œ
Fmaj7
Fmaj7
œœ
œœ
œ
œ
œ
Œ
Œ
7th
7th
3rd
3rd
Rt
Rt
Rt
Rt
Œ
Œ
œœœ œœ œœœ œœ
œ œ
œ œ œ œ
44 œ œ œ œ œœ œœ œ œ œœ œ œ œ œœ œ œ œœ œœ œ œœ œ œœ œœ œœ œ œœ œ œœ œ œœ œœ œ œœ
4 œ
d: i
d: i
B¯maj7
B¯maj7
œœ
œœ
œ
œ
œ
3rd
3rd
7th
7th
5th
5th
Rt
Rt
iv7 (inc.)
iv7 (inc.)
Eø7
Eø7
œœ
œœ
œ
Œ
Œ
Œ
Œ
7th
7th
3rd
3rd
Rt
Rt
Rt
Rt
Œ
Œ
Œ
Œ
VII7
VII7
Am7
Am7
œœ 7th
3rd
œœ 7th
œ 5th
5th
œ RtRt
œ7
3rd
Œ
Œ
Œ
Œ
IIIM7 (inc.)
IIIM7 (inc.)
Dm7
7
Dm7th
œœ
œœ
œ
œ
œ
7th
3rd
3rd
Rt
Rt
Rt
Rt
Œ
Œ
Œ
Œ
œ
œ
v
i7 (inc.)
7
v
i7 (inc.)
? b œ œœ œœ œœ œ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œ œœ œœ œœ œ œ œœ œœ œ œœ œœ œœ œ œœ œœ œ
? œ
œ
œ œ
œ
œœ œ
b
VIM7
VIM7
iiø7 (inc.)
iiø7 (inc.)
∑
∑
∑ Two Violins
∑
∑ RV
Figure 27.2.1
Concerto
for
and∑ Cello in∑ D minor,
& bb Vivaldi,
∑
∑
∑
∑
∑
∑
∑
&
565, V.
36
36
?b
?
b
36
36
?b
?b
36
36
YT: qgJwavKDKgY
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
∑
5
5
CHAPTER 27. VOICE LEADING SEVENTH CHORDS
326
Principle 27.2.2 Voice Leading Successive Root Position 7th chords.
Alternate between complete and incomplete voicings.
If, on the other hand, you are asked to voice lead a circle of fifths progression
involving inverted seventh chords, always resolve the seventh of each chord
down by step and move the other voices smoothly. You will see the following
pattern: two voices will remain on common tones (shown with ties) while the
other two voices resolve downward by step.
&b
b
&
?
b
?
b
164
164
44 œœœ
4 œœ
44 œ
4
4d: ivœ56
4
œœ
œ
œœ
œ
œœ
œ
œœ
œ
œ
œ
VII42
IIIM65
œœ
œ
œœ
œ
œœ
œ
œœ
œ
VIM42
iiø65
œ
˙˙
˙
˙˙
˙
# œœ
œ
# œœ
œ
œ
œ
˙i6
V42
6
Figure d:27.2.3
iv56 Circle
VII42 of fifths
IIIM6progression
VIM42 with
iiøinverted
V427th chords
i6 (alternating
5
5
6
4
and
)
5
24 œ
œ
œ
&b
b
&
?b
?b
164
4 œœ
44 œœ
44 œ
44d: ivœ 7
œ
œ
œœœ
œœ
œœ
œ
œ
œ
VII43
œœœ
œœœ
œœ
œ
œœ
œ
œœ
#œ
œ
# œœ
VIM43
iiø7
V43
œ
IIIM7
œ
˙˙˙
˙˙˙
˙
œ
˙i
3
3
3
3
&4
Figure 27.2.4 Circle
of fifths progression with alternating 7 and 43 chords
œ
œœ
œœ
4
œ
œœ
œœ
˙˙
# œœ
3
&b 4 œ
œ
œ
œ
œ
œ
&
4
˙
? 43 ˙ ˙
7
œ
œ the
œ Vœ to Iœ Progression
27.3 Voice
œ
? 4Leading
˙
? 43 ˙ ˙b 4
7
d: iv
VII
III
VI
iiø
V
i
d: iv7
VII4
IIIM7
iiø7
VIM4
V4
i
M6
M4 four parts,
6
4 must 6deliberately
In voice leading the 56V to I42 progression
in
one
5
5
2
2
choose one of the following methods:
1. “Strict” resolution:
b 4 œœ
& 4 œ
7
œœœ
œœ
œ
œœœ
œœ
œ
œ
# œœ
˙˙˙
(a) Complete V to incomplete I: resolve 7̂ up and 4̂ and 2̂ down. This
œ
œ 3rd of
? b 44resolving
œ the Vœ7 chord (œ7̂ ) up and
means
the
œ the˙7th and 5th
7
of the V chord down. For the sake of consistency in terminology,
4 the chord.
d: iv7
VII43 label
IIIM77̂ , 2̂VI,M43and the
iiø7 7th Vof
i
the examples
below
The
3
incomplete I chord will have a tripled root and one 3rd.
& c ˙˙
˙
?c ˙
7̂
7th
2̂
C: V7
complete
˙
˙
˙
˙
I
incomplete
˙˙
˙
˙
2̂
7̂
7th
V7
complete
˙
˙
˙
I
incomplete
(b) Incomplete V7 (no fifth) to complete I.
& c ˙˙ 7th
? c ˙˙
7̂
C: V7
incomplete
& c ˙˙
˙
?c ˙
7̂
7th
˙˙
˙
˙
˙˙
˙
7th
7̂
˙˙
˙˙
I
complete
V7
incomplete
I
complete
˙˙
˙
˙
˙˙
˙˙
˙˙
˙˙
7th
7̂
˙˙
˙˙
7th
2̂
7̂
V7
complete
˙˙
˙
˙
7̂
7th
V7
incomplete
˙˙
˙
˙
I
incomplete
˙˙
˙
˙
I
complete
˙
7th
˙ 2̂
˙
˙
˙˙ 7̂
˙
?c ˙
˙˙
˙
˙
˙
˙
˙ 2̂
& cC: V˙˙ 7 7th7̂
7th
˙
˙I
˙˙I
˙ 7 2̂
V7 7̂
I
V
CHAPTER 27. complete
VOICE
LEADING
SEVENTH
CHORDS
327
incomplete
complete
incomplete
complete
incomplete
˙
˙
7th
˙ 2̂
˙
˙
˙
7̂
˙
˙
˙
?c
˙
˙
˙
˙
c
˙
7
7
7
V
& C: ˙V˙ 7th
˙˙I
˙V 7̂
˙I
˙˙ 7th incomplete
˙˙I
complete incomplete
complete
complete incomplete
7̂
˙ 7th
˙
˙
˙
˙
˙
? c ˙˙ 7̂
˙
˙
˙˙
˙˙ 7̂
& c ˙˙7 7th
˙
˙
˙
˙
7th
˙
˙I
C: V
I
V
V7
I
˙7 7̂
˙
7th
˙
incomplete complete
incomplete complete
incomplete
complete
˙
˙
7̂
˙
˙
˙
?c ˙
˙
˙
˙
2. “Free” resolution:
c V˙˙7 7̂
C:
I˙
V˙7 7th
I
V7
I
˙
˙˙resolve itincomplete
(a) If &
7̂ isincomplete
not in the
soprano
part,
down bycomplete
the interval
˙ you can
complete
incomplete
complete
˙ 7thto 5̂ . ˙
of a third
˙˙ 7̂
˙
?c ˙
˙˙
˙
˙
c
˙
&
˙
7̂
˙
7th
˙V7
˙˙I
C: V7
I
˙ 7th complete
˙
complete
complete
complete
˙˙ 7̂
˙
?c ˙
˙
˙
C: V7
complete
V7
complete
I
complete
I
complete
In piano music you will sometimes find “improper” resolution of the 7th of a 43
chord because it fits the hand better. This should be considered an exception
and will not be acceptable in voice leading exercises completed for this class.
411
b b c >œ
b
&
Ces
411
-
œ œ
J J
sa,
cru
b
& b b c œœ œœ n œœ œœ
f
>œ
œ œ
? bb c
b
B¯: I6
b
&bb
V46
I
-
œ nœ œ œ œ
œ. œ ˙
del,
tan
ri
œ
œ œ ˙
V24
I6 IV I46
-
to
-
n œœœ œœœ œœ œœœ œœœ œœœ œœ œœ
œ œ
V7
gor!
œœ œ œ
œ œ
˙
I
414
b
&bb
YT: -Hlk8EDA02M
414
Figure 27.3.1 Giuseppe Giordani, Caro mio ben (1783)
6
7
? b Voice∑ Leading
27.3.1
∑ I4 to V
∑
bb
∑
∑
∑
∑
∑
∑
When I64 resolves to V7 , beware of parallel fifths if the fifth is above the root
in the I64 chord. If it is, move all upper voices upward to the closest notes of
the V7 chord, or to an incomplete V7 (no 5th).
b
&bb
420
b
&bb
420
? bb
b
b
&bb
426
∑
∑
∑
CHAPTER 27. VOICE LEADING SEVENTH CHORDS
168
&
˙˙
˙˙
?
&
5th ˙
˙
C: I64
˙˙
|| 5ths
˙
˙
˙˙ 75th
V
˙˙
˙
˙
solution: inc. V7 chord
solution: upper voices ascend
˙˙
˙˙
5th
C: I64
˙˙
V7
|| 5ths
˙˙
328
5th
˙˙
˙˙
˙˙
C: I64
V7
inc.
˙
˙
˙
Root ˙
˙˙ Root
˙ Root
? ˙
˙
˙
&
27.4 The Special Resolution of vii ◦7 (and vii ø7 )
C: ii6
I64
C: I
viio6
? vii◦7 and viiø7 chords consist entirely of tendency tones (7̂ , 2̂ , 4̂ , 6̂ ).
The
Root
|| 5ths
If one resolves all of those tendency tones correctly (2̂ –1̂ , 4̂ –3̂ , 6̂ –5̂ , 7̂ –8̂ ),
◦7
ø7
Root write
Root ˙ on the voicing
one might
5ths depending
˙˙ parallel
˙˙ Root
˙˙ Rootof the vii and vii
&
˙
5th
5th
5th
chord. Therefore, be sure to memorize the following 5th
principle:
˙
˙ the 7th
˙ of a vii◦7 or viiø7 chord
Principle ˙27.4.1 Resolving
vii◦ 7 . When
˙
?
˙
˙ of the chord (scale degree
is &
voiced above the 3rd of the chord, resolve
˙ the 3rd
2̂ ) up by step while resolving all other tendency tones normally (4̂ –3̂ , 6̂ –5̂ ,
7̂ –8̂ ). C: ii6
I64
C: I
viio6
|| 4ths
?
&
?
&
?
7th
3rd
˙
˙
˙˙
C: viiø7
|| 5ths
|| 4ths
˙
˙
˙˙
I
7th
3rd
˙
˙
˙˙
2̂
3̂
˙˙
˙˙
3rd
7th
(solution)
C: viiø7
I
˙˙
˙
˙
|| 4ths
C: viiø7
˙˙
˙
˙
I
Figure 27.4.2 Resolving viiø7
&The third measure above shows that revoicing the chord is another solution,
since parallel 4ths are not objectionable in this situation.
?If the 7th of the chord is voiced below the 3rd of the chord, resolve all
tendency tones normally.
&
27.5
? When to Use Seventh Chords
In your harmonizations of melodies, it is best to use seventh chords to add
& as you approach tonic function. Therefore, sevenths are added most fretension
quently to chords of dominant function ( V and vii◦ ) and chords of pre–dominant
function
? ( ii and, to a lesser extent, IV ). (See the harmonic flowchart.) For
this reason, seventh chords like iii7 , vi7 , IVM7 , and IM7 are less commonly
used and encountered.
165
? ˙˙
˙˙
|| 5ths
CHAPTER
C:
& vii˙˙ ø727.
5th
Root
# ˙˙ œ
# #?
& c œ
œ
? # #7th# c˙ œ
&
˙
˙˙
˙
(solution)
Root
|| 4ths
œ
Root
5th
˙
˙œ
˙
œœ˙
œ
I6
˙˙
|| 5ths
˙
˙
C: viiø7
I
###
œ
œ ˙˙ œ
C: I
3̂
2̂
˙ ii56
˙
vi
œœ ˙
˙˙
C: viiø7
I
œ
3rd
7
˙.
˙˙
˙.
˙
I
˙
˙˙
|| 4ths
˙
˙
C: viiø7
I
329
˙˙ .
.
viio6
7th
(solution)
V
˙
˙
5th
|| 4ths
4
œ
œ œ
œ œ7th ˙ œ
˙
˙
˙
3rd
? A:˙ ii
##
& #
˙˙
˙˙ø7
˙˙ Root C: viiø7
VOICE
CHORDS
I ˙
C: viiSEVENTH
I
˙ LEADING
5th
C: ii6
3rd
4
I
œ
œœ
œœ “Lobt Gott,
œœ ihr Christen,
˙˙ .
œ Chorale
#27.5.1c J.S.
Figure
342,
allzugleich”,
œ Bach,
? # #&
.
BWV 376
YT: 2dxuAKSxgw0
œ
œ œ œ
? ### c œ
œ œ œ
27.6 Practice Exercises
1.
6
?
# ˙˙
˙
˙
˙˙
˙
˙
a: V7
inc.
i
comp.
7
D: V7
comp.
e: V7
i
comp. comp.
I
inc.
B¯: V7
I
comp. comp.
7
c˜ : V
i
A: V7 progression
I
f: V7
i root position
E¯: V7 seventh
I
Voice lead
this
circle
of fifths
involving
167
inc.
comp.
comp.
inc.
comp.
comp.
comp.
comp.
chords. Include the key signature and analyze the figured bass symbols
in order to place Roman numerals in the blanks below the staff.
&
&
?
?
œœ
œœ
7 7
A: ____
b: ____
3.
˙.
˙.
Example
?
&
2.
œ
œ
ii
vi
ii5
I
Voice leadA:each
V7 chord
to the tonic
usingVeither “strict”
or “free” resolution as indicated by the terms incomplete (“inc.”) and complete (“comp.”).
Include key signatures.
&
166
œ
œ
7 7
____
____
œœ
œœ
77
____
____
œœ
œœ
77
77
____
____
77
____
____
œœ
œœ
77
˜
____
____
____
____
____
____
#
Voice lead this circle of fifths progression involving inverted seventh chords.
&
&
?#
?
G: IM65
IVM42
viiø65
iii4
vi56
2
ii4
V56
2
IM42
Click here btob download the homework assignment for this chapter.
b b to download the Unit 8 Practice Test.
& here
&
Click
? bb
?
bb
&
#
f: i42
œœ
iv56
œœ
VII42
œœ
IIIM65
œœ
iiø56
VIM42
œœ
œœ
V42
œœ
i65
œœ
170
170
Chapter
28
& œ
œ
œ
? œœ
œ
œ
œ
8ve
œœ
œ
œ
5th 5th
8ve
œœ
œ
œ
5th
Voice Leading With Non-Chord
& œœ
œœ
œœ
œœ
Tones
C: I
8ve
5th
V
œ
?
& œœ
œ
œœ œ
8ve
vi
p
5th
œ
8ve
œ
œœ
IV
5th 5th
œ
8ve
œ 5th
œ œœ
|| 5
n
C: œI Voice Leading
V
vi
IVTones
œ
28.1
With
Non-Chord
œ
œ
? œ
p
œ
œ
œ
œ
Non-chord tones are common in J.S. Bach’s 371 Chorales, which are our model
&
œ
œ
œ
œœ
œ leading. œV
œ
for voice
pœ
C: I
viœ
IV
|| 5
p
U
|| 5
n
p
œ
œ
œ
œ
œ
œ
œ (œ ) œ œ
œ
œ
?
& bœ c œ
œœ (œ)œ œ
œ
œœ
œ
œœ œ
œœ
p
V
œ
œœ
sus (9 - 7) n
p
œ
œ
œ
œ
I6
œœ p œ œœ œœ (œ)
p
œ (œ ) œ œ
œV6
œI V6 viœœ (œ)
? c œœ
b
&b c œ
F: œ
I
C: I
? #c œœ
b#
& # c œœ
|| 5
vi
p
œ œ (œ)IVœ œ œœ
œ ( œ) œ ( œ) U
œ p œ p uœ
œ
œ
œI
IV
IV6
( )
sus (9 - 7) n
(œ )
œ œœ œœ (œ) œ
œ œœ œ
œœ 9m0RWQbSOWA
œœ
YT:
œ
œ œ
œ (œ) œ œœ
œ œ ()
œœ
œœ p
p
( )
œœ
uœœ
6
I
V6
I V6 323,
vi “WieI6schön leuchtet
IV
IVMorgenstern”,
I
Figure F:28.1.1
J.S. Bach,
Chorale
der
BWV 172
œ
? ### c œ
## œ
& # c œœ
œ
p
œ
( )
p
(œ )
? ### c œ
œ
A: I
œ
œ œ œ
œœ
œœ
œ p œ
œ ( œ) œ
I
IV6
œ œ œ
œ
œ
œ
œ œ
œ
œ
p
œ (œ ) œ
œ
œ
V
ii viio6
œ
œ
œ œ œ
œœ
œœ
œ p œ
œ ( œ) œ
I6
V
œ
U
œ
œœ
œ
œ
u
I
YT: t5rs2a0Cvr4
Figure 28.1.2 J.S. Bach, Chorale 326, “Allein Gott in der Höh’ sei Erh’, BWV
104”, BWV 172
330
CHAPTER 28. VOICE LEADING WITH NON-CHORD TONES
331
28.2 Avoiding Objectionable Parallels
170
170
When adding non-chord tones, one must avoid creating objectionable parallels.
To avoid creating parallel 5ths and 8ves when adding non-chord tones, first
identify intervals of 5ths and 8ves between voices in your original voice leading.
& œœ
œœ
œœ
œœ
8ve
5th 5th
8ve œ 5th
œ 5th
8ve œ
? œœ
œ
œ
œ
& œœ
œœ
œœ
œœ
C: I
vi 5th 5th
IV
8ve V
8ve œ 5th
œ
œ
8ve œ
5th
p
? œ 28.2.1 Progression with 8ves and 5ths identified
Figure
œ
œ
œ
&Avoid
œœ adding non-chord
œœ tonesœ that move
œœ by stepœ into notesœœ separated by a
5thC:orI 8ve.
V
vi
IV
? œœ
& œœ
œ
œœ
? œœ
&
p
œ
œ
œ
C: I
V
C: I
|| 5
|| 5
V
œ
œœ
œ
œœ
p
n
œ
œ
vi
œ
œœ
|| 5
n
|| 5
œ
œ
IV
œ
p
vi
IV
?
&It is best to avoid adding non-chord tones in two voices on the same beat
Figure 28.2.2 Parallel 5ths and 8ves created by non-chord tones
unless they are moving in parallel 3rds or 6ths.
?
28.3 Adding Non-Chord Tones to a Chord Progression
Here are ideas for how to add non-chord tones (or “embellishments”) to one of
the voice parts of an SATB chord progression.
1. Repeated note: add upper or lower neighbor
& œ
œ
œœ
œœ
C: I
V
I
repeated note
? œœ
&
?
&
œ
œ
n
œœ
œœ
V
I
œ œ œ
œ
œ
œœ
n || 5
œ œ œ
œ
œ
V
Figure 28.3.1
2. Step down:
(a) Add a suspension by delaying the resolution of the note
& œ ? œœ
œ œœ
œœœ
œ
&
? œœœœ
œœœ œ œ
œ
œ
œœœ œ œ œœ
œ
œ
repeated note
n
|| 5
n || 5 TONES
repeated
note
CHAPTER 28. VOICE
LEADING
WITH
NON-CHORD
n
œœœ
œ œ œœ
œ œ œœ
œ
œ
œ
œ
œ(less common)
n || 5 sus 6 - 5
repeated note
n
&
C: œ
?
& œIœ Vœœœ œœ œœIœ œ œœ Vœœ œœ Iœœœ œ œœVœœ œœ œ
œ œœ
œ
œ (less common)
œ
œ
step down
4
C: I
V
(b)
?
? œœ
?
(c)
I
œ&
œ
?
V &
step down
C: I
V
C: I
&
n V
œœ œ
œ
œœœ
œ
step down
œœ
œ
œI œœV
C: Iœstep down
V
œ
?
œœ œ
&
œœ
Figure 28.3.3
œ
C: I
V
Add a double neighbor
œ
? œœ
œ
&C: œœI œ V
œ
step down
œœ
œœ
step down
C: I
V
?
Figure 28.3.4
? œœ
œ
œ
(d) Add a chromatic passing
C: I tone
V
step down
& œœ
? œœ
C: I
Figure 28.3.5
(e) Add an anticipation
sus 4 - 3
I
step down
susV4 - 3
I
& œœ
?
œœ
&
V
I
332
V
& œ ?œ œ œœ
œ
œ
œœœ œ œ
œ common)
œ
?œ œœ œ œ œœ œœ œœœœ œ œ œ œœœ (less
œ
œ
œ6 - 5 œ
sus
step down
&C:œœ I C: œIV Vœ I susIœ4œV- 3 V Iœ IVœ œ V
œ œœ
œ
œ
œ œœ
?
œ œ
œ
Figure 28.3.2
œ
œ
(less
common)
step down
sus 6 - 5
sus 4 - 3
Add an escape tone by moving by step in the opposite direction of
C:
Vœ
Iœ
V
Iœ
Vœ
& Iœœ stepwise
œ
?
œ œ
the original
œœ œœœ movement,
œœœ œœœ then
œœ
œ leap
œœ
repeated note
C: I
V
&
I
œœ
œ
œ
V
sus 6 - 5
n || 5
V
esc
œœ œ œ œœVœ
œ
esc œ
œœ œ œ
œ I œœV
Iœ esc Vœ
œœ œ œ
œœ
œ
I
V
œœ
œ
œ
œœ œI œ œ œœV
I
œ œ œ œœ
œ œ
œœ
dn
œœI
dn
I
œ
œ
V
V
chro. p
œœ b œ œœ
œœ
œ
œ
I
V
step up
ret
& œ WITH
CHAPTER 28. VOICE LEADING
œœ œœ œTONES
œstep upœœ NON-CHORD
&
? œœœ œœœ
& œœœ œœœ
œ
œ
?
?C: œœVstep upœI
& œstep upœœ
&C:C: VœœI œœVœI
step up
Figure 28.3.6
? œœ œœœœ
& œœ œœ
Step up:
C: œV tone
œI I
(a) Add a chromatic?
passing
œstep upœ
step up
œ
C:
V
&& œœ œœI œ
œ œ
œ
?? œœstep up
& œœ œœœœœ
œœ
step down
&
?
3.
?C: œV œœI
œstep up
Figure 28.3.7
&C:& Vœ œœI
(b) Add an anticipation
œ
C: V
?? œœ
& œœ
I
œœ
œœ
Iœ
œ
V
333
ret
ant
œ œ
œ œœœ
œ
œI œ
œret
dn
œ
œ
œ
œ
œ IVœ œ œI Vœ œ
œ dn
œ œ
œœ œœ œ œ œ œœœœ
œ
V
œ V I œI
œ dn œ
chro. p
œ œ œ œ œœI
V
œ œœ # œ œ
œ œchro. p œœ
œ œœ # œ œœ
œœœœ.
œ
œœœœV
175
œV
œ chro. p
V
œœ # œ
175
œI
œ
I
œœI
œœ . œ œ
œœ
œœ
C: Vœ
Vœ
œœI
?
œ step up
œ ant
œI
œ . œ œI
& Vœ
C:
V
&
œ
œ œ
œ
Figure 28.3.8
œ
œ
œœ
?? œby leaping
(c) Add an appoggiatura
the note of reso& œ œ oneœ step beyond
step up
ant
lution, placing the appogiatura on the beat, displacing the note of
resolution to occurC:after
V theI beat V
I
?
& œœ
?œ
œ
step up
C: V
Figure 28.3.9
(d) Add a double neighbor
œ
œ
œœ
I
œ
œ
œ
œ
V
app
œ œ
œ
œœ
I
? œ
œ
œœ
œ
œ
œœ
CHAPTER 28. VOICE LEADING WITH NON-CHORD TONES
C: V
I
C: V
I
334
dn
step up
& œœ
?œ
œ
V
œ
œ
œ
œ
œ œ œ œ œœ
œ
œ
œ
œ
œ
I
V
I
Figure 28.3.10
(e) Add retardation &
by delaying resolution of the note (rarely used)
175
? step up
& œ
œœ
œ
6
4.
œœ
ret
œœ œ
œœ
œ œœ
? œ
œ
œ ant
& step down
C: Vœ
œV. œ I œ
œI
&
œ
œ dn œ
œ
Figure 28.3.11 ? step up
œ œ œ œœ œ œ œ
&?œœœœstep down
ant œ
œœ œ
Leap of 3rd:
œI œ œV toneœ œI . œ Vœœ
(a) Fill in the 3rd with
?&C:aœœpassing
œ
œ
œœ
œleap ofœ 3rd œ
œ
œœ p œ
& œœ
?
C: Vœ
Iœ
&
œ V œ œ œIœ
?
C: I
V
I
V
œ
œ
œ
œ
&? leap
p
of
3rd
œ
œ
œ
œ
œ
œ
œ
œœii
œ
œI
iiœ
?&C: œI
œleap of 3rd
œ appœ
œ
?
œœ oneœœstep beyond
œ œ œ the note of resoAdd an appoggiaturaœœby leaping
&
œ
lution, placing the appogiatura
on the
œ
œ beat,œ displacing the note of
Figure 28.3.12
(b)
I
resolution to occurC:after
theiibeat
œ
œ
&
? leap
œ of 3rd
œ
œ
œ
?
&
œI
C: œI
œ
? œœ
œ
&
?
&
?
&
?
&
Figure 28.3.13
C:
&
I
I
I
œ
œ
œI
œ
œ
œ
I
ii
œ
œ
œ œ
œI
app
œ
œ
I
?
5. Leaps of 4th or larger: do not embellish (for now)
Here is a basic framework with all possibilities labeled.
? # 43 œ œ œ œ
œ
œœ œœ
œ
œ
œ
˙
G: I/3rd
ii/3rd
I/5th
V7
I
G: I28.
/3rd VOICE LEADING
ii/3rd
I/5th NON-CHORD
V7
I
CHAPTER
WITH
TONES
#
&#
&
44
44
G
G
˙˙
˙˙
˙
? # 4 ˙˙
? # 44 ˙
4
307
307
D
D
˙˙
˙˙
˙
˙
˙
step down
step
step down
down
step down
repeated note
repeated note
leap of 4th
leap of 4th
Em
Em
˙˙
˙˙
˙˙
˙˙
step down
step down
step down
leap of 3rd
leap
stepofup3rd
step up
G: I
V
G:
I
V
Here is one possible solution:
G
D
esc.
G
D
#
&#
&
309
309
4
44
4
œ˙
œ˙
œ
? # 44 ˙œ
? # 44# c˙
&
œœ
G: I
G: I
œ
(œ )
œ
esc
( œ)
nt
( nt)
..
335
C
C
repeated note
repeated note
repeated note
step up
step up
leap of 3rd
leap of 3rd
vi
vi
Em
4-3 sus
Em
˙(œ ) œ
˙(œ4-3) sus œ
(esc.
)
Œ
˙˙
˙˙
˙
˙
˙
IV
IV
C
nt C
œ˙4-3 sus œ (œnt) ˙˙
(œ )
œ (œ ) ˙˙
˙
( )
4-3 sus
pt
œ
œ (œ )
œ˙
œ (œ )
˙
# œœ V œ
œœ
pt
n
œ
œ
œ
(
( ) œ
˙)
sus
œ (œ )ant ˙
œ
# œœ pt IV ˙
vi œ
app
˙œ
˙œ
(app
)
pt
˙
œ
œ
171
œ
œ
œœ
œ
? # c œœ
œ
œ
œ voices˙ on the same
Notice that, when non-chord
tones are
œ added œto different
sus
ant
V
p
dn
vi
IV
beat, consonant intervals (3rds, 5ths,
6ths, or 8ves) are made. If consonant
p
intervals can’t be made, the voices are staggered rhythmically (as occurs on
e: ____
____
____
____
____
____
____
beats 3 and 4 in measure one of the example above).
## c
&
28.4 Practice Exercises
1.
˙ the staff,
? # # cthe chordsœ with Roman numerals
œ
Analyze
in
below
œ the blanks
œ
œ
œ
then add the specified non-chord tones, specifying suspensions with the 171
˜
appropriate interval numbers.
esc
# c
&
œœ
& b c sus
? # c œœ
?b c
b: ____
e: ____
F: I
&
____
# œœ
œ
œ
____
vi
ant
____
œ
œœ
____
IV
____ n
p
p
œœ
œ
œ
____
V
____
œœ
œ
œ
____
vi
sus
dn
____
# œœ
œœ
____
IV
ant
____
˙
˙
˙
I ____
#
?#
2.
Analyze the figured bass below to write Roman numerals in the blanks below the staff. Then add the following non-chord tones: (1) 3 suspensions,
# passing tone, (3) one neighbor tone, and (4) one anticipation.
(2) one
&
?#
?# c œ
#
& c œœ
œœ
œ
œ
œ
œœ
œ
œ
# œœ
˙
˙
p
˙
ant
sus
CHAPTERe:28.
VOICE
LEADING
WITH
NON-CHORD
TONES
dn
____
____
____ p ____
____
____
____
œ
œ
œœ
œ
? # c œœ
œ
˙
œ
œ
œ
œ
## c
&
esc
œ
œ
#œ
œ
œœ
n
sus
ant
p
? ## c
œ
## c
&
e: ____
b: ____
3.
œ
____
œ
____
____
____
____
____
œ
˙
œ
____
œ
____
____
____
____
vi
IV
____
336
˜
Voice
the following Roman numeral progressionœ then add
˙ the follow? # #lead
œ (1) a œneighborœ tone during
œ beat one, (2)
c œ tones:
ing&non-chord
a neighbor
tone during beat two, (3) an appoggiatura on beat 3,
˜ (4) a suspension on
beat four,
(5) a suspension
on beat
5, (6) an
anticipation
during
b: ____
____
____
____
____
____
____ beat six,
? (7)
# # a suspension on beat 7.
and
&b c
? c
b
F: I
&b
vi
IV
V
I
Click here to download the homework assignment for this chapter.
?
b
leap of 3rd
& œœ
œ
? œ
œœ
œ
œ
Chapter
29
C: I
ii
p
œœ œ œœ
œ
œ
œ
œ
I
ii
app
leapLeading
of 3rd
Voice
Chromatic
Harœ œ
œ
œ
œ
monies
& œ
œ
œ
œ
œ
œ
œ
œ
?
29.1 Voice Leading Secondary Chords
œ
œ
œ
œ
When voice leading secondary chords, one largely follows voice leading rules
for seventh chords:
C: I
I
I
I
1. Resolve the 7th of a chord down by step.
7th
& # œœ
œœ
C: V7/V
V
? œœ
œ
2. Alternate complete voicings with incomplete voicings when voice leading successive root position seventh chords . Note that with secondary
chords, the 3rd of the chord, typically a raised note, will resolve down by
half step to the 7th of the chord, which is a diatonic note that cancels
out the chromaticism of the previous note.
337
CHAPTER 29. VOICE LEADING CHROMATIC HARMONIES
# œ 3rd
& c # œ 5th
? c œœ 7th
Root
nœ
œ
# œœ
C: V7/iii
V7/vi
7th
Root
3rd
Root
#œ
œ
nœ
œ
3rd
5th
7th
Root
V7/ii
338
nœ
œ
# œœ
7th
Root
3rd
Root
V7/V
complete incomplete complete incomplete
177
3. Follow the principle for resolving vii◦7 and viiø7 when dealing with secondary vii◦7 and viiø7 chords.
& œœ
œœ
7th
3rd
? # œœ
C: viio7/ii
œœ œ
& œ
177
œœ
7th
3rd
? # œœ
œœ
ii
(a) An important exception occurs when vii◦7 V or viiø7 V resolves
to V. If the melody requires the 7th of the chord to be voiced above
the 3rd of the chord, solve the example by writing parallel (unequal)
o7
C: vii
ii
fifths instead of the doubling of the leading
tone,/ii
which is considered
less acceptable.
bb
œ 7th n œœ
& b n œ 3rd
œ 7th
n œ 3rd
? b # œœ
bb
# œœ
c: viio7/V
&
?
doubled 3rd
(avoid on V)
n œœ
V
|| 5ths
œ
œ
unequal 5ths
(preferable)
viio7/V
n œœ
V
29.2 Voice Leading Borrowed Chords
Borrowed chords, or chords making use of mode mixture, are handled similarly
to their diatonic versions in terms of voice leading, e.g., iiø7 is handled similarly
to ii7 . In any of the borrowed chords with 26̂ , resolve this tendency tone down
by step whenever possible.
&b
CHAPTER
29. VOICE LEADING CHROMATIC HARMONIES
? b
b
182
339
26̂ down by
Principle____
29.2.1____
Voice Leading
Borrowed
Chords.
Resolve
____
____
I46
V
I
step when it is a chord member of a borrowed chord.
b
&b
&
? b
b
?
c
œœ
b œœ
œ
œ
œc
œ
œœ
b œœ
____
C: I
____
iv
œœ
Bb: ____
C: I
iiø7
œ
œ
____
V
œ
œ
œœ
œ
œ
œœ
œ
œ
œœ
V
viio7
I
œ
œ
œ
œ
Fr+6
C: I
____
I64
b œœ
œ
œ
Figure
b b 29.2.2 Resolving 26̂ down when voice leading borrowed chords
&
c
situation where you may encounter a borrowed chord is the V –2 VI
&Another
cadence, which should be handled exactly as the deceptive cadence in minor is
handled—resolve
the 3rd of the V chord up by step and move the other two
? b
b
voices
in
contrary
motion to the bass.
?c
There are no specific rules for other borrowed chords such as 2 III , 2 VII , i ,
____
____
____
I6
____
V
I
and v ; simply voice lead them as smoothly 4as possible while avoiding objectionable parallels.
œœ
œœ
œœ
œœ
b œœ
b œœ
b œœ
& œœ
29.3
& Voice Leading the Neapolitan Chord
œ
œ
œ
œ
œ
œ
œ
œ
6 œ
œ
?
œ
There œare twoœ rules for voice leading
the N chord in four
œ
œ parts:
œ
?
1. Double theø7bass (the third)
C: I
ii
V
C: I
I64
iv
C: I
viio7
œœ
œ
œ
I
2. Resolve 22̂ down to the nearest note in the next chord.
b
& b b œœ
? bb
œ
b œ
c: i
b œœ
œ
œ
N6
n œœ
œœ
V
c: i
œœ
œ
œ
b œœ
œ
œ
N6
œœ
n œœ
i6
V
œ
œ
œœ
œœ b œœ n œœ n œœ
œ œ œ œ
œ œ #œ œ
c: i
N6 viio7/V V
Figure 29.3.1 Resolving 22̂ down when voice leading N6
&c
29.4 Voice Leading Augmented Sixth Chords
? c be helpful to review the three types of augmented sixth chords before
It may
discussing how one voice leads them.
The salient accidental in all three augmented sixth chords is 44̂ , which
almost always resolves upward to 5̂ .
&
?
CHAPTER 29. VOICE LEADING CHROMATIC HARMONIES
& # œœ
œœ ## œœœœ
& #&
œœ
?
œœ œœœ
? ?
œ
a: It+6a:
ItV+6
# œœ
# œœœ
#œ
œ
œœ
œœ
œ
a: V
Fr+6
œ
œ
V
not used
# œœ # œœ
œ
# œ # œœ ##œœœœ
œœ || 5 œ
œ
œœ œœ œœœ
œ
+6
# œœ
œ
# œœ
œ
œœ
183
not used
# œœ
a: Fr
a:
340
Ger+6 V
V
# œœ
#œ
|| 5 œ
œ
|| 5 œ
œ
œ
+6
not used
a: Ger
V
+6V V
Figurea:29.4.1
It+6 44̂ toV5̂ in resolution
a: Frto
a: Ger+6 V
The 44̂ scale degree also resolves to 5̂ when an augmented sixth chord resolves to the Cadential 64 chord.
& # œœ
œœ
œœ œœœ
? &
#œ
? œœ
a: It+6
i46
a: It+6
# œœ
œœœœ
œ
œ
a: Fr+6
i46
œœ
# œœ
œ œœ
œ
œ
#œ
œœ
i64
œœ
œœœœ
# œœ
œœ
œ
œ
a: Ger+6 i64
& # œœ n # œœ
+6
6
a: Fr
? œœ
œœ
œ
œ
a: Ger+6 i64
i4
œ
œ
Figure 29.4.2 44̂ to 5̂ in resolution to Cadential
6
4
With the enharmonic German augmented
sixth
chord (abbreviated EnGer+6 ,
7
a: Fr+6 V
26̂
42̂
44̂
42̂
44̂
containing , 1̂ , , and ), and resolve upward to members of a major
I64 chord.
&
?
&
###
# # œœ
? # # # n œœ
œœ
œœ
A: EnGer+6 I64
Figure 29.4.3 42̂ to 42̂ resolving upward when in an EnGer+6
The exception to 44̂ to 5̂ occurs when an augmented sixth chord resolves to
7
V , in which case 44̂ resolves to 64̂ , which is the 7th of the V7 chord.
183
183
a: It+6
i46
a: Fr+6
i64
a: Ger+6 i64
CHAPTER 29. VOICE LEADING CHROMATIC HARMONIES
341
& # œœ n # œœ
? œœ
œœ
a: Fr+6
V7
Figure 29.4.4 44̂ to 64̂ in resolution to V7
If you voice lead an augmented sixth chord to something other than V , V7 ,
or i64 , move all of the voices smoothly while avoiding objectionable parallels
and employing proper doublings.
177
29.5 Practice Exercises
178
œ
œœ
& œ
Day One
3rd
1. Analyze the figured bass to provide Roman numerals in the blanks
below the staff, then voice lead the progression. Include
? # œœ the key
œœ signature.
&
C: viio7/ii
?
œ
œ
7th
œ & bœb b n œœ 3rd œ n œœ n œ
Ω
Ω
7
A¯: ____
2.
7th
7
____
doubled 3rd
7
(avoid on V)
7
? ____
# œœ
bbb
Ω
____
n œœ
____
____
7th
˙
n œœ 3rd
ii
|| 5ths
œ
œ
unequal 5ths
(preferable)
# œœ ____ n œœ
Voice lead the following Roman numeral progression. Include the key
b
c: viio7/V
V
viio7/V
V
signature.
tones:
n œœ non-chord
b œœ
& b b b œœ Add the
œœ following
œœ 1 suspension,
œœ
˙˙ 1 passing
tone, 1 anticipation, and 3 neighbor tones.
œ
&
? bb b
& b œ
?
I
?
nœ
œ
bœ
œ
V7/vi
____
A¯: ____
V7/ii
____
œ
œ
œ
comp.
viio7/ii
A: I
inc.
ii
nœ
œ
œœ
œ
œ
V7/V
V
____
____
free res.
4
Vcomp
I6
2
n œœ
˙˙
viio7/vi
____
vi
____
œ
V65 /V
˙
V
4
˜
˜
Day Two &
3
& G: ____
____ bass
____
____ Roman
____numerals
____ in____
3. Analyze
the figured
to provide
the blanks be?the staff, then voice lead the progressions in chorale style. Include
low
the key signatures. Include one suspension in each measure.
?
&
&
?
&
?
7
V42 /IV
D: I
œ œ
F: ___ ___
&
?
œ
œ
viio7/V
¯6
œ
˜
7
˜
nœ
V
viio7/vi
œ œ ˙
œ
a: ___ ___ ___ ___ G: ii7 viio7
4+
2
____
nœ
6
œ œ #œ œ
6
___
b¯: ____
œ
IV6
˙
¯
?
7
6
____
nœ
¯7
¯5
____
œ
nœ
œ
œ œ œ œ
˙
I
e: VI
7
Ω
____
____
Ω
____
vi
œ
n˙
N6 V7 VI
179
œ
&
œ
œ
bœ
nœ
œ
n˙
CHAPTER?29. VOICE LEADING CHROMATIC HARMONIES
184
342
Day Three
Rom. num.: ____
____
____
N6
viio7/V
____
____
&
4. Analyze
the figured bass to provide Roman numerals in the blanks
Harm.
func.:
ton.
dom.
ton.
____
____
dom.
ton.
prol. Include
below the staff. Voice lead the progressions in chorale style.
the key signatures.
?
&
?
&
?
œ
nœ
œ
4
6
Ω3
œ b œ ____
œ
œ
6
4+
3
____
6
4
3
œ
œ
n œ b œ____œ
E: ____
D: ___ ___ ___
nœ
6
6
5
3
œ
Ω7
6
4
œ b____
œ œ
____
6
4
œ
f: ___ ___ ___
œ
G: V43/V EnGer+6 I64
œ
nœ
œ
#œ
Ω5
____
œ
œ
œ
œ
____
b: i6
It+6 V
œ
Day Four
6
6
7
7
¯7
¯7
¯7
4
4
Ω
Ω
Ω
3
& lead the following
5. Voice
Roman numeral progression. Include the key
signature.
following
tones:
an escape
b¯: Add
____ the
____
____ non-chord
____
____
____
____ tone,
____ a 4-3
suspension, an anticipation, and a passing tone.
?
& œ bœ
?
A¯: vi
nœ
œ
bœ
Fr+6
V7
œ
¯VI
œ bœ
N6
œ
viio7/V
œ
œ
V
œ
vi
Click here &
to download the first homework assignment for this chapter.
Click here to download the second homework assignment for this chapter.
Click here
? to download the third homework assignment for this chapter.
Click here to download the fourth homework assignment for this chapter.
Click here to download4 the Unit
9 Practice
Test.6
6
o4
+6
6
7
f ˜: i
V2/V
bb
œ œœ
& b b œœ
œ
nœ
? bb b œ
bœ
b
A¯: vi
Fr+6
esc, 4-3 sus, p, ant
V
vii 3/iv
œœ œ œ
bœ
œ
V7
A b œœ œ
¯VI
IV
b ∫ œœ
Ger
n œœ
œ
œ
bœ
nœ
N6
viio7/V
N
V
œœ .
œ œ
œ
V
vi
œœ
œœ
186
b
&bb
? bb
&
b
###
E¯:
viio43/IV
I
IV6
EnGer+6
I64
viio7/vi
vi
c
Chapter 30
? ### c
œ
œ
œ
œ
nœ
œ
˙
Introduction to Counterpoint
Ω
A: ____
____
7
6
4
3
____
____
____
Ω5
3
____
____
#
& c
30.1 Species Counterpoint
The
ad Parnassum (1725), by Johann Joseph
?seminal
# c œ composition
# œ text,
n œ Gradus
# œ through n“species
œ
˙
œ
Fux, teaches contrapuntal composition
counterpoint.”
Species
counterpoint uses simple rhythmic values and teaches composers how to write
7
4+
6
6
˜
4
one, two, three, or four notes
usually
a whole note. In
Ω against a larger value,
3
this text, we will focus on writing for two voices. In a semester-long college
____ one
____
____
____ voices.
course e:in ____
counterpoint,
typically
learns to____
write for____
up to four
Counterpoint can be thought of as the simultaneous sounding of two or
more melodic lines. An example is shown below.
## #
˙
œ
œ
& # ## # c œ œ œ œ œ œ œ œ œ œ œ œ œ
Melody 3
œ œ
? # # # # # # c ‰ œJ œ œ œ œ
#
Melody 2
j
œœ œ œ œœ œ œ œ œ œ œ œ
œ œœ œœœœ œ
‰
œ œœœ œ œ œ œ œ
Melody 1
œœœ
J
œ
YT: YGHj2CmNz0E
Figure 30.1.1 Bach, J.S., Well-Tempered Clavier, Book I, Fugue 3 in C-sharp
major, BWV 848
Textures made of counterpoint are called “contrapuntal” and can be contrasted with melody-accompaniment textures, which are called “homophonic.”
30.2 First Species Counterpoint
In first species, we will write note-against-note counterpoint in whole notes.
You will be given a melody, called the cantus firmus (abbreviated “c.f.”),
against which you will write a counterpoint.
343
CHAPTER 30. INTRODUCTION TO COUNTERPOINT
4
&4
& 44 w
∑
∑
∑
∑
∑
w
w
w
344
∑
w
c.f. (cantus firmus, a pre-existing melody)
Figure
4 from
Intervallic30.2.1
distance
∑ cantus firmus
∑ to counterpoint:
∑
&4
w
∑
∑
∑
∑
∑
∑
8
Fux ____
enumerates
several rules to follow to write in proper sixteenth-century
style 4
(thewstyle of Palestrina). Since this is a brief introduction to writing in
∑
∑
∑
∑
∑
& 4 counterpoint,
species
the rules below are slightly modified and simplified. You
& 44 w
w
w
w rules in a semester-long coursew in counterpoint.
w
would likely follow stricter
4
&4
∑
∑
∑
1. 4
Begin with an octave or unison.
c.f. (cantus firmus, a pre-existing melody)
&4 w
w
w
Intervallic
distancewfrom cantus firmus to counterpoint:
4
&4
w
w
w
w
4
w
∑a pre-existing
∑ melody) ∑
Intervallic
from cantus
to counterpoint:
firmus,firmus
&distance
4 c.f. (cantus
8
c.f. ____
8
____
& 44 &w 44
∑
∑
∑
Intervallic distance from cantus firmus to counterpoint:
8
____
w
w ∑
w
& 44 c.f.
w
∑
∑
Intervallic distance from cantus firmus to counterpoint:
&2. 44End
w
w
w or unison.
w on an octave
3.
w
w
∑
6
____
w
w ∑
7ˆ
w
w
w
8
____
w
∑
w ∑
8ˆ
w
8
6
8
____
____
&c.f.44 ____
Approach
one of the
2ˆ w motion; 1ˆw
w octave wor unison wby contrary
ww the ending
4
parts
& 4willc.f.end with 7̂ –∑8̂ while the∑ other ends∑ with w2̂ –1̂ . w
& 44 &w 44 ____
8
8
____
ww
w
wwww 3 5 8 6 www 3 5 8 6
w
w
7ˆ
wwww 3 5 6 8 w6
____
w
Intervallic distance from
10 to counterpoint:
10 cantus firmus
ww
& 44 c.f.
∑
∑
all possible consonances
6
____
w
w2ˆ
∑
7ˆ
& 44 w ____
w____
w ____
w
8 ____
66
____
8 w
5
3
3
____
4
www 10 8 wwww 10 8 6 wwww 6 8 ____
&
c.f.4 w4 w
www 3 w5 6 w w3 5
ww 3 5 ww
& 4 &w4
4
c.f.
2ˆ
contrary “perfect”
motion consonance
88ˆ
____
w
ww
1ˆ
8
____
w
8ˆ
88
____
____
ww
1ˆ
4 w
(a)
the
is win G mixolydian,
Dw dorian,____
A aeolian,
use a
w
8 example
8w
____
____
& If44 &
wwC4, and G6w4worrespectively).
w
w
4
w
w
10
10
sharp
to
create
the
leading
tone
(F
,
w
8
4 w
w 8
w 8 ww 6
w
&4
c.f.c.f.
& 44 &w
#w
all possible consonances
www 3 5
6
ww 3 5
6
w 35
w
w
#w
w
all possible consonances
#w
w
w
w
w
Use a sharp to create the leading tone at the final cadence
w
c.f.
& w
c.f.
G mixolydian
w
c.f.
D dorian
w
w
c.f.
A aeolian
w
w
w
4. Create consonant harmonic intervals in each measure (unisons, 3rds, 5ths,
6ths, and their compound versions—10ths, 12ths, 13ths, etc.). Disso∑ 7ths) are not allowed in first species
∑
nances &
(2nds, 4ths,
counterpoint.
&
∑
∑
4
&4
w
w
w
w
7
8
w
w
CHAPTER 30.
c.f. INTRODUCTION TO COUNTERPOINT
2ˆ
ww 10
w 10
wwww 3 5 8 6 www 3 5 8 6
& 44 w
8
____
4
&
& 44 ww
8
____
5
____
ww
wwww 3 5 6 8 w
6
____
all possible
3 consonances
3
____
____
ww
8
____
w
6
____
ww
345
1ˆ
8
____
ww
ww
motion consonance
44
&
w(3rds and w6ths) can be
(a) “Imperfect”
consonances
w
w approached
w
w in any
c.f. contrary
“perfect”
manner
c.f.
i. Do not use more than three consecutive 3rds or 6ths
(b) “Perfect”
consonances
(unisons, 5ths, 8ves, 12ths) may only be apw
#w
w to avoid direct 5ths wand direct
#
w in order
proached
in
contrary
motion
&
#w
8ves (you may wish to review the Types of Motion).
Use a sharp to create the leading tone at the final cadence
5. Only
4ths, 5ths, ascending minor
w following
& the
w leaps are allowed: 3rds,
w
sixths, and 8ves (review thewRules of Melody
withw regard towdirection
c.f.after leaps).
c.f.
changes
c.f.
G mixolydian
D dorian
A aeolian
6. Avoid melodically outlining a tritone by changing directions at two turning points in a melody.
4
&4 w
& 44 w
c.f.
w
w
w
w
melody changes
direction on B
tritone
w
w
w
melody changes
direction on F
w
w
tritone
w
w
w
w
w
melody changes
direction on B
7. Avoid repeating notes in order to create a flowing melody
Following these rules may seem dry and uninspired, but these rules come from
observations of note-by-note details in Renaissance masterpieces by composers
∑and can make any ∑composer better and more ∑aware of what
&
like Palestrina
they are writing.
Go to First Species Practice Exercises.
∑
∑
&
30.3 Second Species Counterpoint
∑
In second species, one writes two half notes against a cantus firmus in whole
notes. (Second species can also include writing three half notes against a cantus
firmus of dotted whole notes in 32 .) The rules are generally the same as first
species except that one simple dissonance is allowed in second species: the
passing tone. Please see the details below.
1. Begin your counterpoint with a half note at the octave or unison on either
the first or third beat of the measure; if starting on the third beat, put
a half rest at the beginning of the measure.
melody changes
direction on B
melody changes
direction on B
& 44 w
w
w
w
w
w
w
CHAPTER 30. INTRODUCTION TO COUNTERPOINT
direction on F
c.f.
Intervallic distance from cantus firmus to counterpoint:
8
____
c.f.
& 44 w
& 44 Ó
∑
˙
w
w
w
∑
w
∑
w
346
w
∑
∑
2. End with a whole note on an octave or unison, using one of these concluding formulas:
(a) If the cantus firmus is in the lower part, approach the final octave
with intervals of a fifth and sixth (6̂ –7̂ against 2̂ in the cantus
firmus).
(b) If the cantus firmus is in the upper part, approach the final octave
or unison with the intervals of a fifth and third (5̂ –7̂ against 2̂ in
the cantus firmus).
(c) Phrygian mode has an exception: if the cantus firmus is in the upper
part, approach the final octave or unison with the intervals of a sixth
to a third (4̂ –27̂ against 22̂ in the cantus firmus).
Concluding formulas:
Int: 5
6
6ˆ
7ˆ
& ˙ #˙
&w
c.f.
8
w
w
cantus firmus
in lower voice
5
c.f.
3
1
˙ #˙
w
w
5ˆ
w
7ˆ
cantus firmus
in upper voice
6
c.f.
w
˙
3
1
˙
w
w
4ˆ
7ˆ
cantus firmus in upper
voice in phrygian mode
3. Of the two half notes you write in each measure, the first must always be a
consonance
& (unison, 3rd, 5th, 6th, 8ve, or∑ compound interval equivalent).
If the second is a dissonance, it can only be a passing tone (approached
and left by step). Otherwise, the second note must be a consonance. The
only allowable leaps are the same as in first species.
&
∑
4. When crossing barlines, apply the following:
(a) “Imperfect” consonances (3rds and 6ths) can be approached in any
manner.
(b) “Perfect” consonances (unisons, 5ths, 8ves, 12ths) may only be ap∑ to avoid direct 5ths and direct
&
proached
in contrary motion in order
8ves.
∑
(c) Do not repeat notes across barlines
5. Avoid &
8ves on consecutive downbeats and avoid 5ths on consecutive
downbeats unless there is the leap of 4th occurring after the 8ve or 5th
on the downbeat
&
∑
&
∑
4
&4 Ó ˙
consonance
˙ ˙
˙ ˙
˙
˙
pt
w
˙ #˙
consonance consonance
˙ ˙
contrary
contrary
Concluding
formulas:
CHAPTER
30. INTRODUCTION contrary
TO COUNTERPOINT
motion
Int: 5
motion
6
8
w
& ˙ #˙
6ˆ
7ˆ
&w
5
c.f.
w
8
˙
4
&4
P4↓
motion
3
6
c.f.
˙
8
1
˙w ˙
w
w
w
5
w
P4↓
w
3
w8
˙w ˙
5
4
& 4 w ˙ #˙
w
c.f.
1
347
4ˆ
7ˆ
7ˆ
cantus
firmus in upper
cantus firmus
cantus
firmus interval numbers
Notice that
dissonant
(2, 4, tt, 7) are circled to highlight that
voice
in
phrygian mode
in
upper
voice
in lower voice
c.f.
5ˆ
they must be handled in a special manner.
&
&
4 w
&4
c.f.
8
___
6 ∑___
7
___
5 ___
3
___
w
w
perfect
consonance
4
&4 Ó ˙
˙ ˙
3 ___
6
___
w
∑
˙ ˙
˙ ˙
pt
contrary
motion
8 ___
3
___
5 ___
3
___
w
w
1
___
˙ #˙
w
perfect
perfect
consonance consonance
˙ ˙
w
contrary
motion
contrary
motion
Go to Second Species Practice Exercises.
∑
& Third Species Counterpoint
30.4
In third species, one writes four quarter notes to each whole note in the cantus
firmus. Use the following rules.
&1.
∑
Begin on an octave or unison. Write four quarter notes to each whole
note in the cantus firmus except for the final measure.
2. End on a whole note on an octave or unison with the penultimate measure
using one of the following formulas:
&
&
∑
(a) If the cantus firmus is in the lower voice, the penultimate measure
of the upper voice can be:
i. 4̂ –5̂ –6̂ –7̂ , or
ii. 2̂ –1̂ –6̂ –7̂ (the cambiata—see 5.b. below)
∑
(b) If the cantus firmus is in the upper part, the penultimate measure
of the lower voice is 7̂ –5̂ –6̂ –7̂ .
Concluding formulas:
Int: 3 4 5 6
8
8 7 5 6
camb.
& œ œ œ #œ w
pt
4ˆ 5ˆ 6ˆ 7ˆ
&w
c.f.
8
3 5
c.f.
œ œ œ #œ w
2ˆ 1ˆ 6ˆ
w
w
7ˆ
c.f.
4 3
w
1
w
#œ œ œ œ w
pt
w
7ˆ 5ˆ 6ˆ 7ˆ
3. Each downbeat should be a consonance.
8
4 apply
3
5the8following:
6
5
4. When crossing barlines,
˙ ˙
(a)
˙ ˙ ˙ ˙ #˙ w
˙ ˙ ˙
& 44 Ó ˙ consonances
“Imperfect”
(3rds and 6ths) can be approached in any
& 44 w
manner.
c.f.
& b 42 „
sus.
sync.
w
w
∑
w
3
5
sync.
w
6
5
sync.
w
7
6
8
sus.
w
w
˙ ˙ ˙ ˙ ˙ ˙ ˙. œ œ œ ˙ w
3 34 56 5
3
8
5 tt
3 3 32 5432
8 ___
5 ___
3
___
6 ___
7
___
3 ___
6
___
8 ___
3
___
5 ___
3
___
w
w
w
4 w
w
w
& 4 30. INTRODUCTION TO COUNTERPOINT
CHAPTER
c.f.
perfect
consonance
perfect
perfect
consonance consonance
1
___
w
348
(b) “Perfect” consonances (unisons, 5ths, 8ves, 12ths) may
only
w be ap#
˙
˙
˙
˙
& 44 Ó proached
˙
in
contrary
motion
in
order
to
avoid
direct
5ths
and
direct
˙ ˙ ˙
˙
˙ ˙
8ves.
pt
contrary
contrary
(c) Do not
repeat notes across barlines
motion
motion
5. Allowable dissonances:
8
˙
4
&4
contrary
motion
˙
˙
5
8
w
5
8
˙
(a) Passing tones are allowable dissonances (but never on the first beat
of the measure).
P4↓ contour in third
P4↓ measure of the exam(b) The cambiata (see the melodic
ple below) is allowed but only with the second note of the measure
as the only dissonant interval.
4
&4 w
w
c.f.
w
6. Direct 5ths and direct 8ves are not allowed and occur when an 8ve or
5th on a downbeat is approached through similar motion.
8 5 13 5 6 78 5 4 3 4 34 5 6 8
œ
œ
œ
œ
œ
œ
œ
4
œ œœœ
œ œ
œ œ œ œ œ œ œ œ #œ w
œ
œ
œ
œ
&4
œœ
pt
8 76 5 3 2 15 8 7 56
4
&4 w
c.f.
pt
w
camb.
w
pt
w
w
w
pt pt
pt
w
w
Go to Third Species Practice Exercises.
30.5 Fourth Species Counterpoint
Fourth species deals with writing suspensions (and syncopations). Because this
is only a brief introduction to species counterpoint, you will only encounter the
cantus firmus in the lower voice in fourth species in this text. See the fourth
species rules below.
1. Start with a half rest, then write a half note an 8ve above the cantus
firmus. The half note on the 3rd beat of every measure but the penultimate one ties across the barline to a half note on the first beat of the
succeeding measure.
2. End on a whole note at the interval of an 8ve above the cantus firmus.
3. The penultimate measure should contain a 7-6 suspension.
4. The half note on the third beat of each measure is always a consonance.
5. If the half note after a tie is a dissonance (4th or 7th), it is a suspension
and must resolve down by step.
(a) Allowable suspensions in the upper part are 4-3 and 7-6; 9-8 and
2-1 are not allowed.
6. If the half note after the tie is a consonance (1, 3, 5, 6, 8), it is a syncopation and can be left in any manner (by step or leap in any direction).
&w
w
c.f.
Int: 3 4 5 6
8
8
c.f.
w
#œ œ œ œ w
w
7ˆ 5ˆ 6ˆ
7ˆ
Concluding formulas:
CHAPTER
30. INTRODUCTION TO COUNTERPOINT
& 4w
& c.f.
4 w
5
2ˆ 1ˆ
sync.
sus.
6ˆ sync.
7ˆ
w
wc.f.
ww
c.f.
8
œ œ œ # œ w5
˙ ˙ ˙ ˙
& 4œ œ œ ˙8# œ ˙4w ˙3
& 4 ptÓ
4ˆ 5ˆ 6ˆ 7ˆ
7 5 6
pt
8
6
w w
3 5 4 3
c.f.
5
7 6
349
1
w
w8
6
˙ ˙ ˙ #˙ w
sus.
#œ œ œ œ w
w ˆ ˆ wˆ ˆ w
7 5 6 7
pt
sync.
Notice that all suspensions and syncopations are labeled and all dissonant
intervals are circled.
8
4
3
5
8
6
5
6
5
7 6
8
Go to Fourth Species Practice Exercises.
44 Ó ˙
&
∑
&
˙ ∑˙
˙ ˙
sus.
˙ ˙
sync.
˙ ˙
˙ #˙
∑
sus.
sync.
30.6 Fifth Speciessync.
Counterpoint
w
4
w
&
w is a freew mixture
∑ counterpoint”)
∑
w∑ (alsowknow as w“florid
wof first
& 4species
Fifth
through c.f.
fourth species. One can observe all species in the opening of Orlande
de Lassus’ Expectatio Justorum.
& b 42 „
&
& b 42 w .
&
∑
˙
∑
w
3
5
˙ ˙ ˙ ˙ ˙ ˙ ˙. œ œ œ ˙ w
3 34 56 5
sync.
3
∑
˙ ˙ ˙ ˙ ˙. œ œ œ ˙ w
sync.
∑Species type: 2nd
p
∑
4th 4th 2nd 1st 2nd
8
5 tt
Ó
p
˙
4th
3 3 32 5432
∑
p
p
p
œ
œ œ∑ œ œ œ œ œ
1st 2nd 3rd
& 30.6.1 Orlande∑ de Lassus, Expectatio Justorum ∑
Figure
YT: wjqd3Mv_wgs
30.7
& Invention∑ Expositions
∑
J.S. Bach’s Two-Part Inventions were not only intended as instructional keyboard pieces but also as examples of how to compose. In this section we will
wed our species counterpoint knowledge with our knowledge of harmony in
order to write a four-measure invention exposition using Bach’s C major and
E minor inventions as models. Note the I–I–V–V–I harmonic progression.
CHAPTER 30. INTRODUCTION TO COUNTERPOINT
m
œœœœœœœœ œ œ œ œ
Theme P5 higher
5ˆ
Theme
&c ≈ œœœœœ œ œ œ œ
œ
œ
m
?c Ó
&c ≈
C:
350
œ
Theme 8ve lower than m. 3
œœ œ œ
≈5ˆ œ œ œ œ œ œ œ œ ThemeŒ P5 higher≈ œ œ m œ œ
œ
œ œ œ œœœœœœœœ œ œ œ œ œ
œ
œI œ œ œ œ œ œ I
m
V
V
I
Theme 8ve lower
5ˆ
187
187
Theme
Theme 8ve lower than m. 3
Theme
5ˆ
œTheme P5Œhigher œ ≈œ œœ œmœ. œ œ œ œ œœ
? c# Ó
œ
œ
œ
M
≈
œ
œ
m
œ
œ
œ
œ
M œ.
œœ
#œ œ œ œ œ
& c ‰ œ œ œ œ œ œ œ . œ YT: E8EvUmq0Zao# œ œ
Theme 8ve lower
5ˆ
FigureC:30.7.1
Bach, Invention
No. 1 in V
C Major, BWV V772
I
I
Theme 8ve lower than m.I 3
œ œ œ œ œ œ Theme P5 higher œ œ # œ # œ œ œ œ
? # c œ Theme
ˆ
œ
5‰
Œ
M
mœ œœ œ œŒ # œ œ œ‰ œ œ mœ .
#
œ
M
œ
œœ œ
œ
.
#
œ
& c ‰ œ œ œ œ œ œ œ. œ
Theme 8ve lower 5ˆ
e: i
i
V
V
i
Theme P5 higher
Theme
8ve lower 5ˆ
5ˆ
œ œ # œ #mœ œ œ œ
# M Theme
œ
œ
œ
œ œ œ œ
œ
œ
?
# œ
œ œ
&
& c c≈ œœ œ Œœ œ œ ‰ œ œ œ œ œœ œ Œœ œ œ œ œ ‰œ œ
œ
œ
m
Theme 8ve lower than m. 3
i Theme 8ve lower
V 5ˆ
V
i
? # e: i
œ
œ
œ
œ
?c Ó
≈ œ œ œ œ œ œ œ œ ThemeŒP5 higher ≈ œ œ œ endœon a 10th
Theme
œ
œ
bb b 2
œ œ
œ
œ
œ
œ
œ
œ
YT:
QHDx0uYaKkY
œ
œ
& C:4 I œ œ œ œ œ œ I
V
V
I
# 30.7.2 Bach, Invention No. 7 in E Minor, BWVTheme
Figure
778
8ve lower than m. 3
&
Theme 8ve lower Theme P5 higher
Theme
œœœ œ
5ˆ
œ
œ
œ
œ
œ
œ
œ
m
œ
M
œ
? b#b 42
œ
m
œ
œ.
Mœ . œ œ œ .œ œ # œ œ œ œ # œ œ œ
œœ œ
b
c
‰
œ
œ
30.7.1
How
to
Write
an
Invention
Exposition
&#
œœœœ
?
Theme 8ve lower than m. 3
Theme altered to end on tonic
In the majority
of examples,
an invention
in than
them.
Theme
8ve lower
3
E¯: I
I you will be given
V
V theme
I first
measure, which you will Theme
write 8ve
anlower
octave
part
in
the
second
5ˆ lower in the bass
œ
œ
œ
#
œ
œ
#œ œ
œ œ œ œ œthanœ the first
measure,
fifthœ higher
measure in the third measure,
? # c then
œ a perfect
Œ
‰
Œ
‰
œ
the fourth measure
will betothe
5̂ third measure transposed down one octave, and,
œleadsendnaturally
œ bass part andœ3̂ in
finally,b you
will
on
the
interval of a 10th—tonicœ in
œ the
2
œ
b
œ
œ
œ
œ
b
œ
œ
&upper
e:4part.
i œ œ Please
V
i
the
œ œ œ œ seei the exampleVbelow.
end on a 10th
Theme
Theme P5 higher œ œ
œ œ œ œ œ œœ
? b bb 42
œœœ œ
œ
œ
œ
œ
œ
œ œœœœœœ
& b bb 42 œ œ œ œ œ œ œ œ
does not emphasize V chord
Theme 8ve lower than m. 3
Theme 8ve lower
œ
œ œœœœœœ œ
œ
œ
? b b 42
œ
œ
œ
œ
œ
b
Theme altered to end on tonic
E¯: I
Figureb 30.7.3
&bb
? bb
b
I
V
V
I
187
e: i
i
V
V
i
œ351
end on a 10th
CHAPTER 30. INTRODUCTION TO COUNTERPOINTœ
b 2
& b b 4 œ œœœœœœ œ
œ œœœœœœ
b 2
& b b 4 œ œœœœœœ œ
œ œœœœœœ œ
Theme
Theme P5 higher
30.7.2 Altering Themes to Fit the Harmonies
Theme 8ve lower than m. 3
œ œ
œ œI œtoœ Vœ œneeds its
1. You
find that a theme thatœ œleads
œ œ naturally from
? may
2
b
œ
œ
œ
œ
b b altered
4
contour
when progressing from V to I in measures 4 to 5 in order
to emphasize the V chord and the dominant-to-tonic
harmonic
motion.
Theme altered
to end on
tonic
Modify E¯:
the Icontour to emphasize
the VV chord at the Vend of the measure,
I
I
altering as few notes as possible.
Theme 8ve lower
leads naturally to 5̂
? b b 42
b
188
188
2.
œ œœœœœœ œ
œ œœœœœœ œ
does not emphasize V chord
œ
œ œœœœœœ œ
b
& b b 42 œ œ œ œ œ œ œ œ
188
œ
œœœ œ
œ
œ
œ
œ
œ
œ
œ
? b bb 422
œ
œ
œ œœœ
œ œœœœœœ œ
& b bb 4 œ œ œ œ œ œ œ œ
œ
note changed to emphasize V chord
b
œ œœœœœœ œ
œ
& b b 42 œ œ œ œ œ œ œ œ
œ
œ
œ œ the
œ œ downbeat
? b b 42 you may beœ given
œ œ œ œ that land onœ3̂ on
Additionally,
themes
œ
œ
œ
b
œ œ œand
of theb bsecond
5̂ that occurred
in theœ Bach
œ
œ œ œCœmajor
b 2 measure, notœ the
œ
&
œ
?
œ
b
œ
œ
emphasize
V chord
E minor
altertothe
theme
at the
b b 4invention expositions.œ You will neednotetochanged
end of measure 2 to emphasize the I chord as well as make the first bass
note
? ofb the third measure 3ˆthe 5̂ scale degree.note changed to emphasize V chord
b
& bb b 43 œ œ œ œ œ œ œ
œ
b œ
& b 43 œ œ œ œ œ œ œ
œ
? b 3 œ
b 4
? b 3
b 4
b
&b
b
&b
? b
b
? bb
œ œœœœœœœœ œ
does not
V
œ3ˆ œ œ œ œ œ œ œ œ œ œemphasize
œœ
œ
œnot
œ
œ
œ
œ
œœ œ
does
œ
œ
œ œ œœœœ œ
œemphasize
œ œTheme
œ œ œVœaltered
3ˆ
œ œ
œ œ œdoes
œ
œ
œ not
œ œ œ œdoes not
œ
to end on tonic
œ3ˆ
B¯: I
I
B¯: I
I
43 œ œ œ œ œ œ œ
œ
œ
43 œ œ œ œ œ œ œ
œ
3 œ
4
43
B¯: I
emphasize I
emphasize V
does not
emphasize I
Vdoes not
emphasize V
V
Theme alteredI
to end on tonic
V
V
I
œ œœœœœœœœ œ
œ œœœœœœœœ œ œ œœœœ œ œ
œœ
œœ
œ
œ
œ œœœœœœœ
œ œœœœœœœ œ
notes changed toœ
œ œ œ œ œ œ œ œ œ œ emphasize harmonies
œ
I
V
notes changed toV
emphasize harmonies
I
3. Finally,
b b when a theme in minor containing the 2̂ and 3̂ scale degrees in the
&
first two measures is transposed up a fifth in the succeeding two measures,
b
scale
& bdegrees 2̂ and 23̂ will be transposed to ↑6̂ and ↑7̂ . The reasoning
is ?
that ↑7̂ is the 3rd of the V chord, and ↑6̂ is a step below, typically a
b b tone. Another way to think of this is to use the melodic minor
passing
scale
? in
b the 3rd and 4th measures.
B¯: I
b
I
V
V
I
CHAPTER 30. INTRODUCTION TO COUNTERPOINT
352
189
2
& b 4 œ œœœ œœ œ
#œ
3ˆ 2ˆ
œ
œ #œ nœ œ #œ œ œ
↑7 ↑6ˆ
↑7ˆ
œ #œ nœ œ #œ œ œ œ
œ œ œ œ #œ œ œ œ
? b 42
2
↑7ˆ
↑7ˆ ↑6ˆ
3ˆ
d: i
3ˆ 2ˆ
ˆ
3ˆ
i
V
#œ
ˆ
↑7
↑7ˆ
œ œ
V
i
2 œ
œ n œ œTheme
œ
œ # the
30.7.3
to
& b 4 Adding
# œ œ œ Statements
œb œ œ Counterpoint
œœ
&œ
33ˆˆ 22ˆˆ
œ #œ œ
ˆ ˆˆ
↑7
↑6
↑7ˆ ↑6
33ˆˆ
ˆ invenAfter copying and transposing the theme throughout this four-measure
↑7ˆˆ ↑6ˆˆ
↑7
↑7
↑6
↑7ˆ œ
ˆˆ 2ˆˆ
ˆˆ
3
3
n
œ
#
œ
œ
2
3
3
œ
œ
œ
œ
tion
you will needœ to
to accompany the# œstatements
?exposition,
œ
œ œadd
œ third,
œcounterpoint
42? b in the second,
# œ and
of theb theme
fourth measures. Unlike species counterpoint, your counterpoint in these invention expositions must emphasize the
V
V
ii
harmonyd:
d: inii each measure.ii
V
V
b
2&
not emphasizing
emphasizing D-F-A
D-F-A
not
& b 42 œ œ œ œ œ œ œ œ œ œ .
#œ
?b
? b 42
∑
œ œ œ œ #œ œ œ œ œ Œ
ii
V
V
2
& b 4 œ œ œ #œ œ œ
œ œ
d: i
?
b
d: i
6
VI
VI6??
V
V
strong beats
beats emphasize
emphasize the
the harmony
harmony
strong
œ.
œ œ #œ nœ œ œ œ œ
#œ
œ œ œ œ #œ œ œ œ œ Œ
Intervals: 55 33 44 33 44 33 66
Intervals:
∑
33
ii
88
V
V
33
œ œ
66 7 6 3 3
œ #œ nœ œ #œ œ œ œ
55 88 tt
tt
?b
42& b
œ œ œ.
œ œ #œ nœ œ #œ œ œ œ
Intervals:
Intervals: 55 88 55 66 66 77 55 33 88
d: iib
d:
&
?b
not emphasizing
emphasizing A-C
A-C˜˜-E
-E
not
66 7 6 3
6
III
III6??
#œ.
3
ii
œ œ
55 33 44 33 44 33 33 33
œ #œ nœ œ #œ œ œ œ
V
V
ii
You may find the need to create “microharmonies” within a measure with
some
& bthemes, such as a I–IV–I or I– vii◦6 –I progression even though the overriding harmony of the bar is the I chord. Examples are found in the first two
measures of the C major invention.
?b
189
189
d: i
i
V
V
i
CHAPTER 30. INTRODUCTION TO COUNTERPOINT
&c ≈œœœœœœœ œ œ œ œ
m
?c Ó
C: I
m
œœœœœœœœ œ œ œ œ
œ
(IV6) V
I
≈œœœœœœœ œ œ Œ
I
(viio6) I
353
V
≈œœ
V
œœœœœ œ
“microharmonies”
YT: E8EvUmq0Zao
Figure 30.7.4 Microharmonies in the C Major Invention by J.S. Bach
Given these pieces of information, you are prepared to begin writing tonal
counterpoint in two parts.
Go to the Invention Exposition Practice Exercises.
30.8 Fugue Analysis
We will now turn to analysis of fugue. Let us set out definitions first.
• A fugue is a contrapuntal composition whose form features sections
called expositions and episodes
• A fugue exposition is a section that contains at least one full statement
of the subject of the fugue.1
• The fugue subject is the primary melodic idea and is stated by each
voice in turn in the first exposition.
• The answer, called “response” in some texts, refers to the statement
of subject in the key of the dominant by the second voice to enter in a
fugue. Sometimes this statement of the answer has intervals altered in
order to start in the tonic before modulating to the dominant. When
the intervals are altered in this manner, we call this a “tonal answer.”
In contrast, a “real answer” contains no alteration of intervals. In the
example below, notice that the third note of the subject in measure 1
descends a perfect fourth to the fourth note. In the answer in measure
3, the third note descends a perfect fifth to the fourth note.
• An episode is a section that does not contain a full statement of the
fugue subject, but instead develops the subject or other prominent ideas
through fragmentation and sequencing.
Here is the first exposition of Fugue 2 in C minor in Book I of the J.S. Bach’s
Well-Tempered Clavier. In the first exposition of a fugue, all of the voices state
1 Some authors reserve the term “exposition” solely for the first exposition and use the
term “middle entry” for later statements of the full subject. Grove Music Online includes the
following in their definition of “Exposition”: “...In German the word Durchführung is used to
refer to all groups of thematic entries in the body of the fugue, after the opening Exposition.
Because there is no equivalent word so used in English, English speakers sometimes, but by
no means universally, apply the word ‘exposition’ to these later thematic groups as well.”
CHAPTER 30. INTRODUCTION TO COUNTERPOINT
354
193
the subject at least once. It is important to note that a answer is considered 193
equivalent to a subject because the intervallic alterations are so minute.
EXPOSITION
SUBJECT
EXPOSITION
EXPOSITION
SUBJECT
b
SUBJECT
& bb b c œ n œ œ œ∑∑ œ
‰
& b b c œ nœ œ œ œ
‰
? b c
∑
? bb b c
∑
bb
b
& bb b
&bb
4
4
4
? b
? bbb b
b
œ œ
b œœ n œ ## œœ œœ
b œœ n œ œ
RESPONSE
œ œ œ œ œ œ nœ œ œ ∑ œ œ œ
œ œ œ œ œ œ n œ œ œ ∑œ œ œ œ œ
œ
œ
∑
∑
‰ œ
‰œ œ n œœ
œ
œ nœ
nœ
n œœ
œ
COUNTERSUBJECT 1
∑
∑
BRIDGE (can only occur within first exposition)
HEAD EXT.
SUBJECT
HEADfirst
BRIDGE
(can
occur
exposition)
SUBJECT HEAD
BRIDGE
(can only
only
occur within
within
first SUBJECT
exposition)
∑
∑
BRIDGE MOTIVE BRIDGE MOTIVE BRIDGE MOT. EXT.
∑
∑
∑
∑
BRIDGE
BRIDGE MOTIVE
MOTIVE BRIDGE
BRIDGE MOTIVE
MOTIVE BRIDGE
BRIDGE MOT.
MOT. EXT.
EXT.
œœ œœ œœ œ œ œ œ
œœ œ œ œ
œ œ
œœ œ œ œŒ œ œ œ œ‰ œœ œœ œœ œ‰ œœ œœ œ nn œœœ œœ œ œœ œœœ
œ œ œ œ œœœ
œœœœ
œ
Œ
‰
‰
COUNTERSUBJECT 2
œ œ œ œ œ n œ œ22 œ œ œ œ œ œ
COUNTERSUBJECT
? b b ‰ œœ n œ œœ œ œ œœCOUNTERSUBJECT
œ œ œ œ nœ œ œ œ œ œ œ œ
n
œ
œ
œ œ
? bb b ‰
b SUBJECT
b
& bb b
&bb
œœ œ œœ
œœ œ œœ
SUBJECT
SUBJECT
SUBJECT
HEAD EXT.
EXT.
SUBJECT HEAD
HEAD
SUBJECT HEAD
HEAD SUBJECT
œ œœ œ
œ œ HEAD
œœ # œœ œ œ œ œ œœ œ œ œ œ œœ œ œœ œ œœ n œ œ œœ n œ œœ œ œœ n œœ œ b œœ œ œœ œ œ œ œ
œ œ
œ
œ
œ # œœ œ œœ œ œœ œ œœ œ œ œ≈ œ œœ œ œœ œ œ œ œ œn œœœ œ œœ n œ œ œ œœn œœ œ b œœ œ œœ œœ œ œ œ
œ
œ
≈œ œœ
COUNTERSUBJECT
COUNTERSUBJECT 1
1
7
7
œ
œœ
œ
COUNTERSUBJECT
COUNTERSUBJECT 1
1
COUNTERSUBJECT 1
7
#œ œ
n # œœ œ œ œœ œ
n œ œ œ œœ œ
RESPONSE
RESPONSE
œœ
œœ
œ #œ
œ #œ
œ
œ œ nn œœ n œ
nœ
œ
SUBJECT
SUBJECT
b
& bbb b
YT: itvGdURMfbM
b
&
Figure 30.8.1 First Exposition of Fugue 2 in C minor from WellTempered
Clavier, Book I (BWV 847)
? b
? bb b
b bridge, if it occurs, is a brief modulatory passage that only hap• bThe
pens within the first exposition, usually to connect the answer to the
subsequent subject statement.
• bAb b countersubject is counterpoint that consistently accompanies each
&
bb
of the subject. “Countersubject 1” is in the alto voice in
& boccurrence
measure 3 and in the soprano voice in measure 7. The alternative to using
? bab countersubject would be for a composer to write different accompanying
(labeled as “CTRPT” in the examples) each time a subject
? bcounterpoint
bb
isb stated.
Within the bridge (bar 5 in the example above), we see motivic fragmentation
of the subject (“subject head”). Subjects, answers, and countersubjects can
be fragmented into head motives and tail motives in episodes in fugues. In
this fugue, we will see the subject, countersubject 1, and countersubject 2
fragmented.
Below is the first episode, which contains motivic fragmentation of the
subject and countersubject 1.
œ
œ
œ œ nœ œ œ œ œ
? b ‰ œ nœ œ œ œ œ œ œ
bb
œ œ œ œ nœ nœ
COUNTERSUBJECT 2
CHAPTERSUBJECT
30. INTRODUCTION TO COUNTERPOINT
355
EPISODE
SUBJECT HEAD
œ #œ œ
‰
b
& b b œœ
œœ
n œœ
J
j
nœ
œ
CTRPT
‰
œ œ œ
SUBJECT HEAD
j
œ
œ
œ œ n œ œ œ œœ œ ‰œ œj
œ
nœ
œ œ
‰ J
CTRPT
œ
œœ œœœ
œ
? bb œ n œ n œ œ œ œ œ œ œ œ œ œ b œ
œœœœœœœœœ
b
bœ œ œ
œ œ
CTRPT
CTRPT
SUBJECT HEAD
CTRSUB. 1 HEAD
CTRSUB. 1 HEAD
SUBJECT HEAD
CTRSUB. 1 HEAD
CTRSUB. 1 HEAD
YT: itvGdURMfbM
Figure 30.8.2 First Episode of Fugue 2 in C minor from WellTempered
Clavier, Book I (BWV 847)
Below are the second exposition, the second episode, the third exposition,
and the third episode.
194
194
194
b
& bbbb bb
b
&
& b
11
11
11
? bb
? bbb b
?
b bb
EXPOSITION
EXPOSITION
SUBJECT
EXPOSITION
œ œœœ
œœœ œ
œ œœœ œ
œœœ œœ œœ œœ‰ œœœœJ œœœ œœœ œœ œœœ œœ œœœ œœ œœ œœ œœ
œ œ œ œœ
œ
‰‰ œJJ
CTRPT COUNTERSUBJECT 2
COUNTERSUBJECT 2
CTRPT COUNTERSUBJECT
CTRPT
œ œ œ ‰œ‰ œ œœ 2 œœ
œœœœ
œ
œ œ b œ œ œ œ œœ œœ ‰œœ œœœœ œœœ œœœ
œ œ œ œœ œœ bb œœ œœ œœ œœœ
œœ
SUBJECT
SUBJECT
COUNTERSUBJECT 1
COUNTERSUBJECT 11
COUNTERSUBJECT
C. S. 1 HEAD
EPISODE
EPISODE
EPISODE
C. SUB. 1 HEAD C. S. 1 HEAD
œœœ
œœ œœ œœ
‰
‰‰œ
œœ
œ œ œœ
œœœ œœ œœœ
C. S.
S. 11 HEAD
HEAD INV
INV
C.
C. S. 1 HEAD
C. S.
S. 22 HEAD
HEAD
C.
C. S.
S. 22 HEAD
HEAD
C.
C. S. 2 HEAD
C. S.
S. 22 HEAD
HEAD
C.
C. S.
S. 2 HEAD
HEAD
C.
C.
S. 22 HEAD
bœ
? b b œœ bb œœœœ
?
œ
b
b
? bbb b œœ
b
œœ
œœœ
œœ
œœœ
œœ
œœœ
œœ
œœœ
œœ
œœœ
n œœœ
nn œœ
EPISODE
EPISODE
EPISODE
j ‰
j ‰ ‰
œ œœjj ‰‰ # œ ‰‰œ n œnn œœ œœ œœjj n ‰‰œ œ
œœ œ≈ œ nn œœ ## œœ œœ nn œœn œœ œ œœ nn œœ nn œœ œœ
nœ
≈≈ œœ n œ
SUB HEAD
SUB HEAD
HEAD
SUB
SUB HEAD
SUB HEAD
HEAD
SUB
C. S.
S. 22 HEAD
HEAD
C.
œœ
œœœ
œœ
œœœ
œœ
œœœ
œœ
œœœ
C. S. 2 HEAD
C. S.
S. 22 HEAD
HEAD
C.
COUNTERSUBJECT 11
COUNTERSUBJECT
œ œ n œœ
œœœ œ
œœ œœ œœœ nn œœ
œ n œœ # œ œœ
œ n œœ œœ
œœ n œœ ## œœ œ
œœ RESPONSE
RESPONSE
‰ Œ
‰ œ œ
‰ œ
œœœJ RESPONSE
‰‰ œœ œœ nnn œœœ ‰‰ œœ
JJ ‰‰ ŒŒ
C. S.
S. 22 HEAD
HEAD
C.
œœ
œœœ
œœ
œœœ
œœ
œœœ
C. S. 2 HEAD
C. S.
S. 22 HEAD
HEAD
C.
œœ
œœœ
œ œ œœ n œ œœ
œœœ œœ œœœ nn œœ œœœ œœœ
œ œ œ œœœ œ
œœ œœ œœ œœ œœ œœ œœ
COUNTERSUBJECT 2
COUNTERSUBJECT 22
COUNTERSUBJECT
CTRPT
‰ # œ n œ œjjjCTRPT
‰ ‰
‰
œ
œ
œ
‰
n œ œ## œ nn œœ œ # œ ‰‰œ œ ‰œ‰œ b œœ n œœ œœjjj
nn œœ œ œ œ ## œœ œœ œœ œ bb œœœ nn œœœ œœœ
CTRPT
b
& bbbb bb œ œœœ‰
& b b œœ ‰
&
œJœJ ‰
J
BRIDGE MOTIVE BRIDGE MOTIVE
BRIDGE MOTIVE
MOTIVE
BRIDGE MOTIVE
MOTIVE BRIDGE
BRIDGE
œ œ
? b b œœœ nn œœ œœœ œ œ œœœ œœœ œœœ n œ œ œœ œœœ œœ # œ œœ
n
œ
?
œ
b
? bbbb b œ
## œœ œ
nn œœ œ
œœ œœ
b œœ
17
17
17
œœ
œœœ
œ
œœœ
œ
EXPOSITION
EXPOSITION 1
EXPOSITION
COUNTERSUBJECT
INV
œ C. S. 1 HEAD INV
nœ œ nœ
b b œœ C. S.œ1œHEAD
n œ œœ b œ œ œ œœ œœ nnn œœœ nn œœ œœ nn œœ nnn œœœ œœ nn œœ œ œ œ
œ
œ
b
& bbb b œ œ œ œ œœ œœ nn œœ œ bb œœ œœ œœ œ œ
œ # œ œ n œ œœ œ œ
& b b œœ œœ œ œ
&
œœ ## œœ œœ œœ œ œœœ
œ
C. S. 2 HEAD C. S. 2 HEAD
14
14
14
C. S.
S. 11 HEAD
HEAD INV
INV C.
C. S.
S. 11 HEAD
HEAD
nINV
œ
C.
œ œ INV
œ œ œ œ œ œ œ œ œœ œœ œœœ œœ œœ œœ œœœ œœ œœ nn œœ
œœ œœ œœ œœ œœ œœ œœ œœ œ œ œ œ œ
C. S. 2 HEAD C. S. 2 HEAD
SUB HEAD
SUB HEAD
HEAD
SUB
‰
‰‰
œ
œœ
SUB HEAD
SUB HEAD
HEAD
SUB
‰
j ‰
‰‰ n œœ œœ œœjj ‰‰
œ nn œœœ œœœ œœœ n œ
œœ
nn œœ
‰
j ‰
‰‰ n œœ œœ œœjj ‰‰
œ nn œœœ œœ œœœ n œ
œœ œ nn œœ
SUB HEAD SUB HEAD
SUB HEAD
HEAD SUB
SUB HEAD
HEAD
SUB
≈ nœ œœœ
≈≈ œœœ nnn œœœ nn œœ œœ œœ œœ
œ œœœœ
œœ nnn œœœ œœœ œœ œœ œœ œœ
œ œ
œœ nnn œœœ œœœ œœ
BRIDGE MOTIVE BRIDGE MOTIVE
BRIDGE MOTIVE
MOTIVE BRIDGE
BRIDGE MOTIVE
MOTIVE
BRIDGE
b ‰
EXPOSITION
EPISODE
& b b EXPOSITION
œ œœ n œœ
EPISODE
œ SUBJECT
SUBJECT HEAD
HEAD
SUBJECT
SUBJECT
20
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w TO COUNTERPOINTœ
w
c.f.
w
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7ˆ 5ˆ 6ˆ
357
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Figure 30.8.4
˙ from
˙ WellTempered
44 Ó J.S.
˙ Bach,
˙ ˙Fugue˙ 2 ˙in C ˙minor
˙ ˙ # ˙ Clavier,
w
Book I&
(BWV
847)
8
4
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5
8
6
5
3
6
sync.
5
7
6
8
sus.
sync.
sync.you will be asked to analyze a fugue with
In homework and sus.
on the test,
regard to 4expositions w
(including the bridge,
episodes, subjects,
w if it occurs),
&4 w
w
w fragmentation.
w
w
answers, countersubjects,
and motivic
c.f.
30.9 Practice Exercises
Species Counterpoint:
Day
w
b 4 „
∑ One
3
& 2
˙ ˙ ˙ ˙ ˙ ˙ ˙. œ œ œ ˙ w
5
3 34 56 5
3
8
sync.
First and Second
Species Exercises p
4
1.
& b 2 w.
˙ ˙ ˙ ˙ ˙. œ œ œ ˙ w
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5 tt
Ó
3 3 32 5432
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For each exercise below, write first species (note-against-note) counterSpecies type: 2nd 4th 4th 2nd 1st 2nd
4th 1st 2nd 3rd
point. Write the intervallic distance from the cantus firmus (“c.f.”) to the
counterpoint in the blanks above the staff. Remember to begin and end
with an octave or unison, to proceed to the last unison by step in both
voices, and use only consonances (1, 3, 5, 6, 8, 10).
Interval: ____
4
&4
& 44
w
c.f.
Interval:
____
Interval:
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c.f.
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444 www
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___
c.f.
___
___
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___ ___
___ ___
___
___
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___ ___
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c.f.
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___
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4
Int:
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CHAPTER
30.
358
Int:
___ INTRODUCTION
___ ___
___ ___
___ ___
___ TO
___ COUNTERPOINT
___ ___
___ ___
___ ___
___ ___
___ ___
___ ___
___ ___
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2.
44
&
44 exercises below, write second species counterpoint—two half notes
For
&the
in each measure
except
the3last.3 Each
downbeat
must
be a3 consonance.
8
5 ___
6 ___
6 ___
5 ___
8 ___
6 ___
3 ___
6 ___
3 ___
1
Int:
___
___
___ ___
___
The only
dissonance
allowed
is
the
passing
tone.
Write
the intervallic
44 c.f.
w
w
&
4 wfromwthe wwcantus
distance
w firmus
ww ww(“c.f.”)
ww towww thewwwcounterpoint
ww ww wwin thew blanks
&
& 44c.f.the
w
w
w
w
w
w
above
staff.
Circle
all
dissonant
numbers
(2,
4,
and
7)
and
label
w
w
w w ww
c.f. w
passing tones with “pt.”
& 44
44
&
& 44
Int:
444
&
&
& 44
Int:
Int:
___
w
___ ___
___ ___
___ ___
___ ___
___ ___
___ ___
___ ___
___
w w ww w www w ww w ww w ww
ww
w
w
w
w
___
___ ___
___ ___
___ ___
___
c.f.
c.f.
1 ___
2
___
c.f.
w
5 ___
6
___
8 ___
6
___
w
w
6 ___
8
___
w
6 ___
8
___
w
w w
ww
___
___
5 ___
3
___
w
1
___
w
__ __ __ __ __ __ __ __ __ __ __
__ __
__ __
__ __
__ __
__ __
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__
__ w__
__
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4
&
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w
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˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ #˙ w
& 44 c.f.
Int:
__
pt __
Int:
__ __
__ __
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__ __
__ __
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__ pt__
__ __
__ __
__ __
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c.f.
w
w
? 444 c.f.
w
w
ww w
w
w
w
w
&
ww w w ww ww ww w ww ww ww ww
& 44 c.f.
w w
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Int: 4 __ __
__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __
c.f.
& 44 w
w w w w w w
w wDaywTwo w
Species Counterpoint:
pt
? 44 Ó ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ pt˙ ˙ pt˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ w
3. For each exercise below, write third species counterpoint (quarter
˙ notes).
pt
Int:
Int:
Circle all dissonant interval numbers and label passing tones and cambiata
figures.
Int: __ __ __ __
& 44
? 44 w
c.f.
& 44 w
Int: __ __ __ __
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c.f.
Int: __ __ __ __
4
&4
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c.f.
Int: __ __ __ __
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__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __
w
w
w
w
w
w
__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __
w
w
w
w
w
w
__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __
w
w
w
w
w
w
__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __
__
w
__
w
__
w
__
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c.f.
CHAPTER 30. INTRODUCTION TO COUNTERPOINT
Int:
Int: __
__ __
__ __
__ __
__
4
&4
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Int:
Int: __
__ __
__ __
__ __
__
4.
__
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
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__ __
__ __
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__ __
__ __
__ __
__ __
__ __
__
w
c.f.
c.f.
359
w
w
w
w
w
__
__
w
& 44
Int:
__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __
Int: __
__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __
4
w
?
w
w
w
w
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w
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w
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w
ww
?
4
ww counterpoint
ww (suspensions
ww
ww
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For
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4
Int:
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Int:
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__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__
c.f.
and syncopations).
Circle all dissonant interval numbers and label sus4 c.f.with “sus” and syncopations with “sync.”
pensions
&4
Intervals:
__
__
Intervals:
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__
__
w
4
w
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ww
ww
ww
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ww
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__
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__
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__
__
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c.f.
c.f.
4
w
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w
w __ __
w __
w __
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w __
w
Intervals: w __
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c.f.
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4
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c.f.
c.f.
Intervals:
Intervals:
44
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CHAPTER 30. INTRODUCTION TO COUNTERPOINT
360
Invention Expositions
5.
190
190
190
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œ #œ œ œ œ
&
&
?
? b# # 43
?
d: i
Fugue&
Analysis
b
6.
i
V
V
i
For this fugue from the second Kyrie eleison of Bach’s Mass in B Minor
? b 232), specify formal sections (expositions and episodes), motives
(BWV
(subject, answer, countersubjects, and fragments thereof), and key areas
for expositions only in the table below. This fugue contains more “counterpoint” (material not derived for subjects or countersubjects) than the
C minor fugue in the body of the text.
CHAPTER 30. INTRODUCTION TO COUNTERPOINT
Alla breve.
breve.
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C „„
&
C
&
# ##
& # ## CC „„
&
# ##
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Soprano
Soprano
Alto
Alto
Tenor
Tenor
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?
#
? # ####
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Ky - ri - e
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son,
Pno.
Pno.
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S
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?
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Bass
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361
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son,
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œ #œ ˙ #˙
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CHAPTER 30. INTRODUCTION TO COUNTERPOINT
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wœ
œ
? # # # ˙ # ˙ ˙ # ˙ ˙ œ œ œ œ œ # œ œœ œœ œœ # œœ œœ
21
S
œ #œ ˙ #˙
-
˙
son,
Kyr
˙
e
˙
17
Pno.
˙
˙
son,
œ œœœ ˙ œ œ w
##
œ
V # ˙ #œ ˙ #˙
son,
B
-
son,
-
son, e - le - i
17
S
ri
˙.
-
#˙
nœ œ ˙ #˙
## ˙ œ ˙
w œ # œ n œœ œ ˙˙ # ˙˙ ˙ œ˙ œ # ˙œ œ # œ
& # ˙˙ œœ # œœœ ˙˙ . # ˙˙ œ ˙˙ .
œ
˙.
œ # œœ
œ
? ### ˙ œ œ ˙
Œ œ œ #œ œ œ œ œ œ œ nœ œ œ #œ
˙ œ œ ˙ ˙ ˙
˙ ˙ ˙˙
-
13
Pno.
-
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son,
B
˙.
Ky
w
˙
13
S
362
e
˙œ œ
-
„
le
-
i
˙˙ œœ œœ ˙˙ œ˙ œ
œœ # œœ # ˙˙ n ˙w
˙ ˙˙
∑
YT: aVYPtNeH7IQ
∑ 232, Kyrie eleison II
& 30.9.1
˙
J.S. Bach, Mass Óin B Minor, BWV
A
Figure
T
B
V
##
& #
21
Pno.
? ###
∑
w
∑
∑
∑
CHAPTER 30. INTRODUCTION TO COUNTERPOINT
363
Table 30.9.2 Mass in B Minor: Fugue Analysis Table
FORM
SOPRANO
ALTO
TENOR
BASS
KEY
Meas.
1
2
3
4
l
FORM
SOPRANO
ALTO
TENOR
BASS
KEY
Meas.
5
6
7
8
l
FORM
SOPRANO
ALTO
TENOR
BASS
KEY
Meas.
9
10
11
12
l
FORM
SOPRANO
ALTO
TENOR
BASS
KEY
Meas.
13
14
15
16
l
FORM
SOPRANO
ALTO
TENOR
BASS
KEY
Meas.
17
18
19
Click here to download the first homework assignment for this chapter.
Click here to download the second homework assignment for this chapter.
Click here to download the third homework assignment for this chapter.
Click here to download the fourth homework assignment for this chapter.
Click here to download the fifth homework assignment for this chapter.
Click here to download the Unit 10 Practice Test.
PDF versions of the textbook, homework exercises, and practice exercises
can be found at musictheory.pugetsound.edu
20
Chapter 31
Introduction to Jazz Theory
This introduction to jazz theory focuses on the types of chords encountered
in jazz, how these chords might be voiced, how to voice lead these chords in
five-part harmony, and scales associated with these chords.
31.1 Jazz Chord Basics
1. Ninth chords are common in jazz.
(a) Four of the five common seventh chord types in classical and popular
music will have ninths added to them; the exception is the fully
diminished seventh chord.
i. The ø7 chord is also labeled as m7 (25) in jazz— Cø 7 is the
same as Cm7 (25) .
44
b
#
b # #
b
E maj9( 5) B notation,
7 9( 5)
(b) In
lead-sheet
adding “9” toE a chord symbol means the 7th
943
is also present.
&
(c) “9” is “2” an octave higher and always comes from the major scale
unless otherwise specified.
& wwwww
b www
ww
C maj9
945
C m9( b5)
b ww
b www
C9
b b b wwwww
C m9
a.
b. , 4, 2, + , m,b.–) are applied
c. as follows:d.
2. Alterations
(maj, ∆
C
Δ9
C # m6
C # (add b 6) C + 7
C b9
C (b 9)
C 7( b 9)
949
(a) “maj”
or “ ∆ ” followed by 7, 9, 11, or 13 meansb the
7th
of the
chord
w
w
b
w
b
www not# the
# www9th, 11th,
# wwwor 13th.
# b www
b ∫ b www n n ww b wwww
is&major,
#
w
# w
# w
w
bw n w w
(b) Lowercase “m” or the minus sign (“–”) means minor and applies to
the 3rd of the chord.
(triangle still
954
956
applies to 7th)
i. The minus sign (–) is equivalent to a w
flat
when placed in front
w
w
&
w
w
2
ww same thing). “ C4 – 6 ”
of 9, 11, or 13 (i.e., 9 and –9b w
mean bthe
w
4
4
4
(equivalent to “ C m6 ”) means a C minor chord (“ C –”) with
4
C 94). “ C C(add
13
C 9(13)
the 6th from major (A
–6),”
which is equivalent to
4
w
ww triadwwwith the 26 added
“ C (add 26) ,” meanswa C4 major
C mΔ7
& b ww
b ww
C mΔ9
b ww
ww “augmented
ww
ww triad” or is equivalent
(c) The plus sign ( + ) can mean
to a sharp when placed in front of 9, 11, or 13. C + 7 means a C
augmented
”) with a dominant
(“7”),
F dim7triad (“C +
F dim7
B b7(13
)
B b7(13
b 9 seventh
b 9 ) not a C
959
w
w
major ∫triad
7th.
w with a major
w
w
w
& b b www
C6
961
& wwww
b n www
C 7(13)
b wwww
w
b b www
bw
364
b n www
bw
enharmonic respellings
b wwww
w
C 7(11)
b www
w
C 7sus
A b 7( #11)
b bn wwww
A b 7( b 5)
b n www
or A¯7(˜11)
44
943
E b maj9( # 5) B b 7 # 9(# 5)
Eb
CHAPTER&
31. INTRODUCTION TO JAZZ THEORY
44
945
943
&
945
&
44
(d) Chromatically altered chord numbers (affecting 6, 9, 11, 13) are
maj9
C9
C m9( bwhether
5)
usuallyC set
apart by parentheses
so asC m9
to clearly designate
w
w
w
ww the added
# 9 (#minus,
b
)
plus,
or
sharp,
or
flat
is
affecting
the
chord
or
w
b
w
b
w
b
E b maj9 ( # 5) B b 7the
5
E
& ww
ww
b www C(29) versus bC7(
b www29).
w example, consider
w
note. For
C29 versus
a.
&
945
956
959
954
961
956
961
# # www
# w
C # (add b 6)
# # # wwww
c.
d.
C +7
C b9
C (b 9)
C 7( b 9)
b ∫ bb wwww n bn www b b wwww
b w n wb w
# b www
w
C9
C m9
954
C m9 ( 5)
mΔ7
mΔ9
section).
( 5) B 7 9 ( 5)
E maj9
b ww E b ww
b.
b.
c.
d.
4. m ∆ 7 Chord:
In addition
to the five
common seventh
chord types,
jazz
+
#
#
b
C Δ9
C m6
C (add 6) C 9C 7
C b9
C (b 9)
C 7( b 9)
C 13
956
includes use of the minor-major
seventh
chordC 9(13)
(a minor triad with a
www haveww a ninth added as well.
major seventh). This chord will
commonly
w
b
w
b
b www
www ( ∆ )wwwwused primarily
You will see the “major” &
symbol
in jazz. Popular
w
music typically uses “maj” instead.
&ww
ww
w
www
ww
# # www
# w
w
∫w
& b b www
C9
b ∫ bb wwww n bn www b b wwww
bw n w w
# b www
w
# # # wwww
F dim7
C maj9
959
b n wwww
w
b www w
&
w b ww
b
B b7( b 9 )
B 7( b 9 )
C
m9
(triangle
still
F dim7
C mΔ7
C mΔ9 applies
b wwwww to 7th) b n wwwww
w
b
w bw
bw
b www b wwb w
13
w
w
enharmonic respellings
13
C m9 ( b5)
b b b wwwww
b b
6
C 7(13)
C 7sus
A b 7( #11)
5. 11th and
Chords:
11thsC 7(11)
and 13ths
always come
a. 961
b.C13th
c.
d. from Athe7( 5)major
C 9 b. C 13
C
9 (13)
scale unless otherwise
specified.
higher
and “13”
ww (“11”
+ 7 an octave
b 6) biswwC“4”
n
w
C Δ9
C # m6b ww
C # (add
C b 9 n w C (b 9)
b
w
is “6” &
an w
octave
higher.)
ww
ww
w
b b ww
bw
w
www
ww
or A¯7(˜11)
C 7( b 9)
www
ww
w
w
w
w
w
w
b
w
b
w
b
w
b w∫ b w
bw b w b b w
# ww&w upwww to #the#highest
(a) All #numbers
wwwwww number
#wwwb www are assumed.
b b wwwC9 means
n2n ww that www
# w
# w
w
bw n w w
w
the 7th is also included below the 9th. C13 means C–E–G–B –D–F–A—everything
up to the 13th. For this reason,
we will use C9(13)—to
specify
13
13
F dim7
F dim7
B b7( b 9 )
B b7( 9 )
C–E–G–B2–D–A—instead of C13, which
would be bused
in the real
(triangle
still
world to describe these notes. In the real world,
a composer
or
C mΔ7
C mΔ9
to 7th)
arranger writing C13 will assume the pianist orapplies
guitarist
knows to
omit the unaltered 11th because it clashes with the major 3rd of the
chord. In this music
theory course
we will be specific as to which
enharmonic
respellings
notes are included and left out.
C6
C 7(13)
C 7(11)
C 7sus
A b 7( #11)
A b 7( b 5)
or A¯7(˜11)
C9
C 13
C 9 (13)
∫w
& b b www
w
b b wwww
w bw
b n wwww
& b www
w
w
b www
b ww
w& b www w
b wwww
w
& www
w
6.
959
b.
C # m6
ww3. If a chord hasb wwa 9th but no 7th, buse
ww the Cterm “add
ww popular music,
(triangle
still
9.”
In
C applies
www sometimes “2”www or “add 2” is bused
www instead (refer
btobtobthe
www7th) Chord Labels
w
w
w
& w b w
#
b
b # #
&
949
& wwww
w
C maj9
&
954
b.
C Δ9
949
a. 943
949
365
ww
w
b n wwww
ww b w
b www
www b bn www ww b n ww
b www b ww b www b ww
w
w
6 chord (C 6 ) instead
chords: If a chord has a 6th and a 9th, call itb a 13
9 B b7(13 )
F dim7
F dim76
B 7( b99 )
b9
9
of a 6 chord. The major 9 uses the major third (C–E–G–A–D) while
6
2
the minor 9 uses the minor third (C–E –G–A–D). The “6” always comes
from the major scale unless otherwise specified. (Refer to the Chord
Labels section for examples.)
6
9
∫w
& b b www
w
b b wwww
bw
b n wwww
w
b n wwww
bw
7. Enharmonic respelling: Jazz musicians
willrespellings
sometimes respell doubleenharmonic
flatted notes and double-sharped notes enharmonically because for some
b 7( #11than
more fromCthe
piano
the
)
C 6musicians theory
C 7(13) was viewed
C 7(11)
7susaspect of the A
A b 7( b 5)
staff. This may at times include enharmonically respelling notes like B4,
C2, E4, and F2 (although these notes sometimes will be used).
& wwww
b www
ww
b www
ww
b www
w
b bn wwww
bw
b n www
bw
or A¯7(˜11)
E b maj9( # 5) B b 7 # 9(# 5)
C 13E b
www
ww
w
b
w
b
w
b
www
& www TO JAZZ
www THEORY
& 31. INTRODUCTION
CHAPTER
w
956
959
945
943
b b ∫ww wwww
&
& ww
w
F dim7
C maj9
a.
B b7(13
b9 )
C m9( b5)
www
b
w
b
bw w
b www b ww
w
b bn wwwbwwww
b wb ww
enharmonic respellings
c.
d.
b.
or A¯7(˜11)
(triangle still
C mΔ9 applies to 7th)
w
31.2 Chord Symbol Specifics
& b wwww
b wwww
C mΔ7
956
959
1. “6” versus “13” rule: label the 6th of a chord “6” only if the 7th is not
present; if the 7th is present,
C 9 label the
C 13 6th asC“13”
9(13)
ww label theww 4th of a chord “sus” only
2. “11” versus “sus” (“sus” means
“4”):w
w
b
w
b
www
blabel
www the 4th an “11” (C7sus
&if the
www 3rd is present,
if the 3rd is not present;
w
w
has C–F–G–B2). (There is an exception to this in more advanced jazz
theory, which is not within the purview of this
text.)
F dim7
F dim7
B b7(13
B b7(13
b9 )
b9 )
411: If the chord has a normal 5th
2–F
4), call the F4
w
w
3. 25 versus
(C–E–G–B
www
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b b ∫(because
wwww a regularb nand
n wwww have a chordb bwith
a&
“411”
you bwon’t
w
b wthe F4 of C–E–B
b ww 2–F4 a “411”
at the same time). Otherwise, you can call
or a “25.”
enharmonic respellings
C6
961
b.
366
B b7(13
b9 )
C m9
F dim7
C9
bb nwwwwwww
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C 9(13)
b 9)
+7
CΔ9
6 purposes
C 7(13)
Abb97( #11)
8. For the
web 6)willCC7sus
assume
the Cbass
note
isb 7(the
C
C #of
m6this text,
CC#7(11)
(add
C (b 9)A
C5)7( broot
whenwanalyzing chords. While
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b ww n wb bare
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wwb ww (E/C,
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#
w
&
#
w
#
b
n
b
w
b
in
jazz,
is
meant
as
an
introduction
the
fundamentals
w
w
w
#
w
w
b
w
n
w
& ww
www
ww ww of
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bb bwwwwof nslash
wb chords.
jazz harmony
and
the use
bw
bw
949
961
954
C9
& www
w
(no 7th)
C 7(13)
b wwww
w
b wwww
w
C 7(11)
b www
w
C 7sus
(no 3rd)
A b 7( #11)
b bn www
b ww
A b 7( b 5)
b n ww
b ww
(no regular 5th)
31.3 Altered Dominant Seventh Chords
Typically, a dominant seventh chord is considered altered if either or both
the 5th or 9th are chromatically raised or lowered. (“G7alt” might mean a G7
with both an altered 5th and 9th, but is vague in that it doesn’t specify how
the 5th and 9th are chromatically altered.)
1. Root, 3rd, and 7th of dominant seventh chord remain unchanged.
2. 5th may be raised or lowered (45 or 25, which can also be written with
pluses and minuses as + 5 or –5) and can be respelled enharmonically (the
45 of a C745 could be written as an A2 instead of G4) for ease of reading
because the chromatic spelling agrees with B2 (the 7th of the chord)—it
is easier to read a chord where the accidentals agree (all sharps or all
flats).
3. 9th may be raised or lowered (49 or 29, which can also be written in the
lead-sheet symbol as +9 or –9). The 49 is often spelled enharmonically on
the staff as 210 for ease of reading; therefore, a dominant seventh chord
with a 49 will appear to have both a major and minor 3rd (C–E–G–B2–E2).
You may be tempted to call such a chord a minor chord with a 211, but
211 is not used because it is the major third of a chord.
or A¯7(˜11)
CHAPTER 31. INTRODUCTION TO JAZZ THEORY
367
4. Both alterations of 5 and 9 may occur simultaneously (±9/±5).
5. 213 is the enharmonic equivalent of the 45. In this text, 45 is preferred
to 213, but you will see both on lead sheets. Also, 213 implies that the
unaltered 5th occurs in the chord, while 45 does not.
2.
C 7( b 5)
3.
C 7(# 5)
b b www
& b n b wwww
w
respell ˜5 to agree with ¯7
?
∑
2
C 7(# 9)
C 7( b 9)
b b www
ww
b b www
n ww
respell ˜9 to agree with ¯7
∑
4.
199
5.
_
9
C 7+
+_
b bb www
5
¯5
˜5
b b ww ˜9
n ww
¯9
C 7( b13) or C7(˜5)
bw
bw
ww
∑
preferred
If you are composing or arranging and want to know when to use altered
chords, know that dominant sevenths are usually altered (with altered 5th or
6
9th or both) when they have dominant function (i.e., when the root is going
& down by a fifth). Dominant sevenths are often unaltered when they
to resolve
have tonic function, i.e., the first chord in a blues.
?
31.4 Chord Labels
The following list of chords is edited and condensed from The New Real Book
22 published by Sher Music Co.
(Vol. 1),
45
964
964
964970
964970
970
975
970
975
975
981
&
w
& wwC w6 ?
wwC w(add 9) b wwC wm (add 9) wwwC w
b wwCwwm6
b wwCwwm
w
w
w
w
www#
wC 9 with added
& CwwC6w7 31.4.1 Triads
wwm6
www(add 9)notes
wwmw(add 9)Cw9(13)Cwwww
C 9( # 11) b C
Cb13(
b
wwm11)
C
C
C
Figure
w
w
ww
w # ww
w
w
#
w
w
b wwww www#
& bwwCwwCww67
wwCwbm6wwCww9
wwCw(addb 9)wwCww9(#11) b wwCwm (add 9)b wwCww9(13)wwwCw
C
b
wwC m11)
wwwb13(
w
w
w #w w
w
w
#
&
bwCwwww9
b wwww9(#11) CwΔ13(# 11)b Cwwww9(13)wwCwΔ7(# 5) b Cwwww13(wwCwΔ7(
& bCwwCwwwwwΔ77
Cw
Δ9
Cw
Δ9(# 11)C
b
w
w
bwwwww w ww
b ww #11)b 5)
w
w
w
w
w
w
w
#
w
#
#
w
#
w
www b ww
www b ww www b ww # ww
w
& bwwCwwwwwwCΔ77?31.4.2 Dominant
wwwC 9(#11) CwwΔ13(# 11) wwwC 9(13)CwwΔ7(# 5) b wwwwCb13(wwCwwΔ7(
#11)b 5)
wwΔ9wwwC 9 seventh
wwΔ9(# 11)chords
C
C
Figure
w
#
w
#
w
#
w
#
w
www b ww
www #b ww www # b ww # ww # b wwb ww #
& bCwwwwwwwwΔ7C m7
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b 5) 11)
C m11
C m7(11)
C m13(
C
C
11)w
11) w
wwΔ9C m9
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ww CwwΔ13(
ww CwwCwΔ7(m135) www CwwΔ7(
w
#
w
#
w
w
w
w
#
w
w
w
w
wwb www
wb www #
wb w #
& bwwwwCbΔ7wwCwm7
#bwwwwCb wwwCwΔ7(m13# 5)
bbwwwwCb wwwCwΔ7(m13(
wwC Δ9Cwwm9
bwwwC Δ9(
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C
C
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#
w
#
w
w
w
w
#
wwwb ww
wwwb ww C m9( b5) wwwb w
ww #
wwb Cwwwm13
m7( b 5)
C m11( b 5) b w
& bwwwwb CwwwCm731.4.3
#
w
w
w
w
C
m9 seventh
C
m11
C
m7(11)
C
w
w
w
w
w
w
b
w
b
w
b
w
b
Figure
Major
chords
ww
www w
www
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wwwwwm13( 11)
wb w
#
& b b wwwwCw?m7( b5) b www
b wwb wwwCwm9( b5) b ww
bb wwb wwwCwm11( b 5) b www #
&
b wwC m7
wwC m9
b bwwwC m11
b wwC m7(11) b bwwwC m13
b wwC m13( 11)
wwb
w
w
w
w
# ww b 9
bw
ww
wwb Cwwwm9( b5) Cb13sus
wwb Cwwwm11(
9
&
b
Cb9sus
C
7sus
w
b
b 5) b Cw13sus
b
b
& bbCbbsuswwwwCwwwm7( b5) Cb7sus
www
w
w
w
w
b ww ww
bw ww
bw wwwww
bww
w
b
b
b
w
b
w
b
w
b
w
b
ww b 9
b www
b www
b wwwb 9
& bwCwbwsus
w7sus
w9sus
wCw13sus
w7sus
b
b
w
w
w
w
w
C
C
C
C
b
b
b
b
b
C
m7(
5)
C
m9(
5)
C
m11(
5)
w
w
w
ww13sus
w
ww
w
Figurew31.4.4 Minor seventh chords
w
w
b
w
b
w
w
#9
b CCwwb77sus
bb#9 wCwww13susCb 97 b 9
#w9b w
b9
wbCwww7( b5) bCCwww7(7sus
w# 5) C 7(bbC9)wwwb9sus
wb b wwwC 7(# 9) b wCww13sus
& bCwwbsus
w
C7 b5
C
7
#
b5
b
w
5 w
w5 w
wb w
w
ww
b
b
w
w
w
b
w
b
w
b b www bbwwCw9susb ww # b wbwwCb 13sus
ww # 9 b bb wwwCww#7sus
b b wwb wCb13sus
b b wwwb 9b 9
& bwwCbwsuswwCw7( b5) b bbwCwwwwCw7(w7sus
9 b 9 b w b 9 ww
# 5)
w
n
w
n
w
n
w
w
n Cww7 b 5
9)
C
7(
C
7(
9)
C
7
C
7
C
7
#
b
#
w
w
w
w
5
5
w
w
w
w
w
w5
w
w
w
b
w
b
w
b
w
b
w
b
w
b
w
b
w
b
& bwwbwCwww7( b5) b b Cbwwwww7(ww# 5) b Cwww7(bb 9)wwww b n Cwww7(# 9) b wb wwwb n Cwww7 #b 59 b b bn Cwwwww7##w95 b b Cww7wbb#95 wwwwb b#n Cwwww7 bb 95
w
wC mΔ9 w C dimb ww
w C 7 #119w
C mΔ7
bCwwwo7 # 9 b b wwwC# dim(Δ7)
b
w
b
w
b
w
b
w
b
w
b
w
b
b
& b wwwC 7( b5) b wwC 7(ww# 5) wwC 7( b 9) n wwC 7(# 9) b n wwC 7 b 5 b n wwC 7w# 95 b wwCw7b#b95b b wwwb b bn wwwwC 7 bb 95
& b wCwwwmΔ7 wb wCwwmΔ9 w b b wCwwdimb ww b # wCwwb wwwo7
bww# Cwwwdim(Δ7)b ww n wCww7 ##b119ww
b
b
w
& b bwwwww b b wwwwww b wwww b n wwww b b n wwww b b n wwwww b b wwwwb b b wwwb b# n wwww
& b CwwwmΔ7
w
b CwwwmΔ9
b b Cwwwdim
b # Cwwwow7
b # Cwwdim(Δ7)
n b Cwww7 #119
bw
w
C6
30
38
975
981
987
981
987
981
990
987
990
987
990
996
990
996
996
996
C m6
C (add 9)
C m (add 9)
6
C9
6
C m9
6
9
6
9
6
9
6
9
6
9
6
9
45
45
45
975
981
975
975
981
987
981
987
981
990
987
987
990
996
990
990
996
996
996
# ww
www
www
# www b # wwww # wwww
bwwwwwC m7
b
b
www wC m13(# 11)
ww Cbm9
&
w
w
w
C m11
m7(11) w # wC m13
& wwwCwΔ7
wwwC Δ9ww
wwwC Δ9(
wwwCCΔ13(
# 11)w
# 11) w w
#
w
wb www#CwwΔ7(b 5)
C
Δ7(
5)
w
w
w
w
w
# wwwb www # TO JAZZ
# wb w THEORY
bw
b ww
b CwwwwΔ7(b 5) 368
wwb Δ9wwww
CHAPTER
# 11)
&
C
bCwwΔ9(
wwm1111) bCwwwwwCwwΔ13(
b CwwwwCwwΔ7(m13# 5)
& bCwwwwΔ7wCwwm7 31. INTRODUCTION
wwwCwm9
#
b bwwwCwwm13(# 11)
C
m7(11)
#
w
#
w
w
w
w
w
w
w
w
w
wwb wC m7( b5) wwb ww
wwb ww C m9( b5) wwb w
wwb wwC m11( b 5) b ww# wwww
&
#
wwwwC m9
wwb wwC m13(# 11)
& bww wwwC m7
bwwwwwCbm11
bwwwwwC m7(11) b wwwwwCb wwwm13
w
w
ww
b
w
w
w
w
w
#
& b b Cwwwm7
b
w
b
w
w
w
w
b
w
b
w
b Cwwm11
wm9( b5) b b Cwwwm7(11) b Cwwwm13
wm11( b 5) b b Cwwwwm13(# 11)
C
C
& b wwwCwm7( b5) b Cwwwwm9
b
w
ww
wwwwwb 9
# www b 9
ww
b wwwwb wwwseventh chords
b
b
b
w
Cb7sus
Cb9sus
Cb13sus
C
7sus
w
w
w
& bbCbbsusbwwwwwwwC31.4.5
b
w
Figure
Half-diminished
b bww wwC m9( b5) wb ww
b bwwwwC m11( b 5) bCwwww13sus
wm7( b5) b w ww
w
w
b
b www b ww b b www
b wwwwb wwwb b b b wwww b
&
w
w
w
w
b
w
b
9
5)
& bCwbsusCwwm7( 5) Cw7sus
wb9sus
wb 7sus
ww13sus 9
C
C
C
b Cwwwwm9( 5) Cww13sus
b Cwwwwm11(
w
& bwbwCb www7( b5) bCww7(w# 5) C 7(bb 9)wwwbwb b wwwC 7(# 9) b wwww C 7 #b 59 b bCwwwb7##bw95b wwwb 9 C 7bb#95b wwww Cb79bb 95
&
wC susw
wC 7sus b w wC 9susbww
wCb13sus
wC 7susw b w wC 13sus
w
b
w
b 9b b wwb b Cw
ww b b wb Cwww7sus b ww b Cwww9susb ww b b bCwww13sus
ww # 9 b b b wb Cww#7sus
b b wwwb 9b 9
&
b
13sus
b 9 ww
9
& bCwwbwsus
w
w
w
w
n
w
n
w
n
w
w
#
#
w
w
w
w
b
b
Figure
31.4.6
Sus
chords
w
w
C
C
C
w7( 5) Cww7( 5) Cw7( 9)ww Cw7( 9) ww Cw7 b 5
wb ww7# 5
w7# 5b ww n wCw7 b 5
b
w
b
w
b
w
b
w
w w b w b ww b w
& w
w bw w bw
wb w
& bwwb wwwwC 7( b5) b b wwwCww7(# 5) b wwwwC 7( b 9)ww b n wwwwC 7(# 9) wb bwn wwwwCo 7 #b 59 b b n wwwCww7## 95 b b wwwCw7b#95 wwb b#n11wwwwC 7 bb 95
C mΔ7
C mΔ9
C dim
C 7
C dim(Δ7)
C7 #
#9
#9
b 9 b w b9w b 9
b
w
b
w
b
w
b
w
b
w
#
#
b
b
& b wwb Cwwww7( 5) b b Cwwwwww7( 5) b Cwwww7( 9)b w b n Cwww7( 9) b#bwn Cwww7 b 5 b b n Cww#7ww# 5w b b Cwww7w#b5b wwwb b# n Cwwww7 b 5
&
bw
bw
b w b b ww b b wCwb wwo7
bbw w b b b www n wCw7b#b119ww
& b Cwb wwwwmΔ7 b b wwwCwmΔ9 b b wwwww Cwdim
www b n www b b n wwwwCwdim(Δ7)
n
ww b b wwb n www
w
Figure
chords
& b wwwwC mΔ731.4.7 Altered
b wwwwC mΔ9
b b wwwC dim
b # wwwCwo7
b # wwwCwdim(Δ7) b n wwwwC 7 ##119
b b Cwww7 ##11
o7
wwmΔ9
w
w
b
C
mΔ7
C
C
dim
C
C
dim(Δ7)
w
&
w
w
b
w
& b ww
b ww
b ww
b # www
b # www
n b www 9
b
b n www
& b wwww
b wwww
b b www
b # wwww
b # wwww
w
&
&
&
One finds that almost any combination of triad or seventh chord plus any
perfect 11th with no 3rd = "sus"
&
alteration
or combination of alterations
is possible.
lowered 9th
lowered7th
&
major 6th is "13" when 7th is present
b b b wwww
& w Jazz Chords
31.5
& How to Write
Figure 31.4.8 Other chords
46
no 5th (incomplete voicing is normal)
no3rd
root
To
& write a jazz chord after being given a lead-sheet symbol, begin with all of
the major notes up to the 13th.
major
13th
Let’s work through this with the
following
label: Dm ∆ 11.
perfect 11th
Dm means D–F–A. The ∆ 11 means
there
is
a major 7th, regular 9th, and
major 9th
major 7th11th. Remember, D11 would mean a
regular 11th, not that there is a major
perfect 5th
D7 chord with the 9 and 11 (all chord
members up to the 11th—D, F4, A, C,
major 3rd
E, G). D ∆ 11 would mean a D ∆ 7root
chord with all members up to the 11 (D,
F4, A, C4, E, G).
b wwww
& www
www
#
& www
D mΔ11
"11" means 7, 9, and 11 are present
"Δ" means Δ7
"Dm" means D minor triad
411 Let’s try this with another chord: E7 449 .
5
E7 means &
we have E–G4–B–D. When we look at the altered notes, we see
45, so we add a B4, then change it to a C6 because that agrees chromatically
with the 7th, D. When we add 49, we add F5, which looks overly complicated,
so we enharmonically respell it as G6, which agrees chromatically with the D
(7th) and C (45). The 411 can be an A4, an augmented 2nd above the G (the
&
&
www
ww
w
b
w
b
b
b
w
b
w
CHAPTER 31. INTRODUCTION
TO
JAZZ
THEORY
369
&
w
w
w
&w
b
w
b
w
b
w
w
b
w
b
w
b
w
w w
# www w 2 w 4 2 w
4
987
981
&
D mΔ11
ww
C m7
C m7 ( b 5)
C m9 ( b5)
C m9
C m7(11)
"11" means 7, 9, and 11 are present
meansA
Δ7 and B are acceptable, although
9), or we can respell it as a B "Δ"
. Both
the upper990
notes987
of D–G–B
form"Dm"
aC
Gmeans
minor
triadtriad
and therefore
(Cb D
)minor
( b5)
m7
57sus
m9
C2sus
C 9sus are easyC to
C 13sus
sightread.
w
w
b b bbwwwwwww
ww
b wwww
w
& #&
w b b b wwww b www
w
11
w
#w9
www
w
w
b ww b b www b ww
b ww b ww b ww
C m11( b 5)
C m11
b
C 7sus 9
b b wwww
w
C
b bb
#
#
b
#
b ww C Cb ˜sus C # C˜ 7susC b CC 9sus
C 13sus
C b
C #
CC 7#
ww b w
w
˜
b
w
b
w
w
w
b
w
& #&wwb&b www w˜w b b ww˜w b wwb wwww b n wwwb www b b n www b wwwb b n www b bbb wwwwwwww
ww w ww
ww
w w w
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996 990
E7 #5
9
7 5
9)
7( 5)11 spelled7as( B¯;
5) A is also
7( acceptable
7( 9)
9 respelled as ¯10 on staff
5 respelled as ¯6 on staff
E7 is E-G -B-D
C 7( b 5)
C 7(# 5)
C mΔ7 Jazz CChords
mΔ9
31.6 How
& to Analyze
996
&
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b&
w
o
C 7(# 9)
C 7
C 7( b 9)
C dim
9
7 5
7
#9
#
C7 b5
C 7#
C dim(Δ7)
b b www w b b b www w b b b www
nbww# www n wwb # www n ww
b b wwww b wwwwb b wwww bbb bwwwwwww
w
w
To analyze a jazz chord, on scratch paper write out all the major chord members up to the 13th. These include the major 3rd, perfect 5th, major 7th,
major 9th, perfect 11th, and major 13th.
&
b wwww
&&b bb wwwwwww
C mΔ7
w
b
www
&
& b b www
major 13th
C mΔ9
perfect
11th
major 9th
major 7th
perfect 5th
major 3rd
root
ww
b www
C dim
b b www
In order to analyze the following chord, determine the
following:
major
13th
perfect 11th
1. The quality of the 7th chord
major 9th
major 7th
2. The upper structure (9, 11, and 13)
perfect 5th
3. Any alterations to any of the chord members
major 3rd
root
4. If any of the notes are enharmonically respelled
w
b
w
b
w
b
& b www
Work through each step (see the example below). Compare this chord to
the scratch paper version with all the major notes up to the 13th. We have an
E2 dominant 7th chord. The G2 can’t be the minor third because we already
have a G6. If we consider the G2 enharmonically as an F4, we see we have a 49,
which we noted earlier is often spelled as 210 so as to agree chromatically with
the 27. The A is the 11th, but it is an A6, so it is a 411. It is not 25 because we
would not have both a perfect 5th and altered 5th in the same chord. There
is no C in the chord, so there isn’t a 13th.
o
C 7
b # wwww
C
b # www
ww
b
& b ww
w
b
w
b
w
b
& b www
major 9th
major 7th
perfect 5th
major 3rd
CHAPTER 31. INTRODUCTION TO JAZZ THEORY
root
370
no 13th
raised 11th
¯10 = ˜9
lowered 7th
perfect 5th
major 3rd
root
4 The final label is E27 411
9 .
Let’s try another chord.
46
b bwwb b wwww
b ww w
&
& w
46
www
b
w
b www ww
w
&
w
& ww w
perfect 11th with no 3rd = "sus"
9thno 3rd = "sus"
perfect lowered
11th with
lowered7th
major 9th
major 6th is "13" when 7th is present
lowered7th
no 5th
(incomplete
is normal)
major 6th
is "13"
when 7thvoicing
is present
no3rd
no 5th (incomplete
voicing is normal)
no3rd root
root
Again, work through each step. First, write all the major notes up to the
13th.
46
b b b wwww
& &w
&
major 13th
perfect 11th
major 13th
perfect major
11th 9th
major
major 9th 7th
perfect 5th
major 7th
major 3rd
perfect 5th
root
major 3rd
root
Compare the “all major and perfect” 13th chord above to the chord to be
solved.
&
&
b wwww&
& & www
perfect 11th with no 3rd = "sus"
lowered 9th
lowered7th
major 6th is "13" when 7th is present
no 5th (incomplete voicing is normal)
no3rd
root
We notice we don’t have an A, and we remember that we might have a sus
chord where the 4 (or sus4) substitutes for the 3rd. We see we have a B2, which
confirms this. We also do not see a C,major
but13th
we remember that it is common to
perfect 11th
omit the 5th in a chord (see Incomplete
Chords).
Therefore we have F–B2–E2,
major 9th
making an F7sus chord. When we examine
for
upper
structure notes (the 9,
major 7th
perfect
5th and a D (the 13). Remember,
11, and 13), we find a G2 (the 29 of the
chord)
major
3rd
the B2 is the sus (the 4th), not the 11th,
because
we have no 3rd (see 11 versus
root
Sus).
The final label is F13sus(29).
“F13” means we have root, 3rd, 5th, 27th, 9th, 11th, and 13th. “Sus” is
a modifier that means we have the 4th, which eliminates the 3rd as well as
the 11th because “sus” and 11 refer the same note (B2). “29” means the 9th is
lowered chromatically.
&
&
200
19
200
24
19
200
24
28
24
28
28
33
j
j
‰ œj Œ ˙
& c b œœœ ... œœœ ‰ œœœ ... œœ .. œœ Ó
˙˙˙ b œœ .. œj w
œœœ b ˙˙
b œ . œ œ . œœ .. œœ
b œ . n œœ ww
˙
CHAPTER 31. INTRODUCTION TO JAZZ THEORY
?c ˙
j # ˙ n œ . œœ ww 371
Ó
j
b˙
c b œœ .. œjœ ‰˙ œœ .. œ . œj Ó ‰œ .œj Œ œ ˙œ . œ ˙œ . œb œœ .. Jj
&
31.7 Jazz
œœ .. œœœ .. Voicings
œ
œœœ b ˙˙
b œœ .. œœ Chord
˙˙ bJ œœ .. n œœœ www
˙
. œœ
.± types of jazz
In?
this
guide tones and learn about two
E m7(
c section
˙ b5) weA˙ 7 will bdefine
˙ C m7 Ó F 7 . Fjm7œ . œjB b7# ˙ n œœE. b 7œœ Awwb7
chord voicings.
˙
œ œ
J
#
œ. œ
&c ˙
j ˙‰
jŒ
j
J
c
Ó
‰
j
& b œœœ ... œœœ œœœ ... œœœ .. œœœ
œœ b ˙˙˙
.
˙
b
œ
œ
˙
b
œ
œ
œ
˙
œ
. Tones
31.7.1
œ . œ .. œ
œ
b œ b..±n œœ wwb w
˙
? c EGuide
b
b
m7( 5) A 7
m7
F7
F m7
E 7
b ˙B 7
˙ the 3rd ˙Cand
b ˙A 7
˙of a chord.˙ In any
.
˙ ˙ are
˙
Guide
7th
circle
ofn œbfifths
progressions
? c Tones
j
#
˙
œ
#
˙
Ó
j œ . œ move by step.
œ ww
b˙
& ˙ ii–V–I˙˙and iii–vi–ii–V)
œ
(including
theœguide
. œ tones
.
J
œ. œ
J
F maj7
A m7 D m7
G m7 C 7
F maj7
? c G m7 C 7
˙
b˙
˙
b˙
˙
˙
˙
b
˙
±
˙
˙
3rd
7th
˙˙ b3rd
˙˙ 77th ww C m7
b7
5) A
F 7b c ˙ 3rd
F m7
B b 7 ˙ 3rd ˙E b7th
7
w
& b cE m7(
˙
˙
˙ 3rd w A3rd
7th # ˙ 3rd
7th
˙
3rd
7th
7th
7th
&c ˙
˙
? b c ˙G m7 ˙C 7 wF maj7
wF maj7
c ˙A m7 ˙D m7 ˙G m7 ˙C 7
b
?
˙ 7th
& cb c ˙˙7 3rd ˙˙ 7 7th wwM7˙ 3rd ˙ b c ˙˙ 73rd
b ˙ ˙˙7 3rd b˙˙˙7 7th wwbM7˙3rd
˙ vi˙7 3rd
F:˙ ii 7th V 3rd
I 7th
F: iii 7th
ii 7th V 3rd I 7th
27,
˙ dominant˙ 7th chords (C7–F7–B
Play through
with
˙ ˙the entire
w circle of fifths
w
33?
c
c
˙
˙
b
b
etc.) with Gthe
the left hand Aand
tonesC 7(3rd and
m7 bass
C 7 noteFin
maj7
m7 the
D m7guide
G m7
F maj77th) in
b hand
the&right
and
observe
how
the
3rd
and
7th
are
the
same
for
bass
notes a
F: ˙ii7 3rd ˙
V77th w
IM7 3rd
b cF: iii˙˙ 73rd vi˙˙7 7th ˙˙ii7 3rd V˙˙ 7 7th wwIM73rd
& b cfrom
tritone
each˙ other.
˙ 7th
w
7th
3rd
7th
3rd
3rd
7th
7th
C7
F 7 ˙ B b7 E b7 A b7 D b7
G b7
B7
E7
A7
D7
G7
?
˙ ˙
? bb6 c œ˙ b œ œ bwœ œ b œb c ˙ ˙
w
& 4 bœ œ bœ œ bœ œ
b b œœ # œœ n # œœ # n œœ n # œœ n œœ
F: ii7
V7
IM7
? 46 Cœ 7 Fœ7 b Bœb7 b Eœb7 A b7 b Dœ b7
œœ b œ œ b œ b œœ b œ
6
b
œ bœ œ bœ œ
&4
F: iii7
vi7
ii7
V7
IM7
3rd and 7th are enharmonically equivalent
33
tritone
b
b Gœ 7 n Bœ 7 œE 7 œA 7 œD 7 n œG 7
b b œœ # œœ n # œœ # n œœ n # œœ n œœ
27(49)—with the right hand
?
6 andœ 7(49)œ chords—C7(13)–F7(
b œ b œ b œ 49)–Bc 27(13)–E
chords
&
4
b
œ
n
œ
b
œ
nœ a
descending chromatically. This can be repeated with œall ofœ the bass
œ notes
4
35
3rd and
are enharmonically
equivalent
Also, you
can7thplay
through the
circle of fifths alternating between 7(13)
tritone away (starting on F in the left hand) and the qualities are exchanged
tritone
for?all the chords.
35
C 7(13) F 7(# 9) B b 7(13) E b 7(# 9) A b 7(13) D b 7(# 9)
œœ b b œœ
& 46 b œ œ
? 46 œ
œ
œ bœ
b œœ b œœ
bœ
bœ
œ nœ
b œœ n œœ
bœ
bœ
c
G b 7(13) B 7(# 9) E 7(13)
b b œœœ
bœ
A 7(# 9) D 7(13) G 7(# 9)
œ #œ nœ nœ bœ
# œœ # n œœ n # œœ # n œœ n œœ
nœ
œ œ nœ
œ
31.7.2 Jazz Chord Voicings
In this section we will examine two categories of voicings.
1. The first category (“spread” voicings) has 5-note chords with the root,
3rd, and 7th as the lowest notes with other chord members voiced above,
often in the interval of a fourth or fifth. (The root will always be the
lowest note, while the 3rd can be voiced above or below the 7th).
2. The second category (“close” voicings) has 5-note chords with the bass
note in the left hand and the other four notes in “close position” in the
CHAPTER 31. INTRODUCTION TO JAZZ THEORY
372
right hand, usually with the 7th or 3rd of the chord as the lowest note
in the right hand.
201
“Spread” voicings
37
C 9(13)
c ˙ voicings
“Spread”
&
˙ 13th
37
“Close” voicings
˙˙
C 9(13)
C 9(13)
7th
3rd
9th Root
˙
b˙
& c ?˙˙ c 13th
˙˙
b ˙˙˙ 9th
C 9(13)
b ˙˙˙˙ 9th
13th 7th
C 9(13)
“Close”
voicings
˙ 13th
9th
13th
˙˙ 3rd
˙˙ b9th
13th 7th
9th
C 9(13)
C 9(13)
3rd
7th
(lowest)
˙ 13th 3rd
b ˙˙˙ ˙9thRoot
7th
3rd
(lowest)
b ˙˙˙˙ 9th
13th 7th
C 9(13)
˙
Root3rd
b ˙ 7th
b ˙˙ 3rd
? cchords
7thdo not have a 3rd, and some do not have or a
˙˙ 3rd
Some
(like sus chords)
˙ Root
˙ Root
˙ Root
6
6
Root
(lowest)
(lowest)
39 C Root
7th (like
or C 9 ). In those cases, voice the sus4 like you would the 3rd, and
likewise&
voice the 6th as you would the 7th.
39
C 13sus
& ˙˙?
? b ˙˙˙
47
7th
sus
Root
&
43
˙˙
˙˙ sus b ˙˙˙˙sus
b ˙˙
C 13sus
b ˙˙
˙
C 13sus
sus
7th
Root
˙
6
˙
˙
6
C 13sus
C9
C9
˙
˙˙
˙
˙
˙
˙
˙˙
6th
3rd
Root
sus (4th) substituting for 3rd
6
3rd
6th
Root
˙˙
˙˙ 6th
6
C9
C9
(lowest)
˙
˙˙˙
˙ 6th
˙
6th substituting for 7th
?
Sometimes you will need to omit the fifth to maintain five parts.
&
31.8 Standard Chord Progressions
61
# ww
b www
202
#9
www
? w?II–V–I
31.8.1
63
67
w
w
b n www
˙
b ˙˙˙ # ˙
˙ b˙
w
# ˙˙˙ b n ˙˙
n˙
˙
b˙
The
is one of most common progressions in jazz, especially in tunes like
&II–V–I
7
7
7alt.
I7 Leaves,”VI“What
I7 “Tune-Up,”
¯III7
II7 “Pent
¯II7 Up
“Autumn
Is iiThis
ThingVCalled
Love,”
3rd phrase
House,” “Lady Bird,” and “Firm Roots,” to name
just a few. In major the
63
25)–G7alt–Cm 69 .
progression
is
Dmin9–G9(13)–C
∆
9.
In
minor
it
is
Dmin7(
?
&
D m9
& œœœœ?
71
?
&œ
69
#9
9(13)
7 # 5 focus only
D m9 on the ii–V–I
G7 #5
C 9(13) E b 9(13)
D 9(13)
D b 9(13)
In?
thisC55section
we Awill
progression
and the
iii–vi–ii–V
progression.
b w in Section˙ 9.3.n ˙˙
˙ b˙
w mentioned
& w& Bothn wwere
w already
?
G 9(13)
C maj9
œœœ
œ
˙˙˙
˙
˙
œ
D m9
œœœ
œ
œ
#9
6
Figure 31.8.1
Progression
in Major
D m9( b5)TheGII–V–I
7#
C m9
D m7( b 5)
b
& b b n œœœœ
? bb œ
b
b
&bb
71
? b
bb
bœ
b n œœœ
œ
5
˙
n ˙˙˙
˙
œœœ
œ
œ
G 9(13)
C maj7
œœœ
œ
œ
#9
G7 #5
b œœœ
œ
œ
˙˙˙
˙
˙
6
C m9
n ˙˙˙
˙
˙
201
œ
61
202
69
61
202
67
67
69
69
71
71
œœ
˙˙
œœ
#9
? œC 9(13)
œ# 9
œ
˙ D 9(13) D b9(13)
G7 #5
C 9(13) E b 9(13)
œ A 7 # 5 ˙ D m9
œ
CHAPTER
n www
wwwœ THEORY
www TOb bJAZZ
˙˙˙ n ˙˙˙ ˙ # ˙˙˙ b n b ˙˙˙ 373
& www 31. INTRODUCTION
#w
w
˙ n˙
bw
nw
b˙ #˙
#9
#9
D m7( b 5)
G7 #5
Cm
? bw D m9( b5) G 7 # 5 wC m
b
˙
˙ b˙
˙
wb œ#œ9
#9
w
& b Cb 9(13)n œœœœ
˙
b
bAn7œœ# 5
˙
œœœ E 9(13)n ˙˙D 9(13) D b9(13)
D˙m9
G7 #5 œ
C 9(13)
b
n
˙
œ
7
7
7
7alt.
7
7
œ
I
ii
V
I
n wwVIw
n¯III
˙˙˙7 ˙# II˙˙7 n ¯II
b
w
b
˙
w
w
˙
&
3rd
phrase
w
w
˙
ww˙
b n ww œ b ˙˙˙ œ # ˙ ˙ ˙˙ b n ˙˙
? bbwww œ
#w
b
œ
œ
œ
˙
? w
b
˙
w
˙ b˙
˙
D m9
G 9(13)
C maj9
G 9(13)
C maj7
w
w D m9
Figure
in
7
71
& œœœœI731.8.2 œœThe
˙˙˙ Progression
œ 7II–V–I
V7alt.
œœœMinor œœI7œ ¯III7 ˙˙ II7 ¯II7
bb b
œ VI
˙ ii
3rd phrase
˙
&
?
œ
œ
˙
31.8.2
œ III–VI–II–V˙
œ
œ
œ
D m9
Gprogression
9(13)
C maj9
D m9
G 9(13)
The
is called a turnaround
becauseC˙ maj7
it replaces the
? iii–vi–ii–V
b
staticbœharmony
of
the
I
chord
in
the
last
two
measures
of
a
tune
with harmonic
b
œœœ # ˙˙
& œœœthat leads
#9
œ
œ
˙
˙
motion
to
the
I
chord
that
will
occur
upon
repetition
9
œ
œ G7 #5 ˙ C m
œ D m7( b5)œœ G 7 # ˙ C mto the top of
D m9( b5)
the form.
This also applies
to the I–VI–II–V progression. 5 ˙
b
bœ b can
?
œ so all œfour
˙ ˙ are dominant
&One
˙ 7˙˙˙ 7turnaround
n œœœœ modify
b b7n œœœaœ iii–vi–ii–V
œœ7œ chords
œ
b
œ
œ
7
7
7
seventh chords: III –VI –IIn ˙–V (or V /vi–V
˙˙ 7 –A 7 –D 7 –G 7
œ œœ /ii–V /V–V˙7n —E
in ?
lead sheet symbols). Turnarounds made solely of dominant
seventh chords
œ
˙seventh chord
œ
œ
˙
b b b employ
can them
tritone
(substituting
a dominant
œ # 9 substitutions
œ
#
9
œ tones).
˙ m E 7 –A 7 –D 7 –G 7
b5)
b 5) GFor
a tritone away
have
D m9(because
G 7 #they
C m the same guide
D m7(
7 # 5 example,
C
5
7
7
7
7
b
2
2
becomes
–D .
& b b En œœœœ–E –D
˙
b bn œœœœ
œœœ show tritone
b œœœ substitutions
n ˙˙˙
n ˙˙˙
arrows
? bEbm7 œA m9 D m9 G 9(13) E˙7 A 7 D 7 œG 7
œE 7 E b7˙ D 7 D b7
b
œ
œ
& œœœœ œœœœ œœœœ œœœ # œœ # n œœ n # œœ œn œ
# œœ b n œœ ˙ # œœ n œ
œ
œ
œ
œ
˙
6
9
6
9
6
9
6
9
6
9
6
9
?œ
œ bœ œ bœ
œ m9 Dœ m9 Gœ 9(13) Eœ7 Aœ 7 Dœ 7 Gœ 7
E m7 A
E7
E b7
D7
D b7
œœœ œœœ œœœ # œ n œ # œ n œ
& œœœœ 31.8.3
# œœ shown
œœ Tritone
n œœ
œ #Progression
b n œœ #with
Figure
œ The
œ III–VI–II–V
œ n œ inœMajor and
œ
arrows show tritone substitutions
Substitutions
substitutions,
V7 .
?Because
œ 2 œ of tritone
œ œ the 72œII479 chord can œbe substituted
b œ œ for
œ
b
œ
In C, D 9(13) is oftenœ substituted for G 45 . œ
D m9
74
& c œœœœ
?c
œ
#9
G7 #5
tritone substitution
C maj9
bœ
b n œœœ
n ˙˙˙˙
œ
˙
identical voicings
D m9
D b 9(13)
C maj9
œœœ
œ
bœ
b n œœœ
n ˙˙˙˙
œ
bœ
˙
Figure 31.8.4 The 2II 7 substituting for V 7 in a Tritone Substitution
31.8.3 The Blues Progression
Below are two choruses of a common jazz version of the blues progression. The
first chorus uses the first category of voicings (“spread” voicings) while the
? c ˙˙
˙
3rd
3rd
Root
Root
˙
7th
7th
Root
Root
˙
Root
Root
Root
Root
CHAPTER 31. INTRODUCTION TO JAZZ THEORY
39
39
39
C
13sus
C 13sus
C
13sus
C 13sus
6
66
C
C 999
C
13sus
C 13sus
sus (4th) substituting for 3rd
43
43
43
6
66
C
C 999
&c
?c
ww
ww
w
F
F 9(13)
9(13)
ww
b ww
w
5th
5th
9th
9th
6th
6th
3rd
3rd
Root
Root
6
C:
C: II996
49
49
374
˙
˙
˙ 7th
second
with
b ˙˙˙˙sus (“close”
˙˙˙ sus category
& ˙chorus ˙uses the second
˙˙ voicings
˙
˙˙˙the 3rd˙˙˙ or6th
6th
sus
sus
as the ˙lowest note).
b˙
˙
2
6th
4
6th
Notice that˙ the
voicings for the A7 495 and E˙ 93rd
(13) are
identical (not
(lowest)
sus
(lowest)
sus
3rd
b
˙
b
˙
2
7th
6th
˙
˙
9
7th
6th
7th
?
˙
6th
counting
a tritone
7th because
sus
6th substitution
˙ the
˙ Root
˙ the ˙ E (13) ˙˙is 3rd
˙ Root
˙
˙ for the
sus roots)
3rd
2
4 Rootis true for the G7 49 Root
Root
A7 495 . Root
The same
and theRoot
D 9 (13) . The Roman
45
Root
numerals below
areforsimplified.
sus the
(4th) staves
substituting
3rd
6th substituting for 7th
C
13sus
C 13sus
C
C 9(13)
9(13)
& ww
? b www
II77
C
C 9(13)
9(13)
ww
b ww
w
9th
9th
13th
13th
3rd
3rd
7th
7th
Root
Root
7
IV
IV7
##9
9
A
A 77 ##55
nw
w
# ww
w
7
VI
VI7
II77
##9
9
C
C77 ##55
ww
nw
ww
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ii
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b b ww
n ww
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V
V7alt.
6
66
C
C 999
F
F 9(13)
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F 13sus
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b ˙˙
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9
G
G 77 ##55
6
66
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b ww
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1st
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D
D m9
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F
F 9(13)
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IV
IV7
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b ww
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7
IV
IV7
2nd
2nd phrase
phrase
b 9(13)
C
C 9(13)
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E b9(13)
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b ˙˙
b˙
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b˙
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b 9(13)
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D b9(13)
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II
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b b ˙˙
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55
6
66
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F 9(13)
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202
C 9(13)
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C
C 9(13)
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b www
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9
C
C77 ##55
(E respelled
b b bb wwww(E asrespelled
as F¯)
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II77
F
F 9(13)
9(13) F
F 13sus
13sus
F
F 9(13)
9(13)
b ˙˙˙˙ b ˙˙˙˙
7alt.
II7alt.
b wwww
w
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7
IV
IV7
7
IV
IV7
1st
1st phrase
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A7 #5
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2nd
2nd phrase
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b bn wwww
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V7alt.
C 9(13) E b 9(13)
˙˙˙ n ˙˙˙
b˙ #˙
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D 9(13) D b 9(13)
# ˙˙˙˙ b n b ˙˙˙
n˙
˙
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b˙
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67
Notice that the voice leading is very smooth for each part with the exception
of &
the bass line. All voices move by step or by 3rd.
31.9
? Scales
In this section on scales, our primary concern will be understanding how
scales relate to corresponding chords in order to allow one to improvise a jazz
solo. Similarly, understanding chord-scale relationships can allow one to write
&
?
&
˜
13. B9(13)
15. E¯7 ˜11
9
14. G¯69
16. A¯Δ9(˜5)
˜
CHAPTER 31. INTRODUCTION TO JAZZ THEORY
375
¯5) 9(¯5)
11 A¯m95. D7 ¯9
5. D69 (˜11)
B¯m9(¯5) 2. B7(˜5) 7. G3.Δ7(Em
1. 6.
G9sus
4. C˜m8.
¯5
chordal solos (like a sax soli or shout chorus in a jazz ensemble piece) where
˜11)corresponding
6. tones
GmΔ9come 7.
A¯Δ9(
8. D¯69 scale.9. E¯Δ9(˜5)
10. FΔ7(¯5)
non-chord
from
the
¯5
4
¯3
j
j
j
13
7
9
œ
œ 11. E ‰susœ ‰ b œ 12.
‰ D¯œ ˜˜5 ‰ j œ
The blues scale is identical to the minor pentatonic scale (1̂ –23̂ –4̂ –5̂ –œ27̂ )
31.9.1 The Blues
Scale œ
add94 œ
9. C˜mΔ7
10. F˜V
4
8ˆ
¯7ˆ
5ˆ
ˆ
ˆ
ˆ
except with an added 25̂ /44̂ (1̂ –23̂ –4̂ –25̂ –5̂ –27̂ ).
4 œ œ œ b œ 7 11
&69 4
œ ˜9œ œ
G¯
15. E¯
˜
8ˆ
13. B9(13)
14.
¯7ˆ
5ˆ
¯5ˆ
4ˆ
¯3ˆ
1ˆ
16. A¯Δ9(˜5)
Figure 31.9.1
The Blues Scale
(Descending)11
1. G9sus
2. B7(˜5)
3. Em9(¯5)
4. C˜m
5. D7 ¯9
¯5
A
well-known
example
of
the
blues
scale
occurs
in
“Sunshine of Your Love”
6. GmΔ9
7. A¯Δ9(˜11)
8. D¯69
9. E¯Δ9(˜5)
10. FΔ7(¯5)
by Cream.
&
¯5
4
¯3
4 œ œ œ œ ‰ œj ‰ b œj ‰ j ‰ j
V4
œ
œ œ
8ˆ
¯7ˆ
5ˆ
ˆ
ˆ
ˆ
1ˆ
œ
& 44 œ œ œ b œ œ œYT:œKWKXNoKgLQU
&
Figure 31.9.2 Jack Bruce and Eric Clapton, “Sunshine of Your Love”
In the blues scale, the 25̂ and 23̂ are considered to be “blue notes” because
they are not chord tones (of a major triad or dominant 7th chord). Blue notes
are commonly used in jazz and popular music.
In terms of using the blues scale as a soloist, you will find that some players
use the blues scale over any and every chord, and that listeners’ ears often find
this acceptable.
31.9.2 The Bebop Scale
The bebop scale (known more specifically as the “bebop dominant” scale in
jazz theory texts) is identical to the Mixolydian scale except is has an added
↑7̂ . The added chromatic note (↑7̂ ) occurs in descending passages (from 8̂ –7̂
–27̂ ) as a chromatic passing tone. The bebop scale is most often used over the
dominant 7th chord. In the most rudimentary form of improvising, one can
use the bebop scale in descending eighth notes beginning on the downbeat of
a measure, starting on the root, 3rd, 5th, or 7th.
1ˆ
œ
4 œ œ œ bœ
&4
œ œ œ
CHAPTER 31. INTRODUCTION TO JAZZ THEORY
8ˆ
¯7ˆ
5ˆ ¯5ˆ
4ˆ
¯3ˆ
1ˆ
& 44 œ œ b œ œ œ œ œ œ w
Root
œœœœœ
œ bœ œ w
&
5th
376
œ œ œ œ bœ œ
œœ w
3rd
b œ7thœ œ œ œ
œ œ nœ bw
Figure 31.9.3 Descending C Bebop Scale starting on Root, then 3rd, then
5th, then 7th
31.9.3 Table of Scales
The scales below are represented by scale degrees. Synthetic scales like whole
tone, diminished, and diminished-whole tone have many acceptable enharmonic respellings.
Table 31.9.4 Table of Scales
CLASSICAL SCALES
Major (“Ionian”)
1̂ –2̂ –3̂ –4̂ –5̂ –6̂ –7̂
Natural Minor (“Aeolian”)
1̂ –2̂ –23̂ –4̂ –5̂ –26̂ –27̂
Harmonic Minor
1̂ –2̂ –23̂ –4̂ –5̂ –26̂ –7̂
Melodic Minor
1̂ –2̂ –23̂ –4̂ –5̂ –6̂ –7̂
MODES AND HYBRID MODES
Mixolydian
1̂ –2̂ –3̂ –4̂ –5̂ –6̂ –27̂
Lydian
1̂ –2̂ –3̂ –44̂ –5̂ –6̂ –7̂
Dorian
1̂ –2̂ –23̂ –4̂ –5̂ –6̂ –27̂
Phrygian
1̂ –22̂ –23̂ –4̂ –5̂ –26̂ –27̂
Locrian
1̂ –22̂ –23̂ –4̂ –25̂ –26̂ –27̂
Locrian 42
(6th mode Melodic Minor)
1̂ –2̂ –23̂ –4̂ –25̂ –26̂ –27̂
Lydian-Dominant
(4th mode Melodic Minor)
1̂ –2̂ –3̂ –44̂ –5̂ –6̂ –27̂
Phrygian-Dorian
(2nd mode Melodic Minor)
1̂ –22̂ –23̂ –4̂ –5̂ –6̂ –27̂
Lydian-Augmented
(3rd mode Melodic Minor)
1̂ –2̂ –3̂ –44̂ –45̂ –6̂ –7̂
Mixolydian-26̂
(5th mode Melodic Minor)
1̂ –2̂ –3̂ –4̂ –5̂ –26̂ –27̂
JAZZ AND SYNTHETIC
Blues
1̂ –23̂ –4̂ –25̂ –5̂ –27̂
Bebop Dominant
1̂ –2̂ –3̂ –4̂ –5̂ –6̂ –27̂ –7̂
Bebop Major
1̂ –2̂ –3̂ –4̂ –5̂ –45̂ –6̂ –7̂
Whole Tone
1̂ –2̂ –3̂ –44̂ –45̂ –27̂
Octatonic (Half-Whole)
(“Diminished” scale)
1̂ –22̂ –23̂ –3̂ –44̂ –5̂ –6̂ –27̂
Octatonic (Whole-Half)
(“Diminished” scale)
1̂ –2̂ –23̂ –4̂ –44̂ –45̂ –6̂ –7̂
Diminished-Whole Tone
(also “Altered” scale or
7th mode Melodic Minor)
1̂ –22̂ –23̂ –24̂ –25̂ –26̂ –27̂
CHAPTER 31. INTRODUCTION TO JAZZ THEORY
377
31.10 How to Determine Chord-Scale Relationships
To discover a chord-scale relationship for almost any chord, write all of the
notes of the chord (including upper extensions and altered notes), then fill
in the thirds with the most logical choices, avoiding augmented seconds and
consecutive half steps.
In the example below, we determine the scale that best fits G∆7 (411) by
doing the following:
1. Identify the notes in the chord
2. Write all chord tones as a scale within the span of an octave
3. Fill in any gaps, avoiding augmented 2nds and consecutive half steps
4. Analyze the resulting scale
Identify notes
in chord
G maj7 ( # 11)
& # # www
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49
Write notes as scale
within an 8ve span
œ
root
(gap)
œ #œ œ
3rd ˜11 5th
#7th
œ
(gap)
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and consective half steps
œ #œ œ
œ
#
œ
œ
œ
œ
w w
h
w
w
w
h
Figure 31.10.1 How to Determine a Scale for a Chord
&
The G Lydian scale is the most correct scale to play over G∆7 (411) .
Principle 31.10.2 Determining Chord-Scale Relationships. When constructing the scale, avoid augmented seconds and consecutive half steps
31.10.1
List of Chord-Scale Relationships
&
Below is a list of common chord-scale relationships. When there are two scales
listed for a single chord, it is because the chord has a minor third that can
be filled with half step then whole step or whole step then half step. This
knowledge of chord-scale relationships ultimately becomes second nature to an
improvising jazz musician.
&
CHAPTER 31. INTRODUCTION TO JAZZ THEORY
378
Table 31.10.3 List of Chord-Scale Relationships
CHORD
C∆7
C∆7 (411)
C∆7 (45)
Cm7
Cø 7
Cø 9
C◦ 7
Cm ∆7
Cm 69
C7
C7 (411)
C7 (45)
C7 (25)
C7 (29)
C7 (49) 4
C13 411
9
C7 alt
CORRESPONDING SCALE(S)
C major scale or C Lydian scale
C Lydian scale
C Lydian-Augmented scale
C dorian scale or C natural minor
C locrian scale or C locrian 42
C locrian 42
C Octatonic Whole-Half
C melodic minor ascending
C Dorian or C melodic minor ascending
C Mixolydian
C Lydian-Dominant
C Whole Tone scale
C Whole Tone scale
C Octatonic (Half-Whole)
C Octatonic (Half-Whole)
C Octatonic (Half-Whole)
C Diminished-Whole Tone
This list is not exhaustive. Follow the process above (“How to Determine
Chord-Scale Relationships”) for chords not listed in this list.
Additionally, it is often important to look at the relationship of a chord to
the overall key of a tune to determine the appropriate scale. For example, the
Fmin7 at the beginning of “All The Things You Are” by Jerome Kern is the
vi7 chord in A2 major, in which case it would be inappropriate to play an F
Dorian scale because the D6 would conflict with the D2 in the key signature.
One would play an F natural minor (or Aeolian) scale instead.
Identify notes
Fill in gaps, avoiding aug. 2nds
Write notes as scale
in chord
31.11
Harmonizing
the
Bebop
Scale
and consective half steps
within
an
8ve
span
Identify
notes
#
(
)
G maj7 11
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in chord
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and consective
half stepsfor harwithin
an
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In The GJazz
Mark Levine provides
a method
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monizing
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w w œ w# œ h œ œ
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o
B 7
o
B 7
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o
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o
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Figure 31.11.1 Four-Part Harmonization of the Bebop Scale in Major
&
&
C6
C m6
o
o
B 7
B 7
œœœ b œœœœ
bœ œ
œ
b œœœ b œœœ
C m6
C6
C m6
o
o
B 7
B 7
C m6
bn œœœ b œœœœ
œ
bn œœœ b œœœœ
œ
C m6
o
o
B 7
B 7
C m6
o
o
Bœ7
B 7
C m6
C m6
b œœœœ # œœœœ n œœœœ b œœœ
œ
b œœœœ # œœœœ n œœœœ b œœœ
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&Notice that all of the non-tonic chords are vii◦7 chords in various inversions.
&
Figure 31.11.2 Four-Part Harmonization of the Bebop Scale in Minor
49
49
CHAPTER 31. INTRODUCTION TO JAZZ THEORY
379 47
47
One hears a similar approach to harmonizing a scale (though without the
# w
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_____
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_____
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( 11)
## ww
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F
5.
F˜˜m
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?
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b
bb w
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b ww
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1.
2.
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31.12 Practice
Exercises
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5.
6.
7.
8.
5. _____
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6. _____
_____
7. _____
_____ respell notes
8. _____
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it is sometimes
to enharmonically
B4, F2, E4 and altered notes like 45 and 49.
?
?
9
1.
1. G
G9sus
sus
&
&
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6.
6. Gm
GmΔ9
Δ9(˜11)
7.
7. A¯
A¯Δ9(˜11)
?
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Jazz Theory: Day Two
2.
2
2.
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6
?
11
3.
C 7( b 9)
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3.
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11
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7 ¯9
5.
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5. D
D7 ¯9
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6
8.
8. D¯
D¯699
Δ9(˜5)
9.
9. E¯
E¯Δ9(˜5)
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10.
10. F
FΔ7(¯5)
4.
C 7(# 9)
_
9
C 7+
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b www
b bb www ¯5 ¯9
b ww following
b ww chords busing
b b wwwchords symbols.
b
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respell 5 to agree with ¯7 wrespell ˜9 to agree
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15
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&
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6. _____
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b
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b ww b b n www
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Jazz Theory: Day Three
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9. _____ always for10.the
_____
11.voices,
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12. _____
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the rest
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?
&
19
&
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9
b b www
15. _____
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47
?c ˙
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b˙
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CHAPTER 31. INTRODUCTION TO JAZZ THEORY
Db 9
6
79
& c b b ˙˙˙
b˙
? c b˙
50
50
50
79
#9
A7 #5
& c ˙˙
&
#˙
?c ˙
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76
82
#9
C7 #5
˙
F 13sus
˙
E b 7(# 9)
b˙
b˙
#˙
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F # 9sus
G 9(13)
#w
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?1.c_________________________
b˙
˙
1. _________________________ ˙
bb œœ bb œœ bb œœ œœ
bœ bœ bœ œ
_________________________
3. _________________________
&3. _________________________
œœ bb œœ bb œœ
œ
b
œ
œ
œ
b
bœ
bœ
&
& b œ bb œœ œœ œœ b œ œ b œ b œ
&? b œ
5.
5. _________________________
5. _________________________
5. _________________________
Please
& write the following scales.
&
&
&&
6
#˙
5
## œœ
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203
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1. _________________________
82 3.
E maj9(13)
˙
Jazz Theory: Day Four
95
#9
6 the following
4. Please name
scales.
Db 9
C7 #
F 13sus
bœ bœ
&
& œœ œœ b œ bb œœ
& œ œ bœ
B 13sus
380
## œœ # œ n œ# w b œ œ œ
#œ nœ
# œ # œ n œ bb œœ œœ œœ ## œœ
2. _________________________ # œ
B 13sus
E maj9(13)
2. _________________________
˙
2. _________________________
w
bœ
œœ œœ œœ ## œœ ## œœ bb œœ
œ œ œ #œ #œ
4. _________________________
4. _________________________
4. _________________________
œœ
œ
bœ bœ bœ œ
œœ bb œœ bb œœ œœ b œ bb œœ bb œœ œœ
bœ bœ œ bœ
6. œ
_________________________
6. _________________________
6. _________________________
95
1. E Lydian-Dominant
?
?
?
?
&
&
& Day Five
Jazz Theory:
3. F Diminished-Whole Tone
6.
52
2. B¯ Phrygian-Dorian
4. E¯ Octatonic (Whole-Half)
List the appropriate scale for the each chord by writing the chord
tones then filling in the gaps. Avoid writing consecutive half steps
and
& augmented seconds when constructing the scale.
& 7( )
&1. E¯ ˜ ; Scale: ____________________________
&
5
&
&2. B¯7¯5˜9; Scale: ____________________________
&
?
&
&3. Fm7(¯5); Scale: ____________________________
&
&
7(˜5)
1.
1. E¯
E¯7(˜5);; Scale:
Scale: ____________________________
____________________________
1. E¯7(˜5); Scale: ____________________________
&
&
&
CHAPTER 31. INTRODUCTION TO JAZZ THEORY
381
7˜9; Scale: ____________________________
2.
˜9 Scale: ____________________________
2. B¯
B¯7¯5
˜¯59;; Scale:
2. B¯7¯5
____________________________
?
?
?
7(¯5)
3.
3. Fm
Fm7(¯5);; Scale:
Scale: ____________________________
____________________________
3. Fm7(¯5); Scale: ____________________________
&
&
&
Δ7(˜5)
4.
4. A¯
A¯Δ7(˜5);; Scale:
Scale: ____________________________
____________________________
4. A¯Δ7(˜5); Scale: ____________________________
?
?
?
Click here to download the first homework assignment for this chapter.
Click here
download the second homework assignment for this chapter.
?
? to
?
Click here
to download the third homework assignment for this chapter.
Click here to download the fourth homework assignment for this chapter.
Click here to download the fifth homework assignment for this chapter.
Click here to download the sixth homework assignment for this chapter.
?
Click here
? to download the Unit 11 Practice Test.
?
PDF versions
of the textbook, homework exercises, and practice exercises
can be found at musictheory.pugetsound.edu
Chapter 32
Impressionism and Extended
Tonality
204
91
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in the music of Debussy and Ravel: (1) the use of modes, (2) the use of upœ
œ
˙
c œœ the 7th
b œ in chord
œ
b œ construction
& above
per extensions
in tertian harmonies (9ths,
bœ
11ths, and 13ths, which we saw in the chapter on jazz), and (3) parallelism,
also known as “planing.”
œ
? c bœ
93
97
1. Use of modes. Composers such as Debussy and Ravel sometimes wrote
in the church modes (Phrygian, Lydian, etc.—see Scales) as an alternative to the heavily chromatic music of Richard Wagner (listen to the
influential Prelude to Act I of Wagner’s Tristan œund Isolde).
&c Œ
œ
œ b œœ
˙˙ ..
œœ b œœ œœœ œœ
b œœ
Ó
˙
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# œœ b œœ n œ of Debussy’s
#˙.
b œStringœ Quartet inœ G bminor,
(a) The first #movement
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10, begins in Phrygian mode.
Notice
that
the
seventh
chord
that
˙˙˙ ...
b œœœ b œœœ # œœœ # # œœœ in œœœPhrygian.
? c on
œœœ n5̂œœœ scale
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is half-diminished
Π#the
b b œœœ degree
Ó
penultimate chord in this example is not in Phrygian mode.)
b
&b c œ
œ
Gm
? bb c œ
œ
g: i
&b
100
b
? b
ø
D 7/A b
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ø
ø D 7/F
D 7/A b 3
ø
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j
œœ b œœ œ œ œœ œœ
j
œœ œ
œœ b œœ
œ
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i
vø43
j
œ
œ
j
œ
œ
i
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b œ32.1.1
œ œ Debussy, String Quartet in G minor, Op. 10, I.
Figure
(b) The second movement (“Danse profane”) of Debussy’s Danses begins in Lydian mode.
382
? bb c œ
œ
b œœ
# Strings
& # 43 Œ
π
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? # # 43 ˙ .
-̇ .
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CHAPTER 32. IMPRESSIONISM
TONALITY
g: i
vø43
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i vø43
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5
100
.
Œ #œ
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383
i
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YT:
5YFNOsSyv3I
Figure 32.1.2 Debussy, Danses, II. Danse profane
(c) The first movement of Ravel’s Piano Trio Ravel begins in the Dorian
mode. Notice that the penultimate chord is outside of the mode.
.
œœœ. œœœ .. œœ œœœ .. # œœœ œœœ
8
.
.
&8
#œ
J
π
œ.
œ.
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°
104
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8
.
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.
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&
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J Trio, I.
? 843 32.1.3# œRavel, Piano
Figure
π
œ. firstœ. movement
œ of Ravel’s Piano
œ.
œ. Ravel
œ transAt the end of the
Trio,
? 88 the
œ
forms
Œ theme by placing it inœ the Lydian mode. In this example,
œ
120 final two chords are outside of the
the
Lydian
mode.
°
&
.j .
.
. œ
#
œ
œ
œ œœ .. œœ œœ .. œœ œœ œœ
œ œœ .. œœ œœ .. œœ œj b œœ
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œ
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&
œ œ . # œ œ . œ n œœ n œ
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104
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106
128
&
? 43
&
205
108
YT:
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Figure
? 3 32.1.4 Ravel, Piano Trio, I.
4
2. Use of upper extensions in chords. Debussy and Ravel used chords containing ninths, elevenths, and thirteenths, sometimes with chromatic al128 to those upper extensions.
terations
(a) In&bar 15 of Debussy’s “Clair de lune” from his Suite bergamasque,
2
Debussy uses an E m9 chord with the 9th of the chord in the
melody.
?
205
œœ . # œœœ #œœœ.
.
.
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œ.
œ
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œ
?
? w8IMPRESSIONISM
CHAPTER 32.
AND
EXTENDED
TONALITY
384
∑
œ
Œ
& œœ
8
106
œœ œ Jœœ
J. -
œœ
.
°
œœ- œœ œœ- œœ-. œœ- œœ- œœ- œœ- œœ- œœ- œœ- œœ- œ.
98 ‰ œJ œ œ œœj œ - œ œ .œ œœ œœ œœ œ œœ .. . œœ .. 2 œ œœ .. # œœ œœ œœ
œœ œœ .. œ œœ .. œœ j œ
Ϲ
œ œ . # œœ 2 œ . œ n œœœ n b œœ
. # œœ œ . œ J œ
.
2
2
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9 ‰ œj œ œ œ œ œ œ .œ œ œ œ œ
. 205
bb b b lointain
.
8
&
œ
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.
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8
. #œ .
. # œ . œ n œ # œœ
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œ
110
bπb[ E¯m(add9) ] œ- œ - - - - - - - - - b
b
œ
œ
œ
& b
œ. œ œ. œ œœ œ œ œœ œœ œ. œœ œœœ. œœ œœ œ œœ œ- .
? 88b b bŒb 9 ‰ œJ œ œYT:œœ œ œ œ œ œœ œœ œœ œœ œœ ..
& b 8
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2
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Figure 32.1.5 Debussy,
Suite
bergamasque,
III.
Clair
de
lune
2
2
.
.
j .j .
?
9
b
‰
œ
b
œ
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b bœœœDebussy’s
2 7œ œœJ œ-œ œ- œ- œœ œ- œœ ..œ- # œœ œ- œœ .. œ- œœœ- n œœ œ-n b œœœ œ&
œ
œ
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ludes, contains a D in. the- left hand with the notes in
J. ˙
.
handπalternating
between the 49 and. the 29.
lointain
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7( 9)
b.b b
b
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[ E¯m(add9) ]
108
104
108
106
(b)
110
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& b [bE¯m
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108
2
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114
110
(c)
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œœ
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œ
3
œ-œ- œ œ-n œ œ- n œœ- . œ-œ œ œœ-œ
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œ
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Figure 32.1.6˜9Debussy,
Préludes, Book II, No. 3, La Puerto del
¯9
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Vino
b
n
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n ˙˙
˙˙
n ˙˙
¯7
b
? bbb bb b 42 ˙ 3rd
b
œ
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œ piece,
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. 5thsame
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D¯7 ˜11
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b
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? b b b n ˙˙ 3rd
bb
œ
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‰ n n œœ œœ œœ œ
nœ
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n ˙˙
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n n œœ ..
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3
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right hand, in addition to the 49 and 29.
114
œ
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YT:
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Figure 32.1.7 Debussy, Préludes, Book II, No. 3, La Puerto del
Vino
CHAPTER 32. IMPRESSIONISM AND EXTENDED TONALITY
385
3. Use of parallelism (also known as “planing”). In contrast to the prohibition against parallel fifths and octaves in traditional voice leading, both
Debussy and Ravel would take a chord voicing and move all voices in
parallel motion.
(a) In Pavane pour une infante défunte, Ravel writes dominant 9th
chords in parallel motion in bar 27.
E9
206
>
j ‰ œ
œœ
œ
#œ
œ
#
& c œ
# œœœ
117
?# c œ
œ
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119
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44
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>
n œœœ
f
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œ # œ n n œœ # # œœ œœœ
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œ
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U
œ
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œ
œ
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ww
3
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7
œ œ bœ nœ œ nœ bœ œ œ
Œ
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œ
w
w YT:
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Figure 32.1.8 Ravel, Pavane pour une
œ infante
œ ˙ . défuntew
œœ œœ ˙˙ ..
ww
œ œ ˙.
w
?
#
4
J
At 5 bars
after
rehearsal
number
5
in
Prelude
to
the
Afternoon
of
4
Kor - ah,
Syahd - ho,
a Faun, Debussy writes chromatically ascending
dominant seventh
3
chords.
48
3
& 4 bœ
.
Horn
G7
48
48
œ& 43 œ
Strings
? 43 œœ
œ
œ.
œ.
A¯7
œœ
b œœ
bœ
œ.
œ.
œ.
bœ
A7
b œbœ
n b œœ
nœ
œ
œ
G7
A¯7
œœ
œ
b œœ
bœ
œ
œ
œ
œ
œ
œ
œ
A7
bœ
bœ
n b œœ
nœ
parallel voicings
∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
& ∑ ∑ ∑ ∑ ∑ ∑ ∑ YT:
50
9_7loz-HWUM
&∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
50
Figure 32.1.9 Debussy, Prelude to the Afternoon of a Faun
(c) At 4 bars after rehearsal number 2 in the same piece, Debussy moves
seventh
chords in parallel motion. Notice that the chords are not
50
all?of the same quality.
∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑
? 3 œœ
4 œ
48
bœ
nœ
nœ
b œœ
bœ
bœ
nœ
nœ
b œœ
bœ
œœ
œ
CHAPTER 32. IMPRESSIONISM AND EXTENDED TONALITY
parallel voicings
50
3
50
50
œ œ œ œ œ.
.
# # # # Flute
9 œ œ œ nœ nœ œ œ œ œ œ œ
&
8
# ## 9
& # 8 n œœ
œ ..
Strings
? # # # # 98 n œ
3
3
nœ
œ
F˜ø7
# œœ œœœ
#œ œ
œ nœ
3
Bm7 Am7 F˜ø7
Bm7 Am7
œ
œ œ
n œœ n œ
œ n œœ
œ
œœ
œ
œ
386
œœ œ
œ œœ
parallel voicings
F˜ø7
j
œœ
nœ
œ
J
YT:
9_7loz-HWUM
Figure 32.1.10 Debussy, Prelude to the Afternoon of a Faun
32.2 Pandiatonicism
Pandiatonicism refers to the use of all diatonic notes without the need for
scale degrees or harmonies to progress or function tonally (V doesn’t need to
progress to I, 7̂ doesn’t need to resolve to 8̂ , etc.). One often hears it as
a wash of notes from the major scale, or as chords made of non-traditional
combinations of notes from a major scale, often with at least one interval of a
2nd in a chord voicing.
In the first example, notice how Stravinsky creates a wash of sound from
the notes of the major scale.
YouTube: https://www.youtube.com/watch?v=XkM4bKjggKo
Figure 32.2.1 Stravinsky, Petrushka, Fourth Tableau: The Shrovetide Fair
(Toward Evening)
In the second example, Copland uses non-traditional pandiatonic chord
shapes in non-functional harmonic progression.
œœ ‰
œœ
J
>
?# c œ
œ
œœ
œ œœ œœ œœ
œ > >
>
CHAPTER 32. IMPRESSIONISM AND EXTENDED TONALITY
119
&
### œ
? ###
120
&
###
œ
œ
œœ
œ
œœ
>
œœ
387
parallel voicings
œ
œœ
œ
œœ
œ
œ
œœ
œ
œ
œ
œœ
œ
œœ
œ
œ
c
? ### c
YouTube: https://www.youtube.com/watch?v=WVahuS9hk_s
Figure 32.2.2 Copland, Appalachian Spring
The third example is similar to the first, with Copland creating a wash
of sound from the notes of the major scale, with no regard to the dissonant
intervals occurring in counterpoint.
YouTube: https://www.youtube.com/watch?v=WVahuS9hk_s
Figure 32.2.3 Copland, Appalachian Spring
32.3 Quartal, Quintal, and Secundal Harmony
Quartal harmony refers to chords stacked entirely (or mostly) in fourths.
Quintal harmony refers to chords stacked entirely (or mostly) in fifths. Secundal harmony refers to chords stacked entirely (or mostly) in seconds.
Contrast these concepts with the tertian (stacked in thirds) harmony we’ve
encountered in the majority of this text. Alternative methods of stacking
chords became more common after 1900 as composers sought ways to innovate
and break with the past.
The next three examples demonstrate quartal harmony.
CHAPTER 32. IMPRESSIONISM AND EXTENDED TONALITY
388
YouTube: https://www.youtube.com/watch?v=m_hMVzPT9f4
Figure 32.3.1 Schoenberg, Chamber Symphony No. 1, Op. 9
YT: D5-bD372v5s
Figure 32.3.2 John Parker, CHiPs Theme
YT: AQFxpN30DMU
Figure 32.3.3 Merv Griffin and Julann Wright, Jeopardy! Theme
The following is an extended example of quintal harmony.
YouTube: https://www.youtube.com/watch?v=IfOJCKN148M
Figure 32.3.4 Bartók, Piano Concerto No. 2, II.
32.4 Polychords
A polychord typically consists of two triads sounding simultaneously. A polychord could also consist of two seventh chords, or a seventh chord and triad.
Additionally, a polychord could conceivably consist of more than two triads or
seventh chords, since the prefix “poly” means “many.”
Perhaps the most famous polychord is the “Rite of Spring chord,” an E2 7
chord sounding over an F2 major chord, which occurs during the “Dance of the
Adolescents.”
206
? ###
un peu plus lent
U
> >
> > >
# c
j
‰
&
œœ n œœAND EXTENDED
œœ œ
CHAPTER
389œ
œœœ IMPRESSIONISM
œœ b œœ œœTONALITY
œœ
#32.
n
œ
œ
#
œ
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œ
n
œ
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œ
œ
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n œ # œ œœœ
f
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œ
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œ
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œ
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120
œ
œœ F¯œœ œ œœ œœ œ
œœ
J
œ > >
> >
>
117
119
&
### œ
parallel voicings
œ
œ
œœ
? ###
120
& b b œœ
b œœ
œ
œ
œ
œœ
œœ
? b b œœœ
b b œœ
œ
œ
œ
œœ
œ
œœ
œ
œœ
œ
121
E¯7
F¯
&
& b b œœ
b œœ
? b b œœ
b b œœhttps://www.youtube.com/watch?v=BKoO_3-I1dw
YouTube:
?
Figure 32.4.1 Stravinsky, Rite of Spring, “Dance of the Adolescents”
Polychords are notated using a horizontal line between the chords instead
of a slash. (The slash was used for slash chords.)
121
&
?
A¯
A
b b œœœ
# œœœ
(horizontal line means
chord over chord)
b b œœœ
A¯/A (slash means chord
over bass note)
nœ
nœ
Also note that it is not necessary to specify the inversion of each of the
chords in the polychord.
In th example below, Copland voices an A major chord below an E major
chord.
œ
CHAPTER 32. IMPRESSIONISM AND EXTENDED TONALITY
390
53
&
###
A major triad
œ
œ
œ
œ
œ
E major triad
E
A
œ
œœ
œœœ
œ
##
& #
YouTube: https://www.youtube.com/watch?v=WVahuS9hk_s
Figure 32.4.2 Copland, Appalachian Spring
In the example below, features chromatically ascending dominant seventh
chords in the left hand against a repeating three-chord cycle of G–F–C in the
right hand.
YouTube: https://www.youtube.com/watch?v=XkM4bKjggKo
Figure 32.4.3 Stravinsky, Petrushka, Fourth Tableau: The Shrovetide Fair
(Toward Evening)
32.5 Practice
& c œœœ .. œœœExercises
œœœ œœ œœ œ
.
œ œ œœ
C
123
F
C
F
C
G 7/D C/E
œœ
œ
D m/F
G7
œœ œ œœœ
C
G 7/B C
œœ œœ œœœ
œ œ
Day One
? of
c modes.
œ œ and chord symbols
1. Use
the
œ . œ œGiven
œ melody
œ forœ “London
œ
œ
œ
œ
Bridge” in Phrygian mode, analyze the chords as lead-sheet symbols
(“LSS”) and as Roman numerals (“RN”).
LSS:
___
b
& b b c œœœ ..
.
125
? bb c œ .
b
RN:
2.
___
___ ___ ___ ___ ___ ___
œœœ œœœ œœ œœ œ œœ
œ œ œœ œ
œ œ
bœ œ
œ œ
___ ___ ___ ___ ___ ___
___
___
___ ___ ___
b œœ œ b œœœ
œœ œœ œœœ
œ œ
œ
œ œ œ
___
___ ___ ___
œ
___
Use of parallelism. Harmonize the opening of “London Bridge” so
each
note of the melody noteø7is the 9th of a dominant
ninth
ø7
ø7 chord.
127
b
&bb
? b
bb
Cm
i
Fm Cm Fm Cm G /D¯ Cm
iv i iv
i vø43 i6
D¯/F
N6
G
vø7
Cm G /B¯ Cm
i vø65 i
207
? ### c
˙
RN:
˙
___
˙
œ œ ˙
D¯/F
G
___ ___ ___ ___ ___ ___
˙
˙
Fm Cm Fm Cm Gø7/D¯ Cm
Cm
___
˙
___
___ ___ ___
ø7
Cm Gø7/B¯ Cm
391
i vø65 i
CHAPTER 32. IMPRESSIONISM
AND
i
iv i EXTENDED
iv
i vø4 i6TONALITY
N6
vø7
RN:
LSS:
127
___
___
___
___
&
œ c b œœœ œ œ œ
___
___
___
___
___
œ
œ
? c œœœ
? c œœœ
135
F9
LSS:
F9
& c b œœ
133
___
3
___
œ
___
___
___ ___
nœ
œ
___
œ
___
___ ___ ___
œ
___
Day Two
LSS:
___128 and
___Secundal
___Harmony.
___
___ analyzing
___
___given
___ ___
3. Quartal,
Quintal,
After
the
chord as a lead-sheet
& symbol, revoice it in four ways:
&c
(a) as a six-note tertian chord stacked only in thirds
? quartal chord stacked only in perfect 4ths
(b) as a six-note
?c
(c) as a six-note quintal chord stacked only in perfect 5ths
(d)
secundal
chord
RN:as a six-note
___
___
___ stacked
___ only
___in 2nds
___
LSS: ____
139
&
149
4.
154
w
ww
(1) in 3rds
(2) in 4ths
(3) in 5ths
___ ___ ___
(4) in 2nds
209
b www ww
?
b
& w w
LSS: ____
(1) in 3rds
(2) in 4ths
(3) in 5ths
(4) in 2nds
Polychords.
b w Harmonize “London Bridge” using the specified poly? b wRemember that the chords can be in any inversion, but should
chords.
bw
should be playable (i.e., without too big of a stretch for the hands of
the pianist).
D¯
E¯+
B¯
Cm
D
C¯
Dm
___
__
__
___
__
___
__
C¯
b œœ
& c b b b b œœœœ
D¯
E¯
œ
œ
A
bœ
B¯
œ
F
bœ
Gm
˙
?c
D
¯
E
¯+
B
Cm
D
C¯
Dm
__
___
__
___
___
__
__¯
Click here to download the first homework
assignment for this
chapter.
C¯
D¯
E¯
A
B¯
F
Gm
156Click here to download the second homework assignment for this chap˙˙
ter.
b œœ
b œœ
b œœ
n œœ
œ b b œœ
& c b b b b œœœœ
?c
158
&
?
œœ
b
b œœ
nb
b
œœœ
œ
n œœ
n # œœ
(lower chords can be any inversion)
# b n œœœœœ b n n œœœ b n ˙˙˙˙
œ
Chapter 33
Set Theory
33.1 Set Theory
Set theory is the analytical technique we will use to analyze expressionist music. The primary composers associated with expressionism are Arnold Schoenberg (1874–1951), Anton Webern (1883–1945), and Alban Berg (1885–1935).
In this text, we will associate atonal music—music that avoids traditional
harmonies and scales—with expressionism. Instead of scales and chords, intervals are the building blocks of Expressionist music. Although composers
began writing atonal music in 1908, there was no widely-accepted systematic
analytical approach that could show relationships between different pieces until Allen Forte published his seminal The Structure of Atonal Music in 1973, in
which Forte applied set theory mathematics to music. However, our approach
to normal form and prime form will follow the slightly-modified approach set
out by John Rahn in his Basic Atonal Theory (1980), which is the approach
followed by Joseph Straus in his well-known and widely-used Introduction to
Post-Tonal Theory.1
33.1.1 Atonal Music
Listen to the following example by Anton Webern.
YouTube: https://www.youtube.com/watch?v=ELAKF8ZxDmg
Figure 33.1.1 Webern, 5 movements for string quartet, No. 3. Sehr bewegt
Gone are the triadic structures we have studied throughout this text. In
this music, intervals are paramount. Let us examine the intervals we find.
1 Of the 208 sets that exist, only 6 are different between the Forte and Rahn methods for
prime form. See https://www.mta.ca/pc-set/pc-set_new/pages/pc-table/packed.html.
392
CHAPTER 33. SET THEORY
162
210
&
?
393
n bn œœœ
#œ
n b œœ
nœ
m3
+5
m3
m6
œ
Look at the intervallic structure of the first two chords,2 not including
the C4 in the cello part. We see the interval of an augmented 5th below
the interval of a minor 3rd in the first chord, and the interval of a minor
sixth
163below the interval of a minor 3rd in the second chord. Notice that the
names we use for intervals carry tonal implications. An augmented 5th would
function differently than a minor 6th, but in atonal music, these intervals have
the same sound, are separated by the same number of half steps, and have no
tonal implications (they don’t have to resolve any particular way). Therefore,
analysts like Allen Forte used integers to represent pitches and intervals to
remove the tonal implications of staff notation.
&
?
33.1.2 Integer Notation for Pitches
One notable trait of set theory is that we will represent pitches with integers,
as seen in the table below.
Note name:
Integer:
C
0
C4/D2
1
D
2
D4/E2
3
E
4
F
5
F4/G2
6
G
7
G4/A2
8
A
9
A4/B2
10
It may be helpful to remember that the C major triad (C, E, and G) consists
of integers 0, 4, and 7.
Integer notation of pitches means we assume enharmonic equivalence of
notes. For example, D, C5, and E3 are all represented as pitch integer 2. We
also assume octave equivalence, which itself presumes the notion of pitch
class. When we say Beethoven’s first symphony is in C, we refer not to any
specific C (C1 , C2 , C3 , etc.), but to the concept of the pitch class C, which
includes any and all Cs. Therefore, you would label the note C as pitch class
0, no matter the register in which it occurs.
33.1.3 Integer Notation for Intervals
We will also measure intervals using integers, with each interval represented by
the number of semitones (half steps) it contains. The following table contains
the number of semitones in each interval.
2 Some authors call atonal chords “sonorities” to differentiate them from chords in the
traditional triadic sense; we will continue to use “chord” in this text.
B
11
CHAPTER 33. SET THEORY
394
Table 33.1.2 Interval Integers
162
210
162
210
163
163
Interval
m2
M2
m3
M3
P4
TT
&
?
Number of Semitones Interval
1
P5
2
m6
3
M6
4
m7
5
m3 M7
6
+5 P8
n bn œœœ
#œ
Number of Semitones
7
8
9
10
m3
11
m6
12
n b œœ
nœ
œ
In atonal music we will analyze sets of pitch classes, hence
term “pitch-class
b œœthetime
m3 with integers
set &
analysis.” Let us return to the example by Webern,n this
n
œ
m6
m3
n
œ
for pitches and for intervals. n œ
bœ
33.1.4 Pitch-Class Sets
?
&
?
+5
#œ
pitch-class numbers
nœ
11 n œ
3 bœ
2
3 semitones
8 semitones
œ
10 n b œ
&
œ 3 semitones
7
2
The first chord consists
E , 3B,semitones
and D, or pitch integers83,semitones
11, and 2. If
2 n nofœ
œ
œ
11 distance,
11 nbetween
we examine the intervallic
we
find
8
semitones
pitch
integers
bœ
1
#œ
3 semitones
8 semitones
n b œœ
nœ
10
7
11
pitch-class numbers
8 semitones
3 between 11 and 2. Note that we are working in
3 and 11, and 3 semitones
164
a modulo 12 system, meaning we restart our numbering after 11 (0, 1, 2, 3,
4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, etc.). We are used to modulo 12 thinking
1
since we all deal with clocks. If a meeting ran from 11am to 2pm, it lasted 3
hours. Therefore, an interval from pitch integer 11 to pitch integer 2 spans 3
semitones. The second chord has the same intervallic construction.
Now, let’s look at the two chords in the second half of the third measure.
?
&
164
#œ
?
&
?
nœ
n # œœ
9
0
8
#œ
9 semitones
4 semitones
œ
3
0
4
b œœ
nœ
3 semitones
8 semitones
œ
We see right away that the second of these chords has the same construction
as the two chords we examined the in earlier examples (a minor 6th below a
minor 3rd). However, the first chord in this example (G4, C, A, or 8, 0, 9) ap165 to be different, with a diminished 4th from G4 to C (an interval spanning
pears
4 semitones, enharmonically equivalent to a major 3rd) below the interval of a
major 6th from C to A (spanning 9 semitones). To see the relationship of this
chord to the others, we need to learn about normal form and prime form.
&
?
CHAPTER 33. SET THEORY
E
A
395
triad
Normal
Form
œ
œœ
# # # 33.2A major
œ
œ
œœ
œ
&
œNormal œform represents the notes of a pitch-class set (as they œœoccur in the
E major triad
&
54
&
&
###
###
music) in their most compact form.
majorsteps:
triad
To determine normal form, follow E
these
œ
#œ
œ
œ
œœ
œ
2
œ
œœœ
Ascending
numeric
order:
>
œ nœ
n
œ
.
œ
#
œ
2
3
7 œ
œ n œœ bn#œœ n œ
œ
œ
œœ b œœ 11œ œœ
?
œ
œ
6
& # œ &# œ 8 œ # œ n œn œ
#
œ
b
#
œ
b
œ
œ
#œ
œœ œœ œb œ b œb œ
œ #œ #œ
œ
œ
œ
f
œ
œ
& #œ
2
#œ #œ œ œ œ
œ
11
œ
œ
.
3
n œ every
7
possible
of the bnotes
? 2. Examine
œ n œ “scale” ordering
n œ nascending
b œuntilœ you
b
œ
n
œ
œ the
#
œ
œ
œ b œspans
#
œ
œ bthat
smallest
# œfind
œ bone
& the most
n œ compact form—thatœis, the
interval from lowest to highest note.
?
n2œ n œ n œ
# œ n œ order:
bœ bœ bœ bœ œ
# œ n11œ œ numeric
b
œ
œ
.
# œ Ascending
œ
œ
3
2 3 7 7 b œ11
3 7 11 2
7 11 2 3
11 2 3 7
b
œ
bœ œ
&
nœ œ 2
œ
œ
œ
œ
œ
œ
& œ11b œ œ
œ
œ
n œ 7 3 œ .b œ
bœ
M7
m6
m6
AscendingM6
& (92 semitones)
n3 numeric
œ 7 11order:(11
(8 semitones)
3 semitones)
7 11 2
7(8 semitones)
11 2 3
11
2 3 7
œ
œ (there
œ forb œmost œcompact
œ b œversion)
isœ a tie
œ
œ
&
œ
œ
œ
Ascending
œ b œ numeric order:b œ
2 event
3 P5
7that
11two orderings
3 7 11 have
2 the7 same
11 o4interval
2 3 span
11 2from3 lowest
7
3. In the
M6
M7
m6
m6
œthe
b
œ
b
œ
to highest
note,
choose
the
set
that
has
the
smaller
interval
between
œ
œ
œ
(7 semitones)
semitones)
(9 semitones)
(11 semitones)
(8(4
semitones)
(8 semitones)
œ
œ
œ
œ
1 œ
&
œ
œ
œ
first œandb œpenultimateœbnotes.
œ bœ
œ
œ is a tieœ for mostb œcompact version)
(there
&œ
A major triad
œ7
11
2
3
M6 to penultimate noteM7
m6
Measure first
to break the tie: m6
(9
(11 semitones)
(8 semitones)
(8 semitones)
7 semitones)
11
2
3
11
2
3
7
o
P5
4
(7 semitones)
(4iscompact
semitones)
(there
a tie forismost
compact
version)
most
Normal
Form
&
&
&
&
bœ
œ
œ
&œ
œ
œ
Measure first to penultimate note to break the tie:
o4
P5
(7
semitones)
(4
semitones)
7
11
2
3
11
2
&œ
œ
bœ
7œ
b 3œ Form
œ is Normal
œmost compact
bœ
œ
œ
4. In the
of an absolute
tie,
7 event 11
2
3 choose the
11 set that
2 begins
3 on the7 smaller
number. We will use a different set of pitches
to
demonstrate
a complete
most compact is Normal Form
tie. The normal form for the notes below is [2, 3, 8, 9].
P5
& œ bœ bœ nœ
m2
2
3
tt
8
9
œ
bœ bœ nœ
3
8
9
2
P5
bœ
bœ nœ œ
m2
8
9
tt
2
3
bœ bœ
œ
œ
9
2
3
8
In the event of an absolute tie, choose the set beginning on the smaller number.
1 The
53
E
A
œ # œœ
1. Put theœ notes
set œfrom a piece of musicœœœin
œ œofœ a pitch-class
E œ
œ
œpitches.œœ œascending
&
#
œ
#
œ
#
œ
œ
œ
A
numeric order (like a scale). Eliminate
any
duplicate
œ
œ
œ
E major triad
A major triad
53
Forte method for determining prime form would have measured from first to second
note to break the tie instead of first to penultimate note, which is method used Rahn’s Basic
Atonal Theory.
53
CHAPTER 33. SET THEORY
396
5. Normal form is written in square brackets with commas. The normal
form found in step 3 above was [11, 2, 3, 7].
33.3 Prime Form
Whereas normal form deals with the exact pitches as they occur in the music,
prime form is usually a transposition and possibly an inversion of the normal
form to its most essential form, much in the way an E2 major triad in second
inversion belongs to the category “major triad,” or a G 7 /F belongs to the
more general idea “dominant seventh chord.” Perhaps because of the primacy
7
2 ideas
3 2are demonstrated in their relation to the C
of C in music 11
theory—many
Ascending numeric order:
>œ .
major scale—all
prime
forms
are
to and start on C (pitch integer
ntransposed
n
œ
2
3
7
11
11
7
2
3 2
0).
b œ n >œ .
Ascending numeric order:
6
œ
œ
& 8 n isœ thenprocess
œ
œ7
11
Following
for determining primeœ2 form.b 3œ
54
54
6
œ bœ
œ
& 8 f then œnormal form—[11, 2, 3, 7] from
1. Transpose
œ theb œnormalœform example
in the previous section—so it starts on C (pitch integer 0): 0, 3, 4, 8
11
54
& 11œ
&œ
f
œ
7
œ
bœ
3
bœ
œ2
œ
2
3
bœ
3
bœ
œ
œ
7
0
0
4
Normal form transposed to start on 0
n >œ .
# 8œ
# 8œ
nœ
4
nœ
3
start up
on 0now goes down).
2. Invert the transposed
normal
(what to
went
11
7 Normal
2 form
3 form
2transposed
&
nœ
&m3↑68 b œ
&œ
f
0
nœ nœ
m2↑
3
M3↑
œ bœ
#œ
4
Ascending numeric order:
2
3
7
11
œ
œ
0
m3↓
8
bœ
9
œ
m2↓
8
#œ
4œ
œ
M3↓
œ
œ
# œ one of
3. Write this inverted
form
b œ in ascending
œ form
œ 0(4, 4b8,œ 9,8 0),n œ0then4 do
œ
4
8
9
0
8
9
0
4
9
8 9
&
the following:
o4
11
2
3
7
0
3
4
8
œ #œ œ
œ #œ
œ
œ no ties
œ proceed to the
transposed
start on form,
0
(a) If there
were
when
determining
œ œform
œ œtonormal
&
# œ Normal
œstep# œ 4. œ
P4
(b) If therem3↑
were ties, put this inverted version
through
0
9
8every ascending
4
œ which first
b œtie (break
œ tie by#measuring
to penultimate
note) form from
“scale”
ordering
ton determine
is the
most compact
œ
œ
œ below,
& note to penultimate note. In the example
# œ we œsee that
first
m3↓normal form) is the most
the second
ordering
0
3
4 (the “tie
8 loser” from
m2↓
M3↓
compact of the reorderings of the inverted normal form.
m2↑
m6
&
4
8
9
0
& œ #œ œ œ
P4
m6
M3↑
m6
8
9
0
4
œ
#œ œ œ
o4
m6
9
0
4
8
œ #œ
œ œ
œ
œ œ #œ
0
4
8
9
tie (break tie by measuring first to penultimate note)
&
4. Compare the normal form (transposed to 0) to the most compact inverted
form (transposed to 0). The most compact form is the prime form. Prime
form is written in parentheses with no commas: (0148).
& œ #œ œ œ
m6
#œ œ œ
œ œ
m6
œ
CHAPTER 33. SET THEORY
tie (break tie by measuring first to penultimate note)
3
4
8
#
œ
b
œ
n
œ
&œ
0
8
9
œ
#œ
œ
0
4
œ
0
most compact inverted
form of normal form
Normal Form transposed to 0
397
4
8
œ #œ
1
œ #œ
most compact inverted form of
Normal Form transposed to 0
Compare: Most compact version is Prime Form
&
(a) In the event the prime form reaches pitch integers 10 or 11, use T
for 10 and E for 11; for example (013568T)
33.3.1 Application of Normal Form and Prime Form
Let’s determine normal form and prime form of the first set from the Webern
excerpt.
The first chord contained E2, B, and D (3, 11, and 2).
3
11
3
11
11
11
& b œ33
&
& bb œœ
œ
œ
œœ
11
22
2
11
11
22
33
11
2
3
most compact form
(Normal Form)
œ
bœ
œœ
2
bœ
2
œ
œ
œ
œœ
bœ
œœ
3
œ
bb œœ
22
2
œœ
nœ
œ
The
3].
mostBelow
compact
form
11 normal
2 form3is [11, 2, 0most
3 is the
4 calculation
0
compact
form
most
compact
form
form.
(Normal
Form)
(Normal
Form)
(Normal Form)
11
11
22
33
00
33
44
00
11
2
3
0
3
4
0
Normal Form
Normal Form
transposed to 0
Normal Form
Form
Normal
Normal Form
Form 8
8 Normal9 Form 0
9Normal
0
Normal 0Form
transposed
to 00
transposed
to
transposed to 0
&œ
bb œœ
œ
&
&œ
œœ
& b œ88
n œ9
œœ
œ
œ9
9
00
8
9
0
most compact inverted
version of Normal Form
& bb œœ
&
nn œœ
bœ
nœ
bb œœ
nn œœ
œœ
8
bœ
nn œœ
œ
00
0
œœ
9
nœ
œœ
bœ
œ
bb œœ
88
8
bb œœ
nn œœ
œœ
œ
99
9
inverted
88
8
bb œœ
8
bb œœ88
9
nn 9œ9œ
bœ
nœ
bœ
1
œ
bœ
œœ
inverted
inverted
8
inverted
0
88
99
00
8
9
0
most compact inverted
version of Normal Form
bb œœ
11
11
11
to determine
9
8 prime
œœ
œ
11
33
3
00
0
0
3
n 9œ
4
nn œœ
bb œœ
00
11
44
0
1
4
most compact inverted
version transposed to 0
œœ
œœ
most compact
compact inverted
inverted
most compact
compact inverted
inverted
Normal Form
Form
most
most
Normal
most compact
inverted
most
compact
inverted
Normal Form
version
of Normal
Normal
Form
version
transposed
to 00
transposed
to 00
version
of
Form
version
transposed
to
transposed
to
most of
compact
is Primeversion
Form transposed to 0
version
Normalform
Form
transposed to 0Compare:
œ
& # œœ
œ
œ #œ
8
9
0
Compare: most
most compact
compact form
form is
is Prime
Prime Form
Form
Compare:
Compare: most compact form is Prime Form
#œ œ
œ
The prime form is (014).
9
0
8
&
&
9
9
œœ
most
compact
inverted
most
0 compact
3 inverted
4
most compact
inverted
version
of Normal
Normal
Form
version
of
Form
version of Normal Form
00
33
44
0
3
4
Normal Form
transposed to 0
&œ
œœ
&
&
bb œœ
œ
bœ
2
#œ
œ
œ
mostand
compact
Now let’s determine the normal form
primeis form for the third set we
Normal
Form
4
encountered: G , C, and A, or 8, 0, and 9.
8
9
0
0
1
4
0
11
8
& #œ
œ
Normal Form
œ
œ
bœ
œ
Normal Form
transposed to 0
œ
œ
inverted
#œ
55
55
55
55
version ofb œNormaln œForm
œ n œ to 0
version of Normal Form
to 0
œ
œversionb transposed
bœ nœ
& 0œ transposed
3
4
8
9
0
0
1
4
b œ33.Form
n œ THEORY
n œ 398
most compact inverted
Normal
b œ inverted
CHAPTER
SET
œ is Primemost
œFormcompact
n œ form
Compare:b œ
most compact
&œ
version of Normal Form
transposed to 0
version transposed to 0
8 inverted
9
0 most compact inverted
most compact
œ
#œ
œ
œ
œ œ
& #œ
#œ œ
#œ œ
œ
most
compact
is
8
9
0
#œ
9œ
Compare: most compact
form
is Prime Form
Normal
Form
œ
œ
œ
0
œ
œ
œ
&The
#œ
#œ
8#œ
normal9 form
œ is0 [8, 9, 0].0 81 9 4 0 0
8œ
11
8
#
œinvert
œ
In 9the
example
below,
we
transpose
the
normal
form
to
zero,
then
b
œ
most
compact
is
œ
œ
œ
œ
œ
œ
œ
0
œ
œ
œ
œ
#
œ
#
œ
&
#
œ
#
œ
#
œ
it. 8
Normal Form
œ
Normal
Form
8Normal Form
9
0
0
1 compact
4
11
8
most
is 0 inverted
transposed
to 0
b
œ
Normal œForm
œ
œ
œ
œ #œ
œ
& #œ
8
9
0
0
1
4
0
11
8
8Normal
11 Form
0
11 0 8 Normal
0 b œ8 Form
11 œ 0 3 4inverted
0 1 4
œ
œ
œ
œ
œ
# œ to 0
& # œ œ œœ œ œ # œ transposed
œ
œ b œ n œ œ b œ# œ œ
&In# œNormal
the following
put theForm
inverted normal form through the
Form example, we Normal
inverted
reorderings
to
find
the
most
compact
form,
transposed
to
8 11 0
11 0 8
0 8 110then0 compare
3 4 it to
0 the
1 normal
4
transposed
to
0 Normal Form
œ
most
compact
form.
#
œ
#
œ
transposed
b
œ
n
œ
œ
œ œ œ
œ
œ
œ b œ to 0
& inverted
# œ8 11œversion
0
11 0 8
0 8 11
3 4
0 1
4
most compact
œ 0 Compare:
#
œ
#
œ
Normal
œ n œtois0 Prime
œ
transposed
œ Form
most compact
œ œ œ
œ
œ bversion
œ bForm
transposed to 0
&inverted
# œ œversion
9Normal Form
version of Normal Form
version transposed to 0
0 transposed to 0Compare:
most compact form is Prime Form
8
Normal
Form
Compare:
compact
transposed
to 0most
transposed
version is Prime Form to 0
most compact
inverted version
Compare: most compact
version is Prime Form
We see that the third set has the same prime form—(014)—as the other
sets in the opening measures of Webern’s Op 5, No. 3. Prime form can allow
us to see relationships that may not be apparent on the surface of the music.
33.3.2 Segmentation
What about the C4 in the cello part? Should it be included with the three
notes from the chords? Will another similarity be revealed? Segmentation
is the term for “segmenting” or determining which notes to group together
and analyze in a passage. Usually, segmentation is based on the music—notes
sounding together as a chord, or notes in a melodic line. However, analysts
may look at every possible combination of notes to search for deeper layers of
connection.
Below, we examine the first two chords with the C4 included in each.
&
10 semitones
œ
b
œ
œ
#œ
bœ nœ
&œ œ
0
2
3
4
NF transposed to 0
11 semitones
11 semitones
œ #œ
œ bœ
#œ œ
œ
bœ
œ bœ œ bœ
bœ nœ bœ œ
inverted
inverted form
ascending
(most compact)
4 semitones
œ #œ œ bœ
[11, 1, 2, 3]
Normal Form
0 1
2 4
œ #œ œ œ
inversion
transposed to 0
Compare: most compact version is Prime Form
(most compact)
11 semitones
6 semitones
9 semitones
11 semitones
& #œ œ bœ nœ
œ bœ nœ #œ
œ
bœ nœ #œ
œ bœ
#
œ
œ
œ
œ #œ
œ bœ
œ bœ
#
œ
CHAPTER 33. SET THEORY
&
10
10 semitones
semitones
11
11 semitones
semitones
#œ œ
bœ œ
11
11 semitones
semitones
#œ
#œ œ
&
& #œ0œ œ2œœ b bœb3œœ n œ4œœ œœœ bb œœ œœ # œ bb œœ œœ # œ œœ
bœ œ bœ bœ nœ bœ
& #œ
NF transposed to 0
00 22
33 44
œœ œœ bb œœ nn œœ
&
&
inverted
inverted form
ascending
œœ bb œœ œœ bb œœ
bb œœ nn œœ bb œœ œœ
œ bœ nœ #œ
bœ nœ #œ
œ #œ œ bœ
(most
(most compact)
compact)
[11,44 semitones
1, 2, 3]399
semitones
Normal Form
œœ ##1œœ œœ2 bb 4œœ
œ #œ œ œ
0
[11,
[11, 1,
1, 2,
2, 3]
3]
Normal
Form
Normal
Form
inversion
00transposed
11
22to 044
œœ ## œœ œœ œœ
Compare: most compact version is Prime Form
NF
transposed
to
00
inverted
inverted
inversion
(most
compact)
NF
transposed
to
inverted
inverted form
form
inversion
The prime form of the
first
set, when including
the C4 from
the cello,
is
ascending
transposed
to
11 semitones
6 semitones
9
semitones
11
semitones
ascending
transposed
to 00
(0124).
Here is the second chord with the C4 added to it.
&
#œ
œ bœ nœ
œ
œ #œ
œ bœ
Compare:
Compare: most
most compact
compact version
version is
is Prime
Prime Form
Form
(most
compact)
(most compact)
[7, 66 semitones
10,
11, 1]
11
99 semitones
11
11 semitones
semitones
semitones
semitones
11 semitones
semitones
Normal Form
œœ
#
œ
#
œ
b
œ
n
œ
b
œ
n
œ
b
œ
n
œ
#
œ
#
œ
bœ nœ
&
& #0œ 3œœ 4b œ n6œ œœ b œ n œ
#œœ b œ n œ # œ œ[7, 10, 11, 1]
[7, œ10,b œ11, b œ1]
&
bœ bœ nœ œ
Normal
Normal Form
Form
œœ bb œœ
#
œ
œ #œ 3 6
0œ 2
œ œ bœ #œ
œœ bb œœ nn œœ ## œœ
&
&
œœ œœ bb œœ b œ b œ bb œœ nn œœ œœ œœ œœ bb œœ ## œœ
bœ bœ
Compare: most compact version is Prime Form
&
Compare:
Compare: most
most compact
compact version
version is
is Prime
Prime Form
Form
NF transposed to 0
00 33 44
66
NF
NF transposed
transposed to
to 00
&œ
& œ
&
#œ
inverted
inverted form
ascending
inversion
00 22 33 66
transposed to 0
inverted
inverted
inverted
inverted form
form
ascending
ascending
inversion
inversion
transposed
transposed to
to 00
œ
Œ
The prime form of the second set, when including the C4 from the cello, is
(0236).
We do not see any relationship between these first two sets after including
the C4 with each three-note set. One doesn’t know this until one examines this
new segmentation.
&
&
œ
œ
Œ
33.4
& b b œœInterval Vector
& b b œœ
Œ
Ó
An interval vector (also known as “Interval Class Content”) is a list of every
possible interval occurring in a pitch-class set. Calculating an interval vector
is rather straightforward. First, after determing normal form, measure from
the first note to all the other notes. Second, measure from the second note
to all higher notes (not back or down to the first note). Continue measuring
from each successive note to the notes following and you will have completed
the interval vector.
Before demonstrating this, it is important to discuss the term “interval
class.” An interval class (abbreviated “ic”) is the shortest distance between
two notes measured in semitones. In the example below, C up to A is a major
6th. However, the shortest distance between C and A (measure downward) is
a minor 3rd. Therefore, the largest interval class is 6 (the tritone), because
any perfect 5th (for example, from C to G) has an interval class of 5 (a perfect
4th) because C down to G is a perfect 4th.
? bœ
nœ
bœ
#œ
?
#œ
œ
#œ
œ
58
œ œ
bœ œ œ
œ
CHAPTER 33. SET THEORY
&
58 & œ
œ
Major 6th
& bœ œ œ œ œ
œ
œ
400
œ
œ
œ
œ
œ Perfect 5th
œ
œ
& œ b œ œ œ œ œœ
Minor 3rd
(shortest distance
between C and A)
œ
œ
œ
Perfect 4th
(shortest distance
between C and G)
6th an intervalMinor
Perfect 5th
With this in mind, let’sMajor
complete
vector3rd
of the a half-diminished
(shortestorder,
distance
7th chord on G. First, arrange the notes in ascending
then measure from
58 the first note to the second, third, and fourthbetween
notes. C and A)
&
&
&
œ
œ
œ
œ
œ
œ
&
m7=ic2
& Major
Perfect 5th
œ5=ic6œ œ œ Minor 3rd
b œ 6th
œm3=ic3
(shortest distance
œ C and A)
between
b
œ
b
œ
&œ
œ m7=ic2
œ
œ
œ
œ
œ
&
5=ic6
o
o
Perfect 5th
œ
b
œ
b
œ
(shortest
distance
Second, measure &
fromœ the second note
to the œthird and fourth notes. We
b
œ
C and A)
b
œ
add one tally each for
5.
&interval
œ class (ic) 3 andbetween
&
&
Intervalm3=ic3
Class: 1 P5=ic5
2 3 4 5 6
Major
6th
Occurrences m3=ic3
0 1 1 Minor
0 03rd 1
m7=ic2
P5=ic5
o5=ic6
&
& œœ
&œ
bb œœ
bœ
m3=ic3
bb œœ
bœ
m3=ic3
1 2 3 4 5 6
P5=ic5
0 1 M3=ic4
2 0 1 1
m3=ic3
Finally, measure from the third note to the fourth note, and the interval
vector will be complete. We add one tally for ic4; the complete interval vector
is 012011, which tells us a half-diminished chord has zero half steps, one major
2nd (shown in this voicing as a minor 7th), two minor 3rds, no major 3rds,
one perfect 4th (shown in this voicing as perfect 5th), and one tritone.
&
Interval Class:
Occurrences
œœ
œ
M3=ic4
&
& œœ
&
&
&œ
&
&
&
bœ
bœ
Interval Class:
Occurrences
œœ
bb œœ
bb œœ
1
0
2
1
œ
M3=ic4
3
2
4
1
5
1
6
1
An interval vector always contains 6 digits. When an interval class does
not occur (the way the minor second did not occur in the G half-diminished
seventh chord), place a zero in the column for that interval class.
&
&
&
œ
œ
Perfect 4th
(shortest distance
between C and G)
œ
œ
Perfect 4th
(shortest distance
between C and G)
œ
œ
Perfect 4th
(shortest distance
between C and G)
CHAPTER 33. SET THEORY
401
33.5 Forte Numbers
When Allen Forte created a catalog of every possible 3-, 4-, 5-, 6-, 7-, 8-, and
9-note set in Appendix 1 of The Structure of Atonal Music, he labeled each
prime form with two numbers separated by a hyphen. His labels (3–1, 3–2,
etc.) are now known as “Forte numbers,” and are seen in the tables in the
Lists of Set Classes, which include prime forms and interval vectors as well.
33.5.1 Z-Relations
“Z” in a set label (for example, 4–Z29) stands for “zygotic” (“twinned”), and
is used when different prime forms (for example, 4–Z29 and 4–Z15 have the
same interval vector—111111).
33.6 Lists of Set Classes
Below are lists of all set classes with prime form, Forte number, and interval
vectors shown. Allen Forte published the original list of set classes in The
Structure of Atonal Music in 1973. These lists use prime forms as calculated
using the Rahn method. Prime forms of sets are ordered from most packed
to the left to least packed to the left, as is found in the list of set classes in
both John Rahn’s Basic Atonal Theory and Joseph Straus’ Introduction to
Post-Tonal Theory. Sets are listed across from their complements. When
taken together, complements can complete the 12-note chromatic scale when
correctly transposed (and sometimes inverted).
Table 33.6.1 List of Set Classes for 3- and 9-note sets (Trichords and
Nonachords)
Prime
Form
(012)
(013)
(014)
(015)
(016)
(024)
(025)
(026)
(027)
(036)
(037)
(048)
Forte
Number
3–1
3–2
3–3
3–4
3–5
3–6
3–7
3–8
3–9
3–10
3–11
3–12
Interval
Vector
210000
111000
101100
100110
100011
020100
011010
010101
010020
002001
001110
000300
Prime
Form
(012345678)
(012345679)
(012345689)
(012345789)
(012346789)
(01234568T)
(01234578T)
(01234678T)
(01235678T)
(01234679T)
(01235679T)
(01245689T)
Forte
Number
9–1
9–2
9–3
9–4
9–5
9–6
9–7
9–8
9–9
9–10
9–11
9–12
Interval
Vector
876663
777663
767763
766773
766674
686763
677673
676764
676683
668664
667773
666963
CHAPTER 33. SET THEORY
402
Table 33.6.2 List of Set Classes for 4– and 8–note sets (Tetrachords
and Octachords)
Prime
Form
(0123)
(0124)
(0125)
(0126)
(0127)
(0134)
(0135)
(0136)
(0137)
(0145)
(0146)
(0147)
(0148)
(0156)
(0157)
(0158)
(0167)
(0235)
(0236)
(0237)
(0246)
(0247)
(0248)
(0257)
(0258)
(0268)
(0347)
(0358)
(0369)
1 Forte
Forte
Number
4–1
4–2
4–4
4–5
4–6
4–3
4–11
4–13
4–Z29
4–7
4–Z15
4–18
4–19
4–8
4–16
4–20
4–9
4–10
4–12
4–14
4–21
4–22
4–24
4–23
4–27
4–25
4–17
4–26
4–28
Interval
Vector
321000
221100
211110
210111
210021
212100
121110
112011
111111
201210
111111
102111
101310
200121
110121
101220
200022
122010
112101
111120
030201
021120
020301
021030
012111
020202
102210
012120
004002
prime form for 8–26: (0124579T)
Prime
Form
(01234567)
(01234568)
(01234578)
(01234678)
(01235678)
(01234569)
(01234579)
(01234679)
(01235679)
(01234589)
(01234689)
(01235689)
(01245689)
(01234789)
(01235789)
(01245789)
(01236789)
(02345679)
(01345679)
(01245679)
(0123468T)
(0123568T)
(0124568T)
(0123578T)
(0124578T)
(0124678T)
(01345689)
(0134578T) 1
(0134679T)
Forte
Number
8–1
8–2
8–4
8–5
8–6
8–3
8–11
8–13
8–Z29
8–7
8–Z15
8–18
8–19
8–8
8–16
8–20
8–9
8–10
8–12
8–14
8–21
8–22
8–24
8–23
8–27
8–25
8–17
8–26
8–28
Interval
Vector
765442
665542
655552
654553
654463
656542
565552
556453
555553
645652
555553
546553
545752
644563
554563
545662
644464
566452
556543
555562
474643
465562
464743
465472
456553
464644
546652
456562
448444
CHAPTER 33. SET THEORY
403
Table 33.6.3 List of Set Classes for 5– and 7–note sets (Pentachords
and Septachords)
Prime
Form
(01234)
(01235)
(01236)
(01237)
(01245)
(01246)
(01247)
(01248)
(01256)
(01257)
(01258)
(01267)
(01268)
(01346)
(01347)
(01348)
(01356)
(01357)
(01358)
(01367)
(01369)
(01457)
(01458)
(01468)
(01469)
(01478)
(01568) 3
(02346)
(02347)
(02357)
(02358)
(02368)
(02458)
(02468)
(02469)
(02479)
(03458)
Forte
Number
5–1
5–2
5–4
5–5
5–3
5–9
5–Z36
5–13
5–6
5–14
5–Z38
5–7
5–15
5–10
5–16
5–Z17
5–Z12
5–24
5–27
5–19
5–31
5–Z18
5–21
5–30
5–32
5–22
5–20
5–8
5–11
5–23
5–25
5–28
5–26
5–33
5–34
5–35
5–Z37
Interval
Vector
432100
332110
322111
321121
322210
231211
222121
2221311
311221
221131
212221
310132
220222
223111
213211
212320
222121
131221
122230
212122
114112
212221
202420
121321
113221
202321
211231
232201
222220
132130
123121
122212
122311
040402
032221
032140
212320
Prime
Form
(0123456)
(0123457)
(0123467)
(0123567)
(0123458)
(0123468)
(0123568)
(0124568)
(0123478)
(0123578)
(0124578)
(0123678)
(0124678)
(0123469)
(0123569)
(0124569)
(0123479)
(0123579)
(0124579)
(0123679)
(0134679)
(0145679) 2
(0124589)
(0124689)
(0134689)
(0125689)
(0125679) 4
(0234568)
(0134568)
(0234579)
(0234679)
(0135679)
(0134579)
(012468T)
(013468T)
(013568T)
(0134578)
Forte
Number
7–1
7–2
7–4
7–5
7–3
7–9
7–Z36
7–13
7–6
7–14
7–Z38
7–7
7–15
7–10
7–16
7–Z17
7–Z12
7–24
7–27
7–19
7–31
7–Z18
7–21
7–30
7–32
7–22
7–20
7–8
7–11
7–23
7–25
7–28
7–26
7–33
7–34
7–35
7–Z37
Interval
Vector
654321
554331
544332
543342
544431
453432
444342
443532
533442
443352
434442
532353
442443
445332
435432
434541
444342
353442
344451
434343
336333
434442
424641
343542
335442
424542
433452
454422
444441
354351
345342
344433
344532
262623
254442
254361
434541
In the table below, when no set is listed across from a six–note set, it is
self–complementary (that is, it can combine with a transposed and possibly
inverted set of itself to complete a 12-note chromatic scale.
2 Forte
prime form for 7–Z18: (0123589)
prime form for 5–20: (01378)
4 Forte prime form for 7–20: (0124789)
3 Forte
CHAPTER 33. SET THEORY
404
Table 33.6.4 List of Set Classes for 6-note sets (Hexachords)
Prime
Form
(012345)
(012346)
(012347)
(012348)
(012357)
(012358)
(012367)
(012368)
(012369)
(012378)
(012458)
(012468)
(012469)
(012478)
(012479)
(012569)
(012578)
(012579)
(012678)
(013457)
(013458)
(013469)
(013479)
(013579)
(013679)
(023679) 5
(014568)
(014579) 6
(014589)
(023457)
(023468)
(023469)
(023579)
(024579)
(02468T)
Forte
Number
6–1
6–2
6–Z36
6–Z37
6–9
6–Z40
6–5
6–Z41
6–Z42
6–Z38
6–15
6–22
6–Z46
6–Z17
6–Z47
6–Z44
6–18
6–Z48
6–7
6–Z10
6–14
6–27
6–Z49
6–34
6–30
6–Z29
6–16
6–31
6–20
6–8
6–21
6–Z45
6–33
6–32
6–35
Interval
Vector
543210
4443211
433221
432321
342231
333231
422232
332232
324222
421242
323421
241422
233331
322332
233241
313431
322242
232341
420243
333321
323430
225222
224322
142422
224223
224232
322431
223431
303630
343230
242412
234222
143241
143250
060603
Prime
Form
Forte
Number
Interval
Vector
(012356)
(012456)
6–Z3
6–Z4
433221
432321
(012457)
6–Z11
333231
(012457)
(013467)
(012567)
6–Z12
6–Z13
6–Z6
332232
324222
421242
(013468)
(012568)
(013568)
(013478)
6–Z24
6–Z43
6–Z25
6–Z19
233331
233331
233241
313431
(013578)
6–Z26
232341
(023458)
6–Z39
333321
(013569)
6–Z28
224322
(014679)
6–Z50
224232
(023568)
6–Z23
234222
33.7 Transposition (Tn )
Transposition is an operation performed as Tn , where n is the number of
semitones up a set is transposed. For example, [1, 2, 4, 6] at T4 is [5, 6, 8, 10].
5 Forte
6 Forte
prime form for 6–Z29: (013689)
prime form for 6–31: (013589)
CHAPTER 33. SET THEORY
405
59
all notes transposed up 4 semitones (T4)
& 44
[1
#œ
œ
œ
#œ
2
4
bœ
œ
6]
[5
6
bœ
bœ
8
10 ]
When working in a modulo 12 system, remember that numbers larger than
12 have to be reduced to a number smaller than 12 by subtracting 12 from the
larger number. For example, 6, 8, 10, 11 at T9 would result in 15, 17, 18, 20,
which, after subtracting 12 from each number, results in 3, 5, 6, 8.
&
Table 33.7.1
Pitch classes:
at T9 :
Result:
Make numbers modulo 12:
Result:
&
6
8 10 11
9
9
9
9
15 17 18 20
– 12 12 12 12
all notes 3
transposed
5 up 64 semitones
8 (T4)
+
4
& 4(Tn I) œ
33.8 Inversion
#œ
[1
#œ
œ
2
4
6]
59
[5
6
Inverting a set using Tn I is a compound operation. The first step is to invert
each note below C using C as an axis. For example, E is a major 3rd above C,
so E would invert to A2, a major third below C.
& 44
œ
#œ
&
œ
# œinversion at T0œI
C is axis of
œ
bœ
bœ
bœ
bœ
The[ 1second step
is to
So,8 to calculate
T3 I
2 of inversion
4
6 ] apply the
[ 5 Tn interval.
6
10 ]
& first invert E to A2 (this is T0 I), then transpose the
for the note E, one would
A2 up 3 semitones to B. (Theorist Joseph Straus simplifies the nomenclature
to In instead of Tn I, but the outcome remains the same.)
Let’s try inverting a pitch-class set, applying T7 I to [2, 4, 5] (or D, E, and
M3 abovethe
C inverts
M3 below
C at T0side
I
F). Inverting
notes toto the
opposite
of C using C as an axis yields pitch
œ
2
2
numbers 10, 8, and ˙7 (or B , bAœ , and G), which in ascending order is 7, 8, and
&
10. Then transposing [7, 8, 10] at T7 raises each note 7 semitones, resulting in
axis F).
of
[2, 3, 5] (or D, EC2, isand
inversion at T0I
pitches: 5
4
2
inverts to 10
int.: P4↑ M3↑ M2↑
M2↓
&
œ
œ
œ
˙
8
M3↓
bœ bœ
C is axis of
inversion at T0I
7
P4↓
œ
Then transpose:
[7
8 10 ] at T7 = [ 2
œ bœ bœ
8
10 ]
59
M3 above C inverts to M3 below C at T0I
all notes transposed up 4 semitones (T4)
˙
bœ
bœ
bœ
œ
œ bœ œ
3
5]
Therefore, [2, 4, 5] at T7I = [2, 3, 5]
&
33.8.1 Identifying Tn I for Inversionally-Related Sets
To determine n of Tn I for two inversionally-related sets, write the second set
backward and add the notes of the two sets together. Each sum will equal n.
Let’s use our two sets from the previous example above: [2, 4, 5] and [2, 3, 5].
& œ0 2 3 4 œ b œ œ b œ
œ bœ nœ
œ œ bœ
& NFœ transposed to 0 œ binverted
b œ n œ b œ œ œ0 # œ1 2 4
œ is Prime
œcompact
# œmostversion
most œ
compact
Form
bform
œ œCompare:
version
is Prime Form
b œinverted
n œCompare:
inversion
(most compact)
(most
compact)
ascending
transposed
to 0
6 semitones
11 semitones
inverted 11 semitones
inverted
form
inversion 9 semitones
11
semitones
6 semitones
11 semitones
406 9 semitones
ascending
transposed to 0
Compare: most compact version is Prime Form
(most compact)
most compact version
is Prime Form 11 semitones
11 semitones Compare:
6 semitones
9 semitones
[7, 10, 11,
(most compact)
[7, 1]
10, 11, 1]
First
set in order:
2 9 semitones
4 Normal
5 Form
11
semitones
6 semitones
11 semitones
Normal
Form
œ
œœ œ b œ œ b œ
#
œ
#
œ
#
b
œ
n
œ
b
œ
n
œ
b
œ
n
œ
œ
b œœ n œ œ b œ n œ # œ b œ n œ # œ
œ #œ
& # œ &œ
Table 33.8.1
#œ œ
œ
œ bœ
n œ backward:
& Second
œ b œ set
œ b œ n œ # œ+ b œ5 n œ3 # œ 2 œ œ # œ œ b œ
#œ
0 2 30 62
n œ Tn[7,œI: b10,œ 0n11,œ 3#1]œ 40 #b 7œœ36 n œ47 # œ67
œ #œ
&
œ b œn of
# œœ b œ3 # 6œ
bœ nœ
b
œ
œ
#œ
œ
œ
œ
Normal
Form œ b œ n œœ # œœ b œ
b œ b œb œb œb œ nbœœ b œ n œ œ œ
[7, &10, 11, &
1]
This confirms the sets are related
at T7 I.
Normal Form
0 3
4
6
0 2 3 6
to 0
NF transposed
toinverted
0
inverted
inverted form inversion inversion
# œ form
b œ3 n œ4 # œ6 œ NF transposed
b œ3 inverted
œ
ascending
to 0
œ
œ
œ
0
0
2
6
ascendingtransposed transposed
to 0
œ
b
œ
b
œ
n
œ
&
bœ bœ
#
œ
#
œ
b
œ
n
œ
b
œ
œ
33.9 Practice
Exercises
œ
œ
œ
œ
œ b œ b œ b œinverted
b œ nform
œ
& NF transposed to 0
inverted
inversion
NF transposed
to 0
CHAPTER 33. SET
THEORY
Compare: most compact
is Prime
Form
mostversion
compact
version
is Prime Form
ascending Compare:
transposed
to 0
inverted form
inversion
ascending
transposed to 0
Compare: most compact version is Prime Form
#œ
Day One
# œœ
œ &œ
&
1. Put each set into normal form and prime form.
NF transposed to 0
(a)
(b)
(c)
(d)
&œ
&œ
& œ
& bœ
& bb bb œœœ
& bb b œœœ
? bœ
? bœ
?
? bœ
bœ
#œ
#œ
œ
œ
nœ
nœ
#œ
#œ
(e)
& œ #œ
(f)
& œ #œ
(g)
œŒ
inverted
Œ
œ
œ
œ
Œ
Œ
œœ
œ& Œ& œ
Œ
œ
œ b b Œœœ b b œœ
Œ
bœ
Œ
œ & b œŒ & b b œœ
Œ
Ó
?
#œ
b
œ
?
Œ
nbœ Ó n œ ##œœ # œ
#œ
#œ
œ
#œ ?
œ
œ
#bœœ ? # œ
œ
#œ
œ
b
œ
œ
œ
œ
Compare: most compact version is Prime Form
œ #œ
œ &# œ œ
œ #œ
œ
& œ #œ
œ bœ nœ
œ
bœ
nœ
?
bœ nœ #œ
? œ bœ nœ #œ œ œ bœ
Ó
Ó
57
57
œ bœ
Day Two
2. For each of the six sets&in the example below, determine the normal
form, prime
& form, Forte number, and interval vector.
211
# œ œ œ # ## œœœ # œ n n n œœœ
& c # # # ˙˙˙˙ # œ
&
&
#œ
# # œœœ
# œ
?c
2
1
168
Day Three
170
&
?
&
&
&
&
3
4
b b b œœœœ
bœ
6
# œœ
n ˙˙
œ
˙˙
n
œ
b
b b œœ b b ˙˙
5
∑
CHAPTER 33. SET THEORY
3.
407
Transposition (Tn ) of Sets. Transpose the following sets as specified.
,
(a) Transpose [3, 6, 7] at T2 : [
,
(b) Transpose [2, 4, 8, 9] at T7 : [
,
,
(c) Transpose [1, 2, 4, 7, 8] at T9 : [
4.
,
,
,
]
,
,
]
Inversion (Tn I) of Sets. Invert the following sets. Write your answers
in normal form.
,
(a) Invert [7, 10, 11] at T0 I: [
(b) Invert [0, 2, 4] at T4 I: [
5.
]
,
]
,
,
]
(c) Invert [4, 6, 10, 11] at T9 I: [
,
,
,
]
Specify the interval of inversion from the first set to the second set.
(a) [2, 4, 7] inverts to [3, 6, 8] at what Tn I?
(b) [1, 2, 4, 7] inverts to [4, 7, 9, 10] at what Tn I?
(c) [6, 7, 10, 1, 2] inverts to [3, 4, 7, 10, 11] at what Tn I?
Click here to download the first homework assignment for this chapter.
Click here to download the second homework assignment for this chapter.
Click here to download the third homework assignment for this chapter.
PDF versions of the textbook, homework exercises, and practice exercises
can be found at musictheory.pugetsound.edu
Chapter 34
Serialism
Serialism is a term that encompasses the twelve-tone technique of Schoenberg,
Webern, and Berg, who were the major figures we associated with expressionism and atonality in the previous chapter on set theory. We will begin
by discussing classic twelve-tone serialism before discussing non-twelve-tone
serialism.
34.1 Twelve-Tone Technique
YouTube: https://www.youtube.com/watch?v=bQHR_Z8XVvI
Figure 34.1.1 Arnold Schoenberg, Suite for Piano, Op. 25
In a twelve-tone composition, every note can be accounted for as being a
member of the original series or one of its permutations, providing unity to the
piece as a whole. Additionally, a twelve-tone series is a repository of intervals
and can be seen as an outgrowth of atonal music with its emphasis on interval
over chord or scale. The basic premises of twelve-tone music are as follows:
1. All twelve notes of the chromatic scale must occur
2. No note can be repeated in the series until the other 11 notes of the
chromatic scale have occurred (exceptions include direct repetition of a
note, trills, and tremolos)
3. The series can be inverted, retrograded, and the inversion can be retrograded
4. The order of notes in a series remains fixed, without reordering.
408
CHAPTER 34. SERIALISM
409
34.1.1 Row Forms
60
A twelve-tone series is also commonly called a twelve-tone “row,” and we will
use the term “row” throughout this chapter.
The four types of row forms used in twelve-tone technique are prime (P),
retrograde (R), inversion (I), and retrograde inversion (RI). The prime is the
original row. The retrograde is the prime form backward. The inversion is
the original row with all intervals in the row inverted (going in the opposite
R1 (1 means it ends on C˜)
RI7 (7 means it ends on G)
direction
of the original). Finally, the retrograde inversion
is the inversion
retrograded (and therefore might have more appropriately been labeled “inversion retrograded” since “retrograde inversion” sounds like it refers to the
backward form inverted instead of the inverted form backward).
œ œ bœ œ bœ œ œ œ nœ #œ #œ #œ #œ
œ bœ œ #œ œ œ nœ œ
œ
&
#œ #œ
bœ nœ œ nœ œ bœ
œ bœ bœ œ
bœ œ nœ #œ #œ œ œ bœ bœ nœ œ œ
& œ bœ
R1 (1 means it ends on C˜)
RI7 (7 means it ends on G)
œ
b
œ
œ
œ = Prime with
œ b œ =œInversion
# œ œ œbackward
Inversion
Inversion
b œ œintervals
ninverted
œ # œ # œ # œ #Retrograde
œ
œ
nœ œ
œ
œ
#
œ
&œ
#
œ
œ #œ #œ œ œ #œ #œ nœ œ bœ bœ œ
bœ
nœ nœ
& R1 (1œ #means
itœ endsb œonn œC˜)
RI7 (7 means it ends
on G)
œ
n
œ
œ
#
œ
œ #œ œ
œ
œ œ b œ œ œ œ œ n œ # œ # œ # œ #Retrograde
œ b œbackward
œ
n
œ
Prime (Original) b œ
=
Prime
œ
œ
#
œ
&
#œ
b
œ
n
œ
œ bœ bœ œ
œ
34.1.2
Transposition
Numbers
œ
b
œ
b
œ
n
œ
œ
bœ œ nœ #œ #œ œ œ bœ bœ nœ œ œ
&
Each row form can be transposed to start on any note from the chromatic
& (Original)
Prime
Retrograde = Prime backward
scale.
We will use the same pitch integers
as in set theory. For primes and
b
œ
n
œ
b œbackward
Inversion
=
Prime
with
intervals
inverted
Retrograde
Inversion
œ
œ toœ specify
inversions,
we
will
use
P
and
I
accompanied
by a pitch
œ
b
œ
b œ ninteger
œ =œInversion
b
œ
n
œ
b œ œthe
œ
b
œ
n
œ
œ
b
œ
œ
œ
& œ œnote. For example,
#
œ
#
œ
œ
starting
Pœ0#is
a
twelve-tone
row
starting
on
C
(pitch
œ
#
œ
n
œ
#œ 2 #œ
œ
b œ same
ninteger
œ ncase
n œ starting
œ b œThe
&P3 is a# œtwelve-tone
œ œ #isœ the
n œ œ b œ b œrow
0),
on E , and so forth.
for
row forms like I (starting on D), I (starting on F), on so forth.
Inversion
& = Prime with2intervals inverted 5 Retrograde Inversion = Inversion backward
œ n œ the
row
on E¯)
œ # œ nthe
b œstarts
nœ nœ
b œ n œon œC)# œ # œ œ œP3# (3œ #means
œœb row
œ b œstarts
&P0 (0œ means
œ
œ
œ
œ
#
œ
b
œ
œ
b
bœ nœ œ nœ œ bœ
œ œ bœ bœ œ nœ nœ
bœ œ nœ #œ bœ nœ
& œ bœ
P (0 means the row starts on C)
P3 (3 means the row starts on E¯)
&I 0(2 means
œ b œ b œ œ œstarts
b
œ
n
œ
b œ bonœ F)œ n œ
œ n œstarts
the row
Iœ5 (5
means the row
œ b on
œ bD)
b
n
œ
2 œ bœ
œ
n
œ
œ
&œ
œ b œ #b œ œ œ œ b œ œ b œ b œ n œ œ # œ # œ nœœ
œ
#
œ
n
œ
b
œ
n
œ
&
#œ nœ œ
Prime (Original)
60
60
Retrograde = Prime backward
& œ #œ
œ œ bœ bœ œ œ œ bœ œ bœ bœ nœ œ #œ #œ œ
n
œ
b
œ
n
œ
œ
&
#œ nœ
œ bœ bœ bœ nœ œ #œ œ #œ #œ nœ œ bœ œ œ œ #œ #œ nœ
œ
œ
b
œ
n
œ
&œ
R1 (1 means the row ends on C˜)
RI7 (7 means the row ends on G)
œ
& œ
œ œ bœ bœ bœ nœ œ #œ #œ #œ nœ œ bœ œ œ œ #œ #œ nœ
b
œ
n
œ
œ
&
&
I2 (2 means the row starts on D)
I5 (5 means the row starts on F)
However, the retrograde (R) and retrograde inversion (RI) row forms use
R (1 means the row ends on C˜)
RI (7 means the row ends on G)
the 1pitch integer of the last note in the row7 to designate their transposition
level. Therefore, R1 ends on C4, and RI7 ends on G.
&
&
&
œ œ RI4 (ends on 4)
& œœ œœ.# œœ #nœœ œ œb œœ bbœœ n bœœ bœœ# nœœ# œœ b œ ‰ b#œœj # œ n œ œ b bœœ bœœn œœ œœ n#œœb œn œb œn œn œ
&
œ bœ
Inversion = Prime with intervals inverted
172
Retrograde Inversion = Inversion backward
R8 (ends on 8)
œ
CHAPTER
34. SERIALISM
3
3
410
P1 3
0
bbœœ nœœ # œ œ œ . # œ Row Forms
bœ œ
34.2
? ‰ bœœDetermining
œ œ n œ œ b œ # œ œ n œ b œ #bœœœnœœ # œœ. b #œœ b#œœ nœœ œœ œb œœ b œ J nœœ
œ
œ
11
P (0 Imeans
the row starts on C)
P (3 means the row starts on E¯)
bœ œ nœ #œ
&
nœ
3
To determine a row
form’s3 permutation and3 transposition,
examine the
inter3
3
3
vallic composition of each row form. In the example below, each row statement
is Ibased
on the
form
(2 means
the prime
row starts
on of
D) the row in the
I (5previous
means thesections.
row starts on F)
5
b
œ
œ
œ
œ
b
œ
œj œ b œ œ b œb œb œ nnœœ œ # œ # œb œ œn œ
œœ. œ # œ œ n œœ b œ n bœœ b œ n œ
œ
#
œ
œ œ nœ bœ
&& # œ n œ œ b œ
œ bœ ‰ bœ œ œ bœ
2
174
3
b œonœ G)œ
. # œ #the
œ œ œends
œ n row
#b œœ œ n œ b œ # œœRIœ7œ(7##œmeans
œ J
œ
n
œ
b
œ
n
œ
#
œ
œ3 œ b œ 3
œ b œ œ 3 œ œ # œ3 # œ n œ
œ
3
œ
#
œ
3
b
œ
n
œ
œ
&
œ b œ œ row
œ . on
# œ C˜)
R?
1 (1 means the
œ # œ œends
3
‰
Let’s examine the starting intervals of each row form.
P4↑
P0 m2↑
m2↑
M2↓ m2↑
R
bœ bœ nœ œ nœ œ bœ bœ œ nœ 0 nœ nœ bœ bœ nœ œ œ œ bœ bœ œ
œ
&
#œ #œ
m3↑
m3↓ M2↑ m2↓
m2↓ P4↓ m2↓
œ œ #œ #œ nœ œ bœ bœ
& œ nœ #œ nœ œ bœ bœ nœ œ #œ #œ
œ œ #œ nœ nœ
I0
RI0
In examining the first few notes in the upper staff in the short musical
excerpt below, we see an ascending minor 3rd followed by a descending major
2nd. The only row form to start with these intervals is the retrograde. To 211
determine 1the transposition number,
we3 look at the
6 note)
2
4 last note5 (the 12th
in the first measure in the upper staff (A2), which gives us the transposition
level (pitch integer 8), meaning this is R8 . The second measure in the upper
staff begins with a minor 3rd followed by an ascending major 2nd, making this
a retrograde inversion. The 12th note in this measure is an E (pitch integer 4),
making this RI4 . In the first measure of the lower staff, we find a descending
minor 2nd followed by a descending perfect 4th, making this I11 . Finally, the
second measure in the lower staff begins on C4 with an ascending minor 2nd
followed by an ascending perfect 4th, making this P1 .
&
# œ˙ # œ œ œ # ## œœœ # œ n n n œœœ
# # # ˙˙˙
#œ
# # œœœ
# œ
?c
&c
168
170
œ œ. œ #œ œ œ bœ bœ bœ nœ œ bœ
&c
m3↑ M2↓
3
1
4
2 3
3
5 6
7
8
9 10
11 12
b b b œœœœ
bœ
# œœ
n ˙˙
œ
˙˙
n
œ
b
b b œœ b b ˙˙
∑
M2↑
‰ b œj œ œ b œ b œ œ n œ œ n œ b œ b œ n œ
m3↓
1
2 3 4
5 6 7 8
9 10 11 12
m2↑
? c ‰ œ b œ œ œ # œ œ œ . # œ # œ œ n œ b œ # œ œ œ # œ . # œ # œ n œ œ œ œ b œ œJ œ
m2↓ P4↓
1 2
3
3 4 5 6 7
P4↑
3
8 9
10
11
3
12
1 2 3
4
3
The row forms are labeled in the example below.
172
&
?
181
3
3
5 6 7 8
9 9 10
11 12
? c ‰ œ b œ œ œ # œ œ œ . # œ # œ œ n œ b œ # œ œ œ # œ . # œ # œ n œ œ b œ œJ œ
œœ
m2↑ P4↑
3
2 SERIALISM
3
CHAPTER1 34.
3 4 5 6 7
8 9
172
&
œ œ. œ #œ
10
11
3
12
R8 (ends on 8)
3
3
œ œ bœ bœ bœ nœ œ bœ
1 2 3
3
3
4
3
5 6 7 8
9 9 10
‰ b œj œ œ b œ
11 12
411
RI4 (ends on 4)
bœ œ nœ œ nœ bœ bœ nœ
P1
? ‰ œ b œ œ œ # œ œ œ . # œ # œ œ n œ b œ # œ œ œ # œ . # œ # œ n œ œ œ œ b œ œJ œ
I11
3
3
3
3
3
3
174
34.3
Writing Row Forms
&
To write specified row forms from a given prime form, write all four versions
of the row: P, R, I, and RI. Then, simply transpose the specified row form to
the correct pitch, remembering that P and I forms start on the pitch integer
(P3 and I3 would begin on E2, for example) while R and RI forms end on the
pitch integer (R3 and RI3 would end on E2).
To write I9 and RI5 if given P0 :
?
61
1. Write all four row forms (P, R, I, RI).
0
b
œ
n
œ
œ bœ bœ œ
œ
œ
b
œ
b
œ
n
œ
bœ œ nœ #œ #œ nœ nœ bœ bœ nœ œ œ
&œ
P0
R
b œ n œ œ n œRIœ b œ
bœ nœ œ œ œ bœ bœ œ
b
œ
œ
b
œ
n
œ
n
œ
b
œ
œ
n
œ
&
# œ #Rœ0
œ œ
& œ n œ # œ n œ œ b œ b œœn œb œœb#œœn#œœ œ n œ œ# œb œ# œ n œ œ b œ b œ œ œ # œ n œ n œ b œ n œ œ œ œ b œ b œ œ
bœ œ nœ #œ #œ nœ nœ bœ
& I0
RI0
2. Transpose the specified row form to the correctœtransposition
œ level.
# œ # œ œ RI
œ
#œ #œ nœ œ bœ bœ œ œ #œ nœ nœ
I0 n œ # œ n œ œ b œ b œ n œ
&
(a) In this example, transpose I0 up 9 semitones (a major 6th)0 to begin
œ #œ #œ œ œ #œ #œ nœ œ bœ bœ œ
& on A (pitch class œ9).n œ
&
#œ nœ œ bœ bœ nœ
œ #œ nœ nœ
P0
I0
P0
R0
0
I9 (begins on pitch class 9)
& œI9#(begins
œ # œ n œonœpitch
n œ œclass
# œ 9)œ # œ # œ # œ
œ # œ 4th) so the
& œ # œ # œRIn œ0 up
œ # œ œ # œ(a# perfect
œ n5œ semitones
(b) To write RI5 , transpose
RI5 class
(ends on pitch class 5)
last note is F (pitch
œ # œ # œ 5).
nœ œ bœ bœ œ
nœ
bœ nœ nœ
class 5)
& RIœ 5 (ends on pitch
#œ #œ nœ œ bœ bœ œ bœ nœ nœ nœ
&
&
&
One tool analysts create to analyze a twelve-tone composition is a twelve-tone
34.4 Twelve-Tone Matrix
matrix, which shows all 48 row forms in a 12-by-12 grid. Below is a matrix for
the row we’ve been dealing with in this chapter.
61
61
CHAPTER 34. SERIALISM
412
Table 34.4.1 Twelve-Tone Matrix
P0 →
P11 →
P6 →
P5 →
P7 →
P10 →
P8 →
P9 →
P2 →
P3 →
P1 →
P4 →
I0 ↓
C
B
G2
F
G
B2
A2
A
D
E2
D2
E
↑RI0
I1 ↓
D2
I2 ↓
G2
C
G
G2
A2
F
C
B
D2
E2
B
A
B2
E2
E
D
F
↑RI1
D
E2
A2
A
G
B2
↑RI2
I7 ↓
G
G2
D2
I2 ↓
D
D2
A2
I4 ↓
E
E2
B2
C
D
F
E2
I5 ↓
F
E
B
B2
C
E2
D2
G
A
C
B2
E
A
B2
A2
D
G
A2
G2
B
↑RI7
A
↑RI5
B
E
F
E2
G2
A
B
D
C
C4
F4
G
F
A2
↑RI2
↑RI4
I3 ↓
E2
D
A
A2
B2
D2
I10 ↓
B2
A
E
E2
F
A2
F4
B
C
F
G2
G
C
D2
E
G
↑RI3
B
D
↑RI10
To construct a matrix, write the prime form from left to right in the top
row, then write the inverted form from top to bottom in the left column.
Table 34.4.2
P0 →
P1 →
I0 ↓
C
B
G2
F
G
B2
A2
D2
G2
G
F
D
E
E2
B2
A
B
G4
←R0
A
D
E2
D2
E
↑RI0
From there, you can write the transpositions of the prime form, given the
starting notes in the left column. One would continue with each transposition
of the prime form until the matrix is complete.
34.5 Row Form Presentation in Music
In a piece of music, twelve-tone rows may not be clearly presented. One manner
of presentation is overlap, where the final note of one row is the starting note
of the next row.
I9 ↓
A
A2
E2
D
E
G
F
G2
B
C
B2
D2
↑RI9
I11 ↓
B
B2
F
E
G2
A
G
A2
D2
D
C
E2
↑RI11
I8 ↓
G4
G
D
C4
E2
F4
E
F
B2
B
A
C
↑RI8
←R0
←R11
←R6
←R5
←R7
←R10
←R8
←R9
←R2
←R3
←R1
←R4
CHAPTER 34. SERIALISM
413
64
4
œ œ. œ #œ œ œ bœ bœ bœ nœ
bœ nœ
œ bœ œ œ bœ bœ œ nœ œ œbœ
&
R8
RI
3
1 2
3
3 4 5 6
7
8 9 10 11 12
1
2 3 4 5 6 7 8
9 10 11 12
&
Figure 34.5.1 Twelfth note overlapping with first note in successive row statements
Rows may also be presented contrapuntally or harmonically. In the example
below, the row is separated into three tetrachords and presented contrapuntally.
212
212
&
176
176
1
2
3
#œ
œ
‰
& œ b œ≈ n œ ≈ œ
R
R
& R.
.
.
51 2 6
73
P
? 0 b œœ . ‰ œ #n œ .
bœ
& 9œ n œ 10 11œ
R ≈ R ≈ R
.
.
.
P0
4
œ ‰
≈ b œR ≈
.
4
8
œ ‰ #œ
≈ b œR 12≈
.
œ
œ
P0
1
‰œ
P0
œ bœ nœ
bœ
2
œ5
1
3 4
œ bœ
nœ
œ
œ # œ b œ œ œ‰ b œ n œ
#œ
6
7
8
10 2 11
9
3
4 12
œ œ
b
œ
n
œ
œ
nœ
.
.
œ
#
œ
?In the final example in this section,‰the two œrows #areœ bpresenting
&
‰
in
melodyœ
#œ
accompaniment texture, with P containing the melody and R occurring as
534.5.26Two examples
7
8 of tetrachords5 from 6a row presented
7
8
Figure
contrapun178
tally
?
chords.
178
9
10 11
0
12
>œ
0
9
6
10
11
12
9 10 11 12
œ œ œ œ. b œ
b œ n œ.
.
& œ
œ #œ #œ
n œ. # œ
202
>
-1
#
œ
.
.
.
5
#œ
œ7
R
12
&
? Œ 0 œœ 3 2 # œœ 64 ‰ Œ
œœ 8 9 ‰ b b œœœ 10 ‰
J
J
J 11
?An analyst would first attempt to find a clear presentation of a twelve-tone
P0 1
2
3
4
5
7
8
row somewhere in the composition in order to analyze harmonies.
180
& Non-Twelve-Tone Serialism
34.6
209
&
?
Serialism also includes music that is not twelve-tone but does use a series of
notes that maintains its order and employs inversion, retrograde, and retrograde inversion of the series. An example is found in Stravinsky’s Septet from
1953.1
?
1 See
209
&
?
Erwin Stein, “Strawinsky’s Septet (1953).” Tempo. Spring, 1954.
CHAPTER 34. SERIALISM
414
64
64
64
4
œ œ. œ #œ œ œ bœ bœ bœ nœ œ bœ
bœ œ nœ œ œbœ bœ nœ
& R8
œ
b
œ
œ
RI4
3
œ
.
œ
#
œ
3
œ
b
œ
bœ nœ
YouTube: https://www.youtube.com/watch?v=ijSmRoPzMaY
& 1 2 3 4 5œ œ6 b 7œ b œ8 9 n10œ 11œ b12œ œ œ b œ b œ œ n œ œ œ b œ
1
2 3 4 5 6 7 8 9 10 11 12
R8
RI
Figure 334.6.1 Stravinsky,
Septet
3
1 2 3 4 5 6 7 8 9 10 11 12
PR4
1
2 3 4 5 6 7 8 9 10 11 12
RI
8
4
œ
#œ
#œ
#
œ
œ
.
œ
œ
#
œ
b
œ
& œœ
œ
n
œ
# œb œ œ n œ œœ œ b œ b#œœ n œ
b
œ
n
œ
œ b# œ
œ
œ
b
œ
nœ
& P4
œ
b
œ
œ
œ
œ
œ
#œ
nœ
#
œ
3
#
œ
œ
3
œ
& œ1 2 3 4 5 œ6 #7œ 8 9 10 11 12 n œ
#œ
#œ
n
œ
œ
Figure 34.6.2 Series from Stravinsky’s
1 Septet
2 3 4 5 n6œ 7 8 9 10 11 12œ
œ
& œP œœ œ œ # œ ## œœ ## œœ œ n œ ## œœ # œ n œ œœ n œ # œ œ
& œ4
œ #œ
nœ
#œ
#œ
n
œ
pc: 4 11
& œ œ œœ9 œ7 # œ6 # œ8 # œ1 11œ n œ7 #6œ # œ8 nn œœ7 œ9 n œ0 # œ8 œœ9
Here
P4 is the series with pitch-class integers (abbreviated “pc” for pitch class),
and without
registral displacement. Arrows connect repeated notes.
P0
œ
#œ
œ
œ
& œP0 # œ
œ
#œ
# œ8, œ nSeptet
[ 4, 34.6.3
œ 6,Series from
Figure
œ0, n œ pitches
&
œœ9, # œ showing
#11,œ n œ repeated
#1œ ] œ
œœ7, # œStravinsky’s
&Weœœ notice# œœthatœB #(pitch
#
œ
integer 11), A (9), G (7), F4 (6), and G4 (8) are
pc: 4
11
9
7
6
8
1
11
7
6
8
7
9
0
8
9
pc: [ 4,
4 11
9 series,
7 with
6
8A, G,8,
1 and
11G4 79,
6 11,
8 three
7 times
9 each.
0 18]Below
9 is
7,
0,
repeated
in the6,
occurring
the normal form of the 8 pitch classes in the 16-note series.
&
&œ
[ 4,
#œ
6,
œ
7,
#œ
8,
œ
9,
œ
11,
œ
0,
#œ
1]
Figure 34.6.4 Normal form of the 8 pitches in the series from Stravinsky’s
Septet
&Such a series could imply E or A as a tonal center. Note that Stravinsky’s
Septet is not strictly serial but contains serial elements. Such an example
shows us that serialism can be employed in ways other than the strict, original
twelve-tone version.
34.7 Practice Exercises
Serialism: Day One
1. Given the prime form of the twelve-tone row in pitch integers, write
the specified row forms in the staves below.
œ #œ #œ nœ œ bœ bœ
œ bœ nœ nœ nœ
&
CHAPTER 34. SERIALISM
RI5 (ends on pitch class 5)
52
415
P7: 1.
7 E¯
107(˜85); 2Scale:
1 5 ____________________________
3 4 6 0 9 11
R7
& &
I7
62
RI
7
˜9; Scale: ____________________________
2. B¯7¯5
& ?
52
(a) P1
7(¯5)
3. Fm7( 5) ; Scale: ____________________________
P1 1.
E¯ ˜ ; Scale: ____________________________
& &
# œ& œ
62
62
62
œ bœ
œ
œ nœ bœ
œ bœ
bœ
bœ œ œ nœ bœ œ bœ
&
œ
œ
#
œ
b œ œ œ n œ b œ œœ b œ
& ?
&
œ
œ
? ?
#
œ
bœ bœ œ œ nœ bœ
&
bœ
# œ ##Rœœ4 œœ œ b œ œ n œ b œ n œ n œ
b œ Tone
(c) I8? R7(7(¯5)
4
bœ œ nœ
1. Fm
E¯
œE¯ Whole
3.
Scale:
____________________________
#Rœ4˜ );;#Scale:
I8?
œ ____________________________
b œ b œ œ n œ bb œœ nn œœ n œ
& b œ? # œœ # œœ œ b œ b œ œœ n œ b˙œ n œ b ˙ n œ
œ
˙ b œ n œ n œ œ # œn œ
& & b#I˙œ8 # œ œ # œ œ3rd
bIœ8 œ œ
Root
¯7th
˜5th
œ
#œ
#
œ
n
œ
b
œ
n
œ
I
b
œ
œ
8
(d) RI
œB¯ Diminished-Whole
&
10 7Δ7(
œ ____________________________
Tone
˜9; 5)
2.
Scale:
œ
4. B¯
A¯
#
œ
n
œ
¯5 ˜ ; Scale:œ____________________________
b
œ
bœ
n œ œ ##b ˙œœ
œ
&
RI?
œ
10
#
œ
n
œ
b
œ
nœ#œ œ nœ
˙
?
b
˙
n
˙
b œ& b ˙œ b œ
(b)
P1
R4 P7Δ7(
1 5)
˜9;˜ Scale:
4. A¯
; Scale:
____________________________
B¯P1¯5
____________________________
R42.
5
2.
?
œ
bœ
œ ˜9th# œ
œ n œ¯5th œ b œ
3rd
nœ
¯7th
bœ
bœ
n œb œ
œ
œ
œ
œ
œ
nœ œ
# œnn œœb œ œœ
œ
#œ œ
#œ œ
#œ bœ œ
nœ bœ
bœ
œ 10 h form
œw of œa twelve-tone
Given ?
thebRI
prime
œw n œrow,w œlabelb œwthen œrownn œœforms
#
œ
b œ and
hTone
7(10
5); bScale:
œ
E¯
Whole
˜
b
œ
1.
E¯
____________________________
? 7(¯5) bofœ theœpermutations
œ
b
œ
transpositions
given
on
the
staves
below.
œ
#
œ
n
œ
n
œ
F
Locrian
(or
F
Locrian
2)
œ
bœ
nœ bœ
˜
RI10
Root
RI
w
˜ œ bœ
?3. Fm ; Scale: œ____________________________
bœ
œ
& bb ˙œ n œ œb œ b ˙ œ b ˙œ # bœ˙œ œ œb œ n œ ˙ b œ b#˙bœ˙ b œœ b ˙ n œ œ
˙P10b œ b œb ˙ n œœ œ3rd
˙ b œœ b ˙n œ ¯7th
part 2 PRAC EXER
& b œ& Root
œ
P
b
œ ˜b5thœ n œ # œ œ n œ
œ
bPœ7109 b œ (whole
part 2 PRAC EXER
œ between E¯ œand Tone
n œB¯step
&
F and between
b
œ b œ n œA¯ and# œB¯ œ n œ
10
Diminished-Whole
˜
œ
2.
B¯
;
Scale:
____________________________
n œ whole
part 2 PRAC EXER
œ step
œ
& bb œœ¯5 b œ permit
or
half
step
b
œ between F and G)
#œ œ bœ nœ
part 2 PRAC EXER
?
œ œ n˙
(a) Row
& b ˙form:
˙ bœ#œ nœ b˙
b
˙
b
œ
Δ7(
5)
˜
A¯
Lydian-Augmented
4. A¯
; Scale: ____________________________
Root
¯7th
œ 3rd
?
& # œ b ˙œ n œb œ œw ˜9th
œœ w# œ¯5th˙ # œw œœ œw # œ ˙ nwœ b œbbœœ
˙
RI10
œ
œ
& #œ h œ nœ
œ #œ #œ
h
RI10
œ nœ bœ
œ #7th
3rd
œ œ
&3. Fm
#Root
œ7(¯5); Scale:
n œ____________________________
˜#5th
RI10
F Locrianœ(or F œLocrian
2)# œ
œ
˜
œ
œ
#
œ nœ bœ
& #œ œ nœ œ
œ #œ #œ
RI10
#
œ b œn œ b ˙ œ
œ
b
˙
b
œ
(b) Row form: b œ b ˙
b
˙
b
œ
b
˙
b
˙
&
b
œ
œ
bœ ˙
n œ n œ œ œ # œ ˙ # œ# œ œ œ b œ
& & b œœ œœ (whole
I1
b œ œ nnœœ
# œE¯# œand F# œand between
I1
A¯ and B¯ œ
œ stepn œ between
b
œ
#
œ
œ
œ
#
œ
bœ œ nœ
& b œ œ permit
I1
œ step
# œ Fœand G)
or# œ
half step between
œ nwhole
œ
#
œ
bœ œ nœ
&
I1
œ
#
œ
œ A¯ Lydian-Augmented
4. A¯Δ7(˜5); Scale: ____________________________
(c) Row
? form:
œ
˙
œ˙ b œ b œ
R5
R5
& œ & bœ˙ bœœœ b œbb bœœœ b œb˙œ b œb œ œb œ œ œœ n œ n œ n œn œ œ œ b œb œ œœ
b œ œ n œ n œ 7th
R5
& œRoot œ b œ b 3rd
œ
œ
R5
&œ
b œ bb œœ b œ ˜5th
nœ nœ œ bœ œ
P10
&
Serialism: &
Day &
Two
&
3. Construct a 12 by 12 matrix for the prime form of the following twelvetone row, given in pitch integers: 3, 7, 11, 1, 5, 0, 2, 10, 6, 4, 8, 9.
Include labels for all row forms including all transposition levels (P0 ,
R3 , I8 , RI6 , etc.). Use note names in the matrix, not integers.
CHAPTER 34. SERIALISM
416
Table 34.7.1
I ↓
P
P
P
P
P
P
P
P
P
P
P
P
184
5.
I ↓
I ↓
I ↓
I ↓
I ↓
I ↓
I ↓
I ↓
I ↓
I ↓
←
←
←
←
←
←
←
←
←
←
←
←
↑RI
4.
I ↓
→
→
→
→
→
→
→
→
→
→
→
→
↑RI
↑RI
↑RI
↑RI
↑RI
↑RI
↑RI
↑RI
For the following excerpt, determine P5 and identify each row form 213
and statement. This example contains overlap.
œ. . .
. >
.
b
œ
.
œ
# œ n œœ b œ.
#
œ
#
bœ œ nœ
nœ œ. bœ œ. bœ œ
œ w
& c ‰ œ bœ œ #œ
>
p
. .
#
œ
>
w
n œœ # œ n n œœ. >
. b œ œ. . n œ. n œ.
.
?c Œ
#
œ
œ
b
œ
œ
b
œ
‰ J œ
œ
nœ œ bœ
#œ œ b œ œ bœ
Referring to the twelve-tone row used to construct the matrix in the
practice
exercise above (3, 7, 11, 1, 5, 0, 2, 10, 6, 4, 8, 9), find the
187
normal form and prime form for each discrete three-note set from the
& and provide an interval vector for each.
row,
(a) Set 1: 3, 7, 11. Normal form:
? Interval vector:
Prime form:
(b) Set 2: 1, 5, 0. Normal form:
Interval vector:
Prime form:
(c) Set 3: 2, 10, 6. Normal form:
Interval vector:
Prime form:
(d) Set 4: 4, 8, 9. Normal form:
Interval vector:
Prime form:
Click here to download the first homework assignment for this chapter.
Click here to download the second homework assignment for this chapter.
↑RI
↑RI
↑RI
Chapter 35
Minimalism
The rise of minimalism in the 1960s was a significant development in art music.
While four artists are typically associated with minimalism—La Monte Young
(b. 1935), Terry Riley (b. 1935), Phillip Glass (b. 1937), Steve Reich (b.
1936)—we will focus on just two techniques in this chapter. The first, additive
minimalism, is associated with the early minimalist pieces by Philip Glass.
The second, phase shifting, is associated with Steve Reich.
35.1 Additive Minimalism
In Philip Glass’s version of additive minimalism as found at the beginning
of his composition Two Pages (1969), he adds a repetition of a pattern but
subtracts the final note in the repetition. Each addition to the pattern is
another repetition with the final note of the previous repetition subtracted,
as can be seen in the example below. (Note: The music notation below is
a transcription and analysis meant to show the additive process and is not
necessarily how the music is written in the score.)
Pattern:
Pattern:
Pattern:
5
&
& 885
A
A
A
.. œ œœ œœ bb œœ œœ .. 855ˆ484
.œ
. 8ˆ8
A
A
A
+
+
+
B
B
B
œœ œœ œœ ..
.. œ œœ œœ bb œœ œœ
œ
.œ
.
œ
(B
is
A minus
(B
is
minus
(Bfinal
is A
Anote)
minus
final
final note)
note)
B
bb œœ œœ +
œœ + Cœ œ .
55ˆ44ˆ33 ..
œ
œ
œ
œ
œ
&
œœ œ œ
œœ œ œ ..
& 88ˆ88ˆ88 . œœ œ
Pattern:
Pattern:
Pattern:
Pattern:
Pattern:
Pattern:
55ˆ484ˆ383ˆ282
&
8
& 8ˆ8ˆ8ˆ8
88
&
4
&4
A
A
A
A
A
A
+
+
+
+
+
B
B
B
B
B
+
+
+
+
+
C
C
(C
is
B minus
(C
is
minus
(Cfinal
is B
B note)
minus
final
final note)
note)
C
C
C
+
+
+
D
D
D
.. œ œœ œœ bb œœ œœ œ œœ œœ œœ œ œœ œœ œ œœ ..
.œ
.
œ
œ
œ
(D
is
C minus
(D
is
minus
(Dfinal
is C
Cnote)
minus
final
note)
final note)
417
65
65
65
& 85ˆ48ˆ38 .. œ œ œ
œ œ œ
œ œ œ ..
(C is B minus
final note)
CHAPTER 35. MINIMALISM
Pattern:
A
+
B
+
C
+
418
D
bœ œ
œ
& 85ˆ48ˆ38ˆ28 .. œ œ œ YT: emeykTooD9c
œ œ œ
œ œ œ œ œ ..
(D is C minus
final note)
Figure 35.1.1 Glass, Two Pages (1969)
The following example from Music in Fifths (1969) clearly displays additive
process on its own, but is just one of dozens of steps in an additive process.
b
œ
œ œ œ œ œ œ œ œ œ œ
& b b œœ œœ œœ œœ œ œœ œœ œ œ œ œ œ œ œ œ œ œ œœ
Pattern:
b
&bb
A
A
65
+
B
b œ œ . 5 ˆ4 . œ œ b œ œ
œ .
. 88 .œ
.
& 85 .. œ œ œ
œ œ œ
(B is A minus
final note)
YT: 6V1hokSS4TU
Figure 35.1.2 Glass, Music in Fifths (1969)
To hear additive process
listen
Pattern:in Glass’s well-known
A Einstein+on the Beach,
B
+
to the following minute of music from Act 1, Scene
1, œ“Train.” Each chord
in
b
œ
œ
œ œ lengthenedœby adding
œ œ to the œ
a five–chord cadential&
progression
85ˆ48ˆ38 .. isœ gradually
number of subdivisions given to each chord.
C
œ œ ..
(C is B minus
final note)
Pattern:
A
YT: pRerJeYmUgY
5ˆ4ˆ3onˆ2the.. Beach
œ
Figure 35.1.3 Glass, Einstein
&8 8 8 8 œ
+
B
+
C
+
D
œ b œ œ œ œ œ œ œ œ œ œ œ ..
35.2 Phase Shifting
Minimalist composer Steve Reich conceived of phase shifting in his early work
in tape music, noting that tape loops of slightly differing lengths containing the
œœ œphase
œœ œwhenœ
œœ into
œœback
same idea went slowly outb bof phase
and
veryœ gradually
œ
œ
œ
œ
œ
œ
œ
b
œ
& œ(seeœ It’sœ Gonna
œ Rain
œ œfrom 1965 and Comeœ Outœ
they were repeated incessantly
from 1966). Reich applied this phase–shifting process to live performance in
Piano Phase (1967), Violin Phase (1967), and Clapping Music (1972).
ã œ œ œ ‰ œ œ ‰ œJ ‰ œ œ ‰
#
& # 43 œ œ œ œ œ œ œ œ œ œ œ œ
YouTube: https://www.youtube.com/watch?v=lzkOFJMI5i8
Figure 35.2.1 Reich, Clapping Music (1972)
Below is the basic twelve–note pattern of Piano Phase along with a video
demonstrating the phase–shifting.
(D is C minus
final note)
œœ œ œ œ
œ œ œ
ã œ œ œ ‰ œ œ ‰ œJ ‰ œ œ ‰
CHAPTER 35. MINIMALISM
419
#
& # 43 œ œ œ œ œ œ œ œ œ œ œ œ
YouTube: https://www.youtube.com/watch?v=57TuvksMR70
Figure 35.2.2 Reich, Piano Phase (1967)
During the phase–shifting process, one can think of the lower voices in the
examples above as going through rotation. The example below shows rotation
of a five–note pattern. The pattern rotates one note to the left, meaning the
second note begins the pattern on the second line, the third note begins the
pattern on the third line, etc., until the first note starts the pattern again to
66
complete the phase–shifting process.
& 85 œ
œ
2
œ
œ
& 85 œ
œ
œ
2
œ
& 85 œ
œ
œ
& 85 œ
œ
& 85 œ
œ
1
3
4
5
3
4
5
1
3
4
5
4
5
œ
1
œ
œ
5
œ
1
œ
2
œ
œ
1
2
3
œ
œ
œ
2
3
rotating pattern one note
to the right. 2nd note begins
pattern, then the 3rd note begins
the pattern, until the 1st notestarts the
pattern again to complete the process.
4
In a piece of music,&the process would play out similar to the manner
below, where one part maintains the original pattern while the second goes
out of phase by continually rotating the original pattern one note to the left.
In Piano Phase, Reich has the second pianist gradually increase in speed so
the patterns go slowly out of phase, while in Clapping Music, Reich has the
musicians change to the next rotation on the downbeat of a measure, without
gradually speeding up.
Figure 35.2.3 Rotation demonstrated with a five–note pattern
P5
# œœ. # œ. 4
>
12
n
.
. n œ. n œ. w
>
.
œ
b
œ
9
n
œ
œ
.
?c Œ
n
œ
#
œ
‰ J œœ65 œ 8 b b œœ œœ b œ b œ œ
n œ. œ b œ
#œ
CHAPTER 35. MINIMALISM
1
2 3
4 5/6
7
8/9 10/11 12
2
3
1
RI10
7
In phase
187
10
11
1 23 4
5 6 7 8 9 10 11
Out of phase
420
12
In phase
& 85 .. œ œ œ œ œ .. .. œ œ œ œ œ .. .. œ œ œ œ œ .. .. œ œ œ œ œ .. .. œ œ œ œ œ .. œ œ œ œ œ ..
12345
12345
12345
12345
12345
12345
12345
23451
34512
45123
51234
12345
first
rotation
second
rotation
third
rotation
& 85 .. œ œ œ œ œ .. .. œ œ œ œ œ .. .. œ œ œ œ œ .. .. œ œ œ œ œ .. .. œ œ œ œ œ .. œ œ œ œ œ ..
fourth
rotation
Figure
35.2.4 A short phase–shifting process piece
193
&
One hears phase shifting in numerous works by Reich, including the second
movement of his Three Movements.
&
YouTube: https://www.youtube.com/watch?v=XIuJ_my4_-k
Figure 35.2.5 Reich, Three Movements, II.
It is worth mentioning that composers like Stravinsky applied rotation to
serialism, which Joseph Straus details in Chapter 6 of his Introduction to
Post–Tonal Analysis (4th edition).
35.3 Homework Assignments
Click here to download the first homework assignment for this chapter.
Click here to download the second homework assignment for this chapter.
Click here to download the Unit 12 Practice Test.
Appendix A
Answers to Practice Exercises
1 · Basic Concepts
1.6 · Practice Exercises
1.6.1. Answer.
A6, 10. B7
1. A0, 2. F1, 3. D2, 4. G2, 5. B3, 6. E4, 7. A4, 8. G5, 9.
1.6.2. Answer. 1. E5, 2. D6, 3. F4, 4. G3, 5. A4, 6. E4, 7. G3, 8. A2, 9.
E4, 10. E4, 11. G3, 12. C4
3
4
4
3
5
3
2
5
1.6.3. Answer. 1. G and E ; 2. D and F ; 3. G and B ; 4. G and E
2 · Major Scales and Key Signatures
2.4 · Practice Exercises
2 2
2 2 2
2.4.1. Answer. 1. D E F G A B C
4
4 4
2. A B C D E F G
2
2
4
2.4.2. Answer. 1. A ; 2. A; 3. G; 4. E ; 5. F; 6. D; 7. C ;
2
2
4
2
2
8. E; 9. B ; 10. D ; 11. F ; 12. B; 13. C ; 14. G
3 · Minor Scales and Key Signatures
3.4 · Practice Exercises
2
3.4.1. Answer. 1. e ; 2. b; 3.
4
2
4
8. f ; 9. a ; 10. a ; 11. d; 12.
2
4
c ; 4. g; 5. f; 6. e; 7. b ;
4
4
g ; 13. c; 14. d
3.4.4. Answer.
(a) f
2
(b) e
(c) E
2
(d) E
4
(e) a
2
(f) C
4
(g) d
421
APPENDIX A. ANSWERS TO PRACTICE EXERCISES
422
4 · Basics of Rhythm
4.7 · Practice Exercises
4.7.1. Answer.
(a) Compound Duple (or Compound Quadruple)
(b) Simple Quadruple (or Simple Duple)
(c) Simple Triple
(d) Compound Triple
(e) Compound Duple (or Compound Quadruple
4.7.2. Answer. a. Time Signature: 12
16 ; Meter: Compound Quadruple
b. Time Signature: 32 ; Meter: Simple Triple
c. Time Signature: 38 ; Meter: Simple Triple
d. Time Signature: 42 ; Meter: Simple Quadruple
4.7.3. Answer. 1. Dotted quarter note
2. Eighth note
3. Dotted eighth note
4. Half note
4.7.4. Answer.
is simple quadruple
(a) The meter of
4
2
(b) The meter of
9
16
(c) The meter of
3
4
is compound triple
is simple triple
4.7.5. Answer.
Example
1.
379
2.
381
3.
383
387
391
Incorrect
ã 43 œJ .
œ
œ
ã 68 œ
œ œ œ.
(œ œ œ œ œ œ œ œ œ œ œ œ )
3 (œœ œœ œœ
ã4
œ
œœ
œ œ œ œ œ œ œ œ œ)
œœ
œœ
( œ œ œ œ œ œ œ œ œ œ œ)
6 œ˙
ã8
œœ
œ
J
œ
(œ œ
43 œ .
Correct
œ œ œ œ œ œ œ œ œ œ)
œ œ.
3 ( œœ œœ œœ
4
68 ( œœ
5 · Intervals
ø7/C
Ex. D
_____
1. ____
5.6 · Practice
Exercises
?
˜
&
& ˜˜ ˜
5.6.1. Answer. 1. 6, 2. 4, 3. 2, 4. 8, 5. 7
œ œ œ œ
œ œ œ œ œ œ œ œ œ)
œ œ
œ œ
œ œ œ œ œ œ œ œ œ œ œ)
(œ œ
œ œ 68 œ .
( œ œ œ œ œ œ œ œ œ œ œ)
œ œ œ
œ œ œ
œ
œ œ œ œ œ œ œ œ œ œ)
œ
2. ____
?
œ œ
3. ____
E: ii/3rd
1. f: V
2. D:6.IV/5th
3. b¯:viiº
5.6.2. Answer.Ex. 1.
m6, 2. M3, 3. M2,
4. P5, 5. m7,
+4
1. ____
2.2 ____ 2
4 3. ____4
2
24. ____
5.6.3. Answer.
Upper notes: 1. D , 2. G , ?
3. A , 4. B , 5. F , 6. F
?
&
&4
4
4
2
2
5.6.4. Answer. Lower notes: 1. G , 2. A , 3. F, 4. G , 5. F , 6. B
6 · Triads
?
1. g: III
5. ____
5. e: viiº/3rd
395
11
ø7/C
D
_____
3. A¯: ii
2. A: vi
&
_____
6. ____
?
6. d: VII
_____
#
7. ____
7. C˜: IV
_____
4. b: iiº
&
_____
8. ____
8. G: I/5th
_____
APPENDIX A. ANSWERS TO PRACTICE EXERCISES
423
6.7 · Practice Exercises
4
2
2
1. A ◦ , 2. Fsus4, 3. B + , 4. D , 5. Esus2
4
4 4
2 2 2
4 4 4
6.7.2. Answer. 1. BDF , 2. EG B , 3. A B E , 4. C E G , 5. DGA, 6.
2 2
FA C
4 . 4
2.
6.7.3. Answer. 1. Dm/F , 2. Gm/D , 3. A ◦ C , 4. F/A , 5. B F , 6.
6.7.1. Answer.
Cm/G
6.7.4. Answer.
6.7.5. Answer.
4
2 2
2
(lowest to highest) 1. DGB, 2. DF B, 3. FA D , 4. B EG
4 4 4
2 2
2 2 2
1. F A C , 2. GB D , 3. A C E
7 · Roman Numerals and Cadences
7.5 · Practice Exercises
7.5.1. Answer.
. 4
Bm F , ii/5th
4
4 . 4
1. F m , ii ; 2. D ◦ F , ii◦ /3rd ; 3. A , VII ; 4. G , V ; 5.
7.5.2. Answer.
6
6 2
1. C , CE G; 2. G/D , DGB; 3. A◦ , A CE
7.5.3. Answer. a. “Columbia, the Gem of the Ocean”: 1. G , I ; 2. D , V ;
3. G , I ; 4. C , IV ; 5. G , I ; 6. D , V ; Cadence type = Half Cadence (HC)
b. “Could You Be Loved”: 1. D , I ; 2. Bm , vi ; 3. G , IV ; 4. D , I ;
Cadence type = Plagal Cadence (PC)
8 · Seventh Chords
8.4 · Practice Exercises
8.4.1. Answer. 1. D7 , V7
2. G∆7 , IVM 7
4
3. D ø7, iiø7 4. Bm7 .D , iii7 3rd
4
5. C ◦7 E , vii◦7 3rd
8.4.2. Answer. 1. Bm7, B-D-F4-A
2. Aø 7 , A-C-E2-G
4
3. C ø7 , C4-E-G-B
4. G7 , G-B6-D-F
5. Emaj 7 /G4, G4-B-D4-E
2
2
2
8.4.3. Answer. a. “No Scrubs”: 1. D m7 , iv7 ; 2. A m , i ; 3. E 7 , V7 ; 4.
2
A m, i
b. Mozart: 1. C , I ; 2. G7 D , V7 5th ; 3. C , I ; 4. F/C , IV/5th ; 5. C ,
I ; 6. G7 B , V7 3rd ; 7. C , I ; Cadence type: Authentic Cadence (AC)
9 · Harmonic Progression and Harmonic Function
9.9 · Practice Exercises
Day One 9.9.1. Answer. In F major:
1. F-A-C
2. IV = B2-D-F
3. viiº = E-G-B2
APPENDIX A. ANSWERS TO PRACTICE EXERCISES
4. iii = A-C-E
5. vi = D-F-A
6. ii = G-B2-D
7. V = C-E-G
8. F-A-C
####
b
In
B
minor:
&
1. B-D-F4
2. iv = E-G-B
3. VII = A-C4-E
4.b III = D-F4-A #
&5.b bVIb = G-B-D
6. iiº = C4-E-G
7. V = F4-A4-C4
8. B-D-F4
558
563
17
bb
##
###
bbbbb
bbb
b
w
w
9.9.2.
? # #Answer.ww 1. A3, 2. bA4, 3. wD,ww 4. C?4, 5.# G, ww6. G
568
##
&b b
w
w
#
& # 44
473
www
_____
FUNCTION:
_____
9.9.4. Answer.
574
479
_____
_____
_____
Correct
Cadence: _______
Incorrect
㜠œœ
? b 4
b 4
g:
œœ
œ_____œ .
≈
ww
w
œ œ œ œ_____
œ œ œ œ _____œ œ œ_____œ œ
≈
_____
i
_____
VI
9.9.5. Answer. HC = V
FUNCTION:
_____
ã bDC = V-vi_____
PC = IV-I
AC = V-I _____
_____
485
_____
(œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ )(œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ )
576
b
& b b 44
www
iv
iiø7/3rd
V7
_____
_____
_____
_____
_____
_____
_____
V
vi
_____
_____
i
_____
Cadence: _______
9.9.6. Answer.
E¯≤:
FUNCTION:
I
_____
9.9.7. Answer.
491
& b # ww
w
9.9.3. Answer. 1. 4 flats in key signature, iv, B2-D2-F
ø4 4-A 3. G: V6
2. 3 sharps
1. E: in
IV6key signature,2.IV,
c: iiD-F
4. d: viio6
5
3
3. 3 flats in key signature, iiº/3rd, F-A2-D
_____
_____
_____
4. 4 sharps_____
in key signature,
vi,_____
C4-E-G4 _____
5. 2 flats inIncorrect
signature, viiº7, F4-A-C-E2
Correct
( œ6. œ 5œsharps
œ œ œ in
œ œkey
œ œsignature,
œ œ œ œ œ V7/5th,
œ )(œ œ C
œ 4œ-E-F
œ œ4-A
œ 4œ œ œ œ œ œ œ œ œ )
7. 1œflat in key
signature,
i/3rd,
F-A-D
œ
œ
œ
œ
œ
œ
.
ã J8. 1 D:flat in key
IJ signature,
vi7
ii7/3rd
V
I
R iii iii,J A-C-E
14
572
424
# 4
& # 4
D:
FUNCTION:
D
_____
ww
w
I
ton.
_____
In
1.
2.
3.
4.
F major:
F, I
IV vi
ii7/3rd
Dm,
Gm/B
_____ 2, ii/3rd
_____
C, V
F˜m
_____
ww
w
www
w
Bm7
_____
iii
vi7
ton.
prol.
_____
ton.
prol.
_____
In
1.
2.
3.
4.
E major:
C4m, vi
A,I/5th
IV
E,_____
I
B, V
Cadence: _______
7/G
Em
_____
A
_____
ii7/3rd
pre-dom.
_____
dom.
_____
www
w
www
V
D
_____
ww
w
I
ton.
_____
AC
Cadence: _______
10 · Non-Chord Tones
b
&bb
497
b
&bb
503
APPENDIX A. ANSWERS TO PRACTICE EXERCISES
425
10.13 · Practice Exercises
10.13.1. Answer.
Non-Chord Tone Type
RETARDATION
ESCAPE TONE
PASSING TONE
APPOGGIATURA
Approached by
same tone
STEP
step
leap
Left by
step up
leap in opposite direction
step in same direction
STEP
2
2
10.13.2. Answer. Lead-sheet: B , Dm, E , F
Rom. num.: I, iii, IV, V
10.13.3. Answer. a. “Stop! In the Name of Love” example
Lead-sheet symbols: Am, G/B, F, G
Roman numerals: vi, V/3rd, IV IVM7, V
Measure 2: 7-6 suspension in voice part and in right hand of piano, appoggiatura in left hand of piano
Measure 3: 9-8 suspension (or incomplete neighbor) in voice part and right
hand of piano
Measure 4: 6-5 suspension in voice and right hand of piano
b. Robert Schumann example
Pickup measure: appoggiatura in right hand of piano;
Measure 1: appoggiatura in left hand of piano; 7-6 suspension, appoggiatura
in right hand of piano; Roman numeral: iv/3rd
Measure 2: appoggiatura in right hand; Roman numeral: V7
Measure 3: anticipation, appoggiatura in voice part; appoggiatura in right
hand; Roman numeral: ii/3rd, V7, Lead-sheet symbol: E7
Measure 4: 4-3 suspension; appoggiatura in right hand; Roman numeral:
I, Lead-sheet symbol: A
12 · Form in Popular Music
12.6 · Practice Exercises
12.6.1. Answer.
She’s Out of My Life:
• 0:00–0:40, Introduction, approx. 4 bars of keyboard
• 0:40–1:25, A, 12 bars
• 1:25–2:05, A, 11 bars
• 2:05–2:35, B, 8 bars
• 2:35–3:33, A, 13 bars
Penny Lane:
• 0:00–0:20, Verse 1, 8 bars
• 0:20–0:38, Verse 2, 8 bars
• 0:38–0:54, Chorus, 8 bars
• 0:54–1:11, Verse 3, 8 bars
• 1:11–1:28, Trumpet Solo on Verse progression, 8 bars
• 1:28–1:45, Chorus, 8 bars
• 1:45–2:02, Verse 4, 8 bars
• 2:02–2:19, Verse 5, 8 bars
APPENDIX A. ANSWERS TO PRACTICE EXERCISES
426
• 2:19–2:36, Chorus, 8 bars
• 2:36–3:02, Chorus a whole step higher, 9 bars
13 · Phrases in Combination
13.9 · Practice Exercises
13.9.1. Mozart, “Ein Mädchen oder Weibchen,”The Magic Flute.
Answer. Mozart, The Magic Flute, “Ein Mädchen oder Weibchen”:
• Chords: I – V , V – I
• Cadences: HC, PAC
• No Sentences
• Melodic labels: a, b
• Form: contrasting period
13.9.2. Mozart, Piano Sonata K. 333, I. Answer. Mozart, Piano Sonata
K. 333, I:
• Chords: vii◦ – I , vi – V , vii◦ – I , V – I
• Cadences: IAC, HC, IAC, PAC
• The 2nd phrase is a sentence
• Melodic labels: a, b, a, b’
• Form: parallel double period
13.9.3. Edmond Dédé, Chicago, Grande Valse à l’Américaine. Answer. Dédé, Chicago:
• Chords: V , V , V , V , V – I
• Cadences: HC, HC, HC, PAC
• The 1st and 3rd phrases are sentences
• Melodic labels: a, a, a, a’
• Form: parallel double period
16 · Figured Bass
16.6 · Practice Exercises
16.6.1. Answer.
• Lead-sheet: 1. C/G ; 2. B◦ /D ; 3. Dm/A ; 4. G
• Figured bass: 1. I64 ; 2. vii◦6 ; 3. ii64 ; 4. V
16.6.2. Answer.
• Lead-sheet: 1. Em7/G ; 2. G7/F ; 3. Cmaj7/G ; 4. Fmaj7
• Figured bass: 1. iii65 ; 2. V42 ; 3. IM43 ; 4. IVM7
####
&b
558
##
bb
bbb
APPENDIX A. ANSWERS TO PRACTICE EXERCISES
#
bb
b
1.
&•b Lead-sheet:
563
16.6.3. Answer.
◦
# ##
◦7
D /F ; 2. A
427
bbbbb
b
. 4
G ; 3. Eø 7 ; 4. Dmaj7 F
• Figured bass: 1. ii◦6 ; 2. vii◦42 ; 3. viiø7 ; 4. IM65
? ####
568
ww
w
& b
1. E: IV6
?
16.6.5.
Answer.
572
7/B
F/A G
Lead-sheet: ____
____
64 882
572
b
& 44 œœ C
& ww
w
? b C:œ I
? 44 C: I
œ
591
884
66
910
583
7/F
Dm
____
C
____
œ www œ(œ ) www œ
C/E
œ
œ
I6
I/3rd
C
____
6
V
5
____
FUNCTION:
I ton.
C: ____
E¯: ____
C
1
C
____C
œœ
˙œww
ww
vi7
œvi7
œ
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C/G
9-8 susp.
I6
4
I/5th
b www
w
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____
ii56
____
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____
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V7/____
____
2 7
C
____
ton.
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ii
____
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www
w
& b # www
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4. d: viio6
G
____
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____
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w
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vi65
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vi43
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V
____
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587
914
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##
29
w
wwwww
www
w
Am7/C
vi42
w
w
vi7/7th
F____
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I
____
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˙____
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w
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4. A: V6/ii
pre-dom.
dom.
ii
V
V
____
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____
____
____ ____ ____
____ ____ ____
A7
D7
G
3
4 7 5
6
7
87
9
F
E
Am
D
G
____D7 ____
____
____
____
F
C
& 44 ˙˙
˙˙‰˙ j b ˙˙ # ˙˙˙ ‰˙˙ j
4
‰
?
4
&?
4 44 ˙˙ œ ˙ .. ˙˙
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912
892
2. c: iiø43
?#
ww
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#
b
n
w
b
b ____ ____ Dominant
17
· bSecondary
Lead-sheet:
____ ____ ____Chords
____ ____ ____
7
7
b
7/VI
C
Am
Dm3.
4
1.
E¯:
V/ii
2.
g:
V
e: V42/iv
17.7
Exercises
b 44Practice
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&b·
œ
œ
œ
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17.7.1.
˙
˙
˙
˙
˙˙Dm ____
7
7
C˙
E
Am
A
D7
˙
____
____
____
____
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˙
? 4˙
œ#œ˙˙˙ ( œ) œœ˙˙˙˙. œ # ˙˙˙œj œœ ˙˙˙œ œ # ˙˙˙˙œ
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( ˙)
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˙œ7 œ
b C: I
vi7
ii˙
IV6
C: ____
579
wwww
bb
16.6.4. Answer.
____
10
˙˙
˙˙ n # ˙˙˙ ˙˙
˙
˙
# ˙˙
‰ j # ˙˙ ˙ www‰ j
˙
˙˙˙˙ ... ˙ ˙ n œœœ ˙˙˙ ...
w œœ ˙˙
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.
I
IV
IV > V7/____
vi
vi> V7/____
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____
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7
I
V /ii
/V
V
?FUNCTION:
44 C:j ton.
j œ prol. ‰ Vpre-dom.
‰
‰
jœ
œ
˙
ton.
dom.
j
œ
œ
œ
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17.7.2. Answer.
œ ˙ œ œ
œ ˙7
7/B¯
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˙
œ
D . . œ E¯
A/E
G
˜7/F
˜ œ.
A¯
>7/D˜ ____
œ
Lead-sheet:
____
____
____
˙
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.
œb ____
˙
.
>
#
.
##
#
#
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b
>
b
w
#
b
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ww IV
&
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Iw
ww b # www bVb7/V ww
w
w
#
w
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? # # # w b w b b . . # w > # # # # . w. b b b w
b 4 œj ‰ œœ. ≈ œœ bœ œœ œœœ œ. œœ œ œ œ >œœ b œ ‰
b
œ
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& 4b: œ_____
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œ œ f: V_____
œ64/V œ œE:œ_____
V/vi
V
V24/vi
.V56/iv F: _____
c: _____
G: _____
J
591
π 1 œ. 2
3
4
5
. œ. œ. > œ. œ. n >œ œ 6
œ
? b b œœ.
n
œ
b
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œ ≈ œ œ œ œ b œœ œœ œ
?17.7.3.
bb 44b Answer.
J ‰
‰
993
999
995
572
999
579
____
____
____ ____
____ ____
____
428
œ œ œ œ (œœ) ˙ ww
? #b 4 œœ œœ œ
œ ˙
& b #b c4 œ œ œ œ œ œœ œ ( œœ) œ nœœ œ œ# (.œ )# œJœ œ # œ œ u
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? b e:4____
____ ____ ____
____
bb 4
i
iv
V56œ/V œ œ ˙
V
b
œ . # œ _____
Rom. num.:
_____
_____
œ
œ
œ
œ
& b b œ _____
œ
œ
œ
˙ Œ 29
œ
œ
œ
J
œ
C
C/E
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Am7/C Am7/E
Am7/G
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w
#
ww
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&&
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www
b wwb
w
w
w
C: I
I6
I64
vi7
vi65
vi43
vi42
? ##
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C: I
Cm I/3rd
b
17.7.4.
c
& b b Answer.
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____
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b bb b
i
17.7.5. Answer.
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vi7
I/5th
Fm
D7vi
/F7˜/3rd
G
vi7/5thG
œ œ œ œ œ 7œ œ . # œJ œ 7œ œ ˙
œ
E¯
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/D
____
bw
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b
V3.56/V
e: V42/iv
_____
2. _____
g:ivV7/VI
. .˙
˙
c˙˙˙ ‰ œJ œ œ œ# ˙˙˙œ œ œ œ
E7
____
C
____
F
D7/F˜
Fm
1. E¯:_____
V/ii
Rom. num.:
583
71
? b
b# b
U
#
œ
c
œ
œ
(
)
œ
œ
œ
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APPENDIX
A.
ANSWERS
TO
PRACTICE
EXERCISES
(
)
&
œ #œ œ
œ œ( ) n œ n(œ ) ww
____
Am
A7
____
Dm ____
Dm7
____
G /B
vi7/7th
˙F____
˜/A˜
œœœ œœœ œœœ
w
# ww
V
4. A: V6/ii
_____
D7
____
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˙˙œ . j ˙
# ˙˙n œ
˙˙ œ œ#œ˙˙˙œ ‰ ˙˙˙œJ
˙
G
____
C
F
E7
____
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vi
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G
____
V
_____
‰ œJwwwœ . œ œ . œ œ œ œ
w
? c ‰ œœœ œœœ œœœ ‰ œœœ œœœ œœœ ‰ œœœ œœœ œœœ ‰ œœœ œœœ œœœ ‰ œœœ œœœ œœœ ‰œœœ œœœ œœœ ‰ œœœ œœœ œœœ ‰ œœœ œœœ œœœ
b
nœœœ œœ œ
J
J
I mot.1
vi
vi mot.
ii
mot. 2____
aug.
C: ____
V7/____
V72/____
? 44
587
C
C7
____
____
I
F: _____
˙˙
˙˙
b ˙˙˙
˙
# ˙˙˙˙
˙˙
˙
˙
ii mot. 1V7mot.
V 2
____
/____
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____
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_____
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˙˙
D7
____
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# #C: ____ V /____ ____ V /____ ____ V /____
& c ww
w
M3
m3
# www
m3
# # Secondary
18?·
Diminished Chords
c # ww
975
70
I
7
IV
IV
7
vi
vi
7
V
18.5 · Practice
Exercises
?
D: _____
977
18.5.1. Answer.
˜o7
Lead-sheet: A
____
# w
&591 # ww
? bb
? # # #b w
o7
/vi
D: vii
_____
1
_____
983
& b b ww
C____
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ø7/F
G
____
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E
____
b b n # www b b b b ww
w
bb n w b b b w
o6
ø4
vii /V E¯: _____
vii 2 /IV
g: _____
2
3
#
_____
# ww
bb
b b b b b n ww
n ww
bb b b
b
_____
# ww
o4
vii 3/iii
D¯: _____
4
1Vinv.
____
2. inv
ww
ww
V
____
‹o7/E
F____
# # # # ‹ ww b b b
# w b n ww
# # # # w b b b b ww
b
o7/C
A____
vii 2 /V A¯: _____
vii 5 /ii
c ˜: _____
5
6
o4
### w
nw
_____
o6
b b b b n ww
_____
591
˙
ww
˙
˙
4 ˙
˙
˙
IV
vi
V
V
V7/____
____
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b bI www A. ANSWERS
bIVwww ____
wwV7/____
bEXERCISES
b ww ____
& C: ____
w
APPENDIX
TO bPRACTICE
w
w
ww
C: Answer.
¯VI
iv
18.5.2.
ˆ
o7
¯6 as: Root ____
E 3rd
599
iio
5thF____
˜o7/A
www
# ww
n w w bb
b ww b b wwn ww
bw
? b b bw
b b b ww
&
#
1. A¯: viio7/vi
C: ¯III
i
595
18.5.3.
¯3 as: Answer.
Root
3rd
iiø7
viio7
5th F____
˜ø7/C7th
wwww
b www
b www
# ###
b ww
b ww
429
¯VII7
7th
B____
˜o7/A
w
# n # www
b ww
b
w
4. B: viio4/ii
2. c: viio65/V
3. e: viiø43/III
¯VI
¯VII
v
¯III
5th
¯7 as: Root . 3rd
5th
2
4 ◦7
4
• Lead–sheet: 1. F ; 2. Am ; 3. B ; 4. F ; 5. D F ; 6. Gm
605
611
? bb b
b
•# Figured bass: 1. I ; 2. iii ;b w
ww3. IV ; 4.
w
&
b www Mixturew
600 · Mode
19
? b b b· Practice
A is root when
?
19.6
Exercises
b G: ____
stacked in 3rds;
19.6.1. Answer.
C____
˜o7/B¯
616
634
622
640
b
& bb b b www
?
bb
##
### w
b
w
# w b b b ww
b w56/iv
b: V
A: ¯III
____
____
E: ____
F: ____
1
A: iv
f:2V34/V
____
____
____
____
19.6.3. Answer.
### # w
&
# ww
____
f˜: ____
1
&
____
1. E¯: N6
?
658
e: ____
2
bbbb b w
ww
____
B¯: ____
3
#
____
____
2. b: N
c˜: ____
4
w b bw
n # www b b ww
____
3. D: ¯III
____
B¯: ____
4
____
4. c: viio7/V
____
3. G: ¯VII7
3 + 3 + 3 + 3 + 3 +
123 1 2 3 1 2 3 1 2 3 123 1
D/F˜
____
b b b # n www
6/V
c: V
____
6
ww
w
b D¯
w
# www b b ____
b
w
n # www b b b www
A: ____
B¯: ____
____
G
˜o7/F
____
e: viio425/iv
____
____
____
B¯: ¯III6
____
____
#
b
bbb
b
b
w
w
# # # # n w b b ww # # n www
ww
g: viio7/V
A¯: iiø4
G: iio6
____
e: ____
3
iv6
B¯: ____
5
G
wø7/B¯ # #
b ww____
#
b wwww #
____
D: ____
E¯: ____
3
4 iiø65
D: ¯VI
F:
____
____
____
____
f: ____
2
2. a: N
____
1. c˜: N6
664
iiø43
B: ____
4
7/D
G
B¯
____
# # b wwww____
w
b
b
w
bb b b b ww n w # # b n www b bb
n www
c: ____
1
652
viio42/iii
G: ____
3
31
(bass note is
3rd of chord)
E¯m/G¯
____
____
? # # # # n ww
# # ww
& # n www
____
19.6.2. Answer.
Dm
____
E¯: ¯VII7
646
(m3-m3-M3)
C˜ø7/G
b wwww
iiø65
G: ____
# ww # # # # www b b ww
# ww
# nw
bw
¯III
A¯: ____
2
viio42
D: ____
A: ¯VI
1
m3
m3
quality is ø7
A is 2ˆ
C¯
A____
˜o7/G
____
? # # # b wwww n w b b b b b www
&
n ww b
615628
b www
w
6
vii◦7 ii ; 5. VM3
ii ; 6. ii
2
____
4. d: viio65/V
3 + 3
23
3
d: ____
5
b: ____
6
# # b www
w
b b ww
w
____
D: ____
5
____
d: ____
6
____
____
5. B¯: iiø4
6. G: N6
____
____
2
5. F: N46
6. f˜: N6
+ 3 +2+2 +2+ 2
>
1 2 3 1 2 3 12 1 2 1 2 1 2
APPENDIX A. ANSWERS TO PRACTICE EXERCISES
430
32
74
o7
E¯
D
E¯
E¯(maj7)/D
__________
7 /E¯ ped A7__________
o7/C˜
F/A
G¯__________
(¯5)
G____
˜o/B__________
A˜____
____
____
____
œ.
# ww
?&b b b b w12
8w œJ # n www
œ œ œ œ.
bb n ww # # # #( )‹ www( w ) b n # www œ # # # wwwwœ
J
bw
nt pt
espress. dolce
œœ ____
œœ o6/V œb: ____
Ger+6 e: ____
N6 œ B¯:
It+6
Fr+6 œ d: ____
vii
viiœ
g: ____
œœo65
œœ b œc˜œœ: ____
œ
œ
ped
pt
œ 5
œ 6
? b b 12
1
2 œ
3(œ. )
4
b 8____‰ œ. ____
.œ
____
____
____
____
.
œ
*
# w
? # # b # wwww b b b°∫ b www #* b °www # # # # n°# www b b *# n www b b w*w
b
# n w
b w° b ww
E¯7
____
666
672
I
viio7/I ped
I
IM42
E¯: __________
__________
__________
__________
D: ____
A¯: ____ G: ____
B: ____
B¯: ____ c: ____
1C7
2___________
3
5
6
C7
Eo7/F ped4
Fm
__________
____________
___________
628
684
634
689
640
694
b œ
b œ .____
T
____
____
____
____
œ.
œ C¯ A˜œo7____
n
/G
C˜ø7œ/G
E¯m/G¯
D/F˜
b
#
#
#
#
b
J
o4
o4
ø4
6
6
b
b
#
w
b
b b b J n ww vii 2/iiib wwww b ii 3b ww iv# www Vb /V# n www
&&vii# 2 # wwww ¯III
w
b ____
w
w____
____
____
____ œ
____
œ
œ
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b œ œœœbb: ____
www n œœb b f:œœb____
b www # G:œœ #____
œ F: œ____
??# # f˜:b w____
w
#
ped
pt w
w
#
b
bb b 7
b 8 œ. # w9w
# 10n wwœw b b11www œb b b #œn www12
œ
(œ )
œ.
____ G: ____ *____ B: ____ ____
____
D: ____
A¯: ____
B¯: ____
c: ____
°
*
*6
1
2
3
5
°
° 4
*
°
&
____
____
____
____
____
____
__________
V7/ii
___________
V7/ii b w
____________
viio7/ii
___________
ii
ww 5. d:b Gerb www+6
+6 w
wwG: EnGer
# o65/V
2.ww
F: It+6#
3.
? # #1.# #c˜:nFrww+6
ww 4. a:#vii
b
b
w
b
#
w b
#
#
w
b
w
b
ww Neapolitan
b
w
20 · The
Chord
Lead-sheet:
____
____ D: ____ ____
____
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____
____
____
E:w
F: ____
E¯: ____
A: ____
____
& 44·
20.3
Practice
Exercises ____
ww____
w
1
2
3
4
5
6
?
20.3.1. Answer.
C˜o7/B¯
678
Rom. num.:
____
D¯/F
____
Function:
1. Tonic
E¯: It+6
L.S.: ____ ____
?4
? b b4
b
?
bwww
w
c: ____
& www 1 6
6. f: N
646
699
652
N6
##
& # # # www
? b b b ww
bb w
o/E¯
____
____
A¯/E¯ ____ C
D/F˜
Ao/C
C
____
____
____
____
____
+6
+6
4
Mode
mixture
Tonic
__________
2. a: Ger
3. D: EnGer
4. c: V3/V
5. B¯: Fr+6
________ (with ¯6) ____
____
____
____
____
# b ww
bw
w
bb b ww
# # # # n ww
ww
ww
w
b b ww # # n ww
N64
iio6
N6
viio6/VI b: ____
N
G: ____
B¯: ____
ww
www c˜: ____ d: ____
w
2
3
4
5
6
7. A¯: viiø7/V
8. b: Fr+6
9. F: ¯III46
10. c˜: viio42/iv
____
____
____
____
____
ww b b w
b b b b b w # n # wwww b b b b www # # C____
b w/B¯
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A¯/C
w
____
ww
ww
w
____
b
w
b
w
ww # # n w
#
b w
b w____ d:b ____
ww
bw
n ww b b # n www b D:ww__________
5
6
____
20.3.2. Answer.
?
B¯
F
F˜o7
____
____
____
w F¯/A¯
w ____
R.N.: ____
____
____
f
˜
:
____
f:
____
e:
____
B¯: ____
Func.:__________
Secondary of V
__________
1
2
3
4
6
o7
1. E¯:____
N
2. a:____
N
3. D:____
¯III
4. c: vii
____/V
& · Augmented Sixth Chords
21
21.91. E¯:
·NPractice
Exercises
6
2. a: N
3. D: ¯III
4. c: viio7/V
5. B¯:
iiø42
____
6. G:
N6
____
5. B¯: iiø4
6. G: N6
____
____
2
21.9.1. Answer.
658
?
____
1. c˜: N6
____
2. b: N
____
3. G: ¯VII7
3 + 3 + 3 + 3 + 3 +
____
4. d: viio65/V
3 + 3
5. F: N46
6. f˜: N6
+ 3 +2+2 +2+ 2
31
A
32
APPENDIX A. ANSWERS
TO PRACTICE EXERCISES
one degree
one degree
D
775
# www
? bb &
w
##
E¯7
____
666
b
Ger+6
g: ____
1
34
# n ww
w
N6
It+6
e: ____
B¯: ____
2
(relative
keys3with
1 G
1. c˜: Fr+6
f˜
o7
# # # wwww
c˜
Fr+6
viio6/V
viio65
c˜: ____
d: ____
b: ____
5
6
same4key signature)
D 5 Em 6F˜o
2
3
major:
G Am
Bm 4 C
2. F: It+6
3. G: EnGer+6 4. a: viio65/V
739 # #
# w
# # # ww
22
·
b
#b Modulation
# www b b b b n ww
b
w
w
b
w
&
w
b
D major:
D b wEm Fww˜m G wA
& · wPractice
w Exercises
22.8
678
####
785
&# # #
& #
E¯7
684
G____
˜o/B
# # # # ‹ www b n # www
w
b b b n www
# #/C˜
#A#˜____
"sharper"
7(¯5)
A
____
b # www # E¯# 7
7
D¯7#
˜o7b/F˜ n w ____
? # # b # wwww b b b ∫ b www____
w ____
# # # n n # wwwwD____
# b www bB¯b b wwww
b
b
# www
# # # # ‹ www
# #w
#
w
w
b
n
w
b
w
w
#
w
w
& D: ____ A¯: ____
b ww G: ____ b ww B: ____# w B¯: ____ c: ____
734
36
G¯7
____
431
21.9.2. Answer.
A7(¯5)
____
672
36
###
"flatter"
F/A
____
E
22.8.1. Answer.
f˜: ____
f: ____
(a) d: F, g, A, B2, C
7
8
2
2
2
2
7
7
(b)
, b2
G¯ D : e , f, GA, A
(¯5)
785 F/A
&
G: ____
9
G˜o/B
g: ____
10
b: ____
11
A˜o7/C˜
5. d: Ger+6
b # n www o
Bmb wC˜
F: ____
12
(c) f: A2, b2, c, D2, E2
22.8.2.
Answer.
F ____
C7/B¯ ____
F/A ____
Dm C/E
C/G ____
G7 ____
C
Lead-sheet
symbols: ____
____ Dm/F
____ ____
o
7/B¯ F/A
7
R.
N.:
I
ii
iii
IV
V
vi
vii
F
C
Dm
C/E
Dm/F
C/G
G
C
+6
Lead-sheet
symbols: 2.____
____ +6____4. a:
____
____
1. c˜: Fr+6
F: It+6____ 3.____
G: EnGer
viio65____
/V ____
5. F: Ger
Roman numerals: F: I
V42
I6
vi
I
V42 Am
I6
viBm
G major:
G
C I6 D ii6 EmI6 FV˜7o
C : ii
___
Roman numerals: F:
?
689
?
694
C : ii
___
I6
ii6
I46
V7
4 I
GmGG/B
Cm Cm/E¯
F7
B¯
D major:____
CEø7˜o B¯/F
D Em
F ˜m
____A ____ Bm
____ ____
____
____ ____
+6
+6
+6
4
+6
1. E¯: It
2. a: Ger
3. D: EnGer
4. c: V /V
5. B¯: Fr
R. N.:g: i IVV6/ivV iv viiv6 vii3o I
ii
iii
Roman numerals:
Lead-sheet symbols:
B¯ :
___
ii6 viiø7/V
I46
V7
I
E¯
6. f: N
7. A¯: vii /V
8. b: Fr
9. F: ¯III
10. c˜: vii /iv
22.8.3. Answer.
B
B¯A
F
F˜
A¯/C
aC____/B¯ ____
C
f˜F¯/A¯
____
____
____
____
####
F
˜
#
& # # #? b b w
bw
b w
& c˜ b b b ww b www # # n n www b b b # n wwww b b www # b ww
D¯
b N 2. a:DN 3. D: ¯III 4. c: vii /V 5.dB¯: ii 6. G:FN
1. E¯:
6
ø7
+6
6
4
o7
787
o4
2
ø7
787
699
789
####
789
&
####
&
####
&
809
809
778
&
&
####
#&#######
817
817
##
6
e
to parallel
minor
G
o7
ø4
2
g
6
B¯
I
36
785
&
####
? b 4 œ˙ .
b 4 ˙˙ ..
œ
œ
œ
œ.
b œœ
œœ
n œœ
œ ˙
˙
n ˙˙
œ.
b œœ
APPENDIX A. ANSWERS TO PRACTICE EXERCISES
A
____
Lead-sheet
symbols:
22.8.4.
Answer.
A
____
Roman numerals:
Lead-sheet symbols:
Roman numerals:
C
____
____
____
I
V42
A: I
F:
¯III
____
I
I6
7/G Dm/F B¯7 Dm/A
A
A7 ____
B¯
____
____ ____ ____ ____
A
____
7/G Dm/F B¯7 Dm/A
A
A7 ____
B¯
____
____
____ ____ ____
4
A
____
A:
IC7/B¯ ¯III
F
F/A
Lead-sheet symbols:
Roman numerals:
C
____
432
I
V /IV
Dm C/E
C/G
____
____ 2 Dm/F
____ ____
V24/IV
4
6
G7
____
C
____
d :V
i
Ger+6 i64
vi ___
2
4
6
+6
d
___ : V2
i
Ger
i64 7 V7 VI
6
6
6
C :
___
ii
I
ii
I4
V
o7
V7
I
o7
Gm Gm/B¯
A¯/C
D
A¯/E¯
E
Fm
Lead-sheet symbols:Gm____
____ B¯m/D¯
____ B¯m/D¯
____
____
____
o7 Fm ____
Do7 A¯/E¯
E____
____ Gm/B¯
____ A¯/C
____ ____ ____
____ ____
____
Gm G/B
Cm Cm/E¯ Eø7 B¯/F
F7
B¯
Lead-sheet symbols: ____ ____ ____6 ____ ____
____ ____ ____
6
6
6
Roman
numerals:
g:
i
i
N
Roman numerals: g: i
i
N
Roman numerals: g: i
V6/iv A¯
iv 6 iv6 66
A¯ : Iii viio7
___ : I___
viio7/vi
ii6/V viiI64o7/V
I64 viviio7/vi vi
7
B¯ : ii6 viiø7/V I6
___
V
I
4
Lead-sheet symbols:
22.8.5. Answer.
787
___
iio ___III
d:
___
___
___
˙
˙ w o˙ ˙
#
˙ ww in Dm:
E ( ˙ ) ___
( ˙) ( ˙ ___
?Lead-sheet
˙)
)Dm
(w) ___
(F
&b b 44 ˙ symbols
( ˙)
( )
Dm
Eo ___
F
Lead-sheet symbols in F:
___ ___
LSS:
___ ___ ___
Roman numerals:
822
RN:
G: ___ ___ vi
___ ___ ___
vi
___
iv ___ V___ ___
VI ___viio
___
˙˙ ˙ ___˙ ˙___ w ___
( Gm
) ˙ A
B¯
C˜o
( ) ___
___
( ˙ ) ( ˙___
) ( w)___
Gm ___
Am ___
B¯ C
___
___
Roman numerals:
F:
o
vi ___
viiD:___
I___ ___
ii ___ ___
iii___ ___
IV___ ___
V
___
___
___
___
HF:
PD
/V Dom
Ton Dom
____
22.8.6. Answer.
795
___ ___i ___
Em D___
˜ /F˜ ___
Em/G
___
# 4 ˙ ˙
& 4
LSS:
RN:
o
w
i ___
viio6 ___
i6
e: ___
F/A
˜o7 ___
B
___ A___
n˙ ˙
#w
o7
V
N6 vii
___ /V ___
____ Dom Ton PD
Cad64 Dom Ton
7(¯5) Bm/F˜ F˜ Bm
Em
˜7 Bm/D
___ F___
___ G___
___ ___ ___
˙ #˙
˙ #˙
˙ #˙
w
i
iv ___
V7 ___
i6 Fr+6 ___
i64 ___
V ___
i
b:___
HF:
803
Ton Dom
Ton
PD
___ PD
__/ V Dom
22.8.7. Answer.
2m
˜m A2m,EmDm,GD
˜m
(a) Fm:GAm,
Em
PD Dom Ton ___
PD Cad6 Dom Ton
____
4
G ˜m
(b) D2:# ˙F2, F, B
œ 2, œB3 (or# ˙A, enharmonically)
œ œ #˙
?(c)42G:# B˙˙2, B, E,œœ En œœœ2 # ˙˙
p
4
4
4
œœ n œœœ # ˙˙
(d) G m: Bm, B m, Em, E m
23 · Enharmonic Modulation
23.4 · Practice Exercises
23.4.1. Answer.
Em
œ.
n œœœ ...
j
# œœ
# œœ
J
B (no 3rd)
# ˙˙
# ˙˙
˙˙
˙˙
VI
APPENDIX A. ANSWERS TO PRACTICE EXERCISES
42
˙
b˙
& # ˙˙˙& b
888
433
˙# ww˙˙˙
ww # ˙
˙
b ˙˙˙# w
ww b ˙
˙
b w ˙˙
wwb ˙˙
b˙ w
w˙ ∫ ˙
w˙˙
b b ∫b˙w
b ˙ b b ˙˙˙˙
w
a: viio7
V65
c: viio42
+6
V
_____
enharmonicallyg: Ger
resolve
enharmonically respelled
respelled
bb
˙˙ b ˙
˙
& b b ˙&
892
respell
A¯
V7 V4
__ : ____
e¯: viio43
826
#
& E¯:
Roman numerals:
104
C¯
____
A¯
____
F
____
I
¯VI
IV
V /V
b
&
bb cb bœ
830
&
œœ
897
832
Gm
____
? bb c
&
œ
œ
b b#bœœb
œ
œœ
œ
b Vb
& b b____
4
2
b
? # # # # c&œ #b b œ
#
&
844
&
846
_____
œ
# œœ
&
4
o7
œœ
œ
œœ
œ
__ : ____
œ
b www
w
œ
n œœ # n œœœœ n #b œœœœ
œ
E¯7
____
____
vi
____
resolveœœ
____
V7
____
‹ # œœœ
_____
#œ
#œ
œ
b œœ
œ
_____
resolve
œ
/iv
____
resolve
www
œ
n # # www____
œ
____
n œœ
____
bbb
##
œ
____
# n nwwwœw
____
o4
a : ____
vii
__
2
respell
n www
w
c : ____
viio43
__
œ
____
resolve
resolve
n n wwwœ
i____
(or I)
_____
www
i (or I)
_____
b: viio7 resolve _____
V
œœ # n œœœ
œ
A¯
____
˙˙
˙
b˙
____
I
____
˙˙
˙
˙
____
____
n˙
˙
_____
i (or I) ˙
n œœ
[or
œ G¯] __
œ5
fœ ˜ : ____
vii
__ : ____ resolve _____
respell
resolve
b b bœ
iv
_____
b œœ
œ
respell____ n____
b b____
b
&
# # wwww
#
c
#
œœ # œœ œœ o6
&
œ
b: ____
6
Fm
____
f:œ V7/VIœ
____
œœ
? ## c œ
&
842
o7
E¯:
viio7
_____
I
____ +6____
____
____
D:
Ger
respell
resolve _____
E: ____
##
E¯7
____
i6
Ger+6
____
____
A ¯: V 7
____ ____ ____
____
836
+6
resolve
respell
# # # # c œœ # œœ
œ
œ
838 &
834 23.4.4. Answer.
840
n œœœ n œœœ
œ
7/C
D____
Gm/B
____ ¯
i
g: ____
&
7
7
__ : ____
23.4.3. Answer.
V43
Am/E
E /D C
˜ ____
Dm ____
E
____ ____
____
a Ger
___:
i
V2 vii
G: V7/IV
resolve 4 _____
&
828
7
E¯
____
œ bœ
b#b œœrespell
b œœ
b
&
896
I o6
G¯:_____
vii
5
V7
2resolve
23.4.2. Answer.
Lead-sheet symbols:
˙˙
˙˙
enharmonically respelled
n˙
____
39
150
LSS:
Motives:
____
œ
____
____
____
œœ œœ
œœœ
____
œ œ
œ
____
b œ ANSWERS
œ
˙
APPENDIX
TO
J PRACTICE
J J œ J EXERCISES
& b c A.
J
J
œ œ ˙
434
œ œo7 œ œ œ7 œ .œ . œ œ œ. œ œ œ 105
œDmœ œGo7œ/Dœ¯ Eœ¯7œ/Dœ¯ Aœ¯m/C
œ
? b b c œ___
œ1621œC___
œ˜o7œ ___
œ /B¯ œE¯ /B¯ œA¯m œ
Dm
___ ___ ___ ¯ G___
œ œ œ˙ ___b œ # œ___ œ
123
NCTs: Answer.
23.4.5.
150
œ
œ
˙
œ
3
& b 4 œœ& ‰œœ œ œœœ œ b œœœ œ b œœ bœœœ b b ˙˙˙ b œœœ n b œb ˙˙ ... œœ Œ
b
œ
b
˙
œ œ ____ ____
RN in B¯: ____
____
œ œ ____œ ____
p
HF:
____
____
____
____
____
____
. ____
.
LSS:
____
____œ.
____
____ œ. ____
.œ
.œ
œ
œ
.
Motives:
? b 43 œ?# œ œ œœ b œœ œ œ b œ œ œ˙ œ œ b œ n œ œ Œ
œ œ____
œ.œ œ œ ____
b ˙ œ. œ˙
œ ˙ ____œ œ____
LSS: b b c
____
œ œ ____
œœ. œ œ ____
J
J
J
J
&
J J
___
___
___
___
___
œo7o4œ ___
œvii
œ
œ
b 42œ œ i6œ œ œviiœ o6œ5 œœ œV4œ3 œ œi œ œ œ
œ
œ
a
¯
:
vii
V
œ
œ
b
3
œ
œ
œ
œœœ œ
Menuetto
?
œ____
œJ œ J____
œœ œ œ ____
œ˙ œ œ ˙ œ
& bbb cJ# œdiagram:
œ œ ____
Jœ œ œA____
____ ____
#
# c œ and
24 ·
Binary
œœœ œ œœ œForms
NCTs:
&
œœ Ternary
n œœ œ œ œn b œœœœ œ œ n ˙˙˙
n
œ
œ
b
œ
a
b
œ
œ
œ
œ
n
œ____
œ œ Exercises
œœ
œ
/?
:
bB¯:œPractice
œ œ ____
œ ____œ œœ____:/: ____
24.9
RN inb·
____
œ œ œ œ ˙ :/
Trio diagram:
HF:
____
____
____
____
____
24.9.1.
Answer.
. ____
.
.
#
? #____
B
œ
b
œ
1621 A
b
œ
c
œ
œ
œ
œ
œ
#
œ
n
˙
RN:
____
____
____
____
____
____
#
œ
LSS:
____ œ ____
____ œ____
˙˙
œ____
œ œ ____
œ b œ____
‰ œa' ____
HF:
____
____
____
LSS:
____
____
____
____
____
____ œ
œd Œ :/ Œ
a
c____ n œ____
Motives:
&
œ
/
:
:
/
:
œ
œ
œ
œ
œ
œ
œ
œ
A:
____
____
____
____
____
____
____
Motives:
œ
œ
œ
œ
b
œ
œ D: PAC
˙ G: HC œ œp ˙PAC
œ8 Jœ œ Jb œJ œ e:m.JPAC
& b b c œG:œJm.HC
œ
J
œ
œ
4
m.
12
m.. 16 ____
b œJ œJ____ ____
œb œœœ n œœ. ˙ œ. m.˙20
œœ. œœ.____ ____ œœœ. œJ____
œœ. œ œJ ____
œ
&NCTs:
b b b c? œœ œn œœ œ œœ œ œœ œœ œ œ œœ œ œ œ n œœ œ œ œ œ œœ œŒ œ œ Œ
b
?
œ
œ˙˙ TERNARY
œ
&
b
œœ .#œœ ROUNDED
œœœ. œ œœœ CONTINUOUS
NCTs:
TWO-REPRISE
œ#œ œœ œBINARY
b c bœ œ SECTIONAL
œ n n œœœ BALANCED
? b b œ œ œ œ œ œ œ œ œ œ œ œ bœœ œ œ œ œœ œ ˙œ œ œ œ ˙
Motives:
NCTs:
150
..
Œ
..
o7 ___
i vii
i
d: ___
___
? bb b c œ
bb
œ
nœ
œB ˙
&
____ . œn____
____ .
.
œ
œ
œ
œ
œ
bb œ . œ œ œ œ .
œœ ____
œœb. bœ˙œ____œb œ # œ____a' œ œ:/ œ
b
œ
œ
____
____
˙____
œ œ Œ Œ
&
œ
____
____
HC n œ ____ œ PAC
&‰ œ œ œ œ œ
m. 12
m. 18
œ
œ
œ
œ
p
f
œ
œ
b œœœ œ œ. œœ. Bœ œ . .
œ A œœ
?&TWO-REPRISE
b bb aœJ œœ œJ œœ a'œœ. œœœœ.
œœ Jœœ œ Jc œ œb œœœ n œœ ˙ dœ.œ ˙ n œ
b ROUNDED
?
SECTIONAL
CONTINUOUS
BALANCED
BINARY TERNARY
b
/:
:/:
œ
Œ :/ Œ
b
œ
œ
œ
.
.
NCTs:
œ œ
24.9.2.
RN in B¯: Answer.
____
____
120
Œ
œ
œ
____
____
A
HF:
____
____
____
____
1590
RN:
____
____
____
____
HF:
____
____
____
a 1621 ____
a'
:/:
/:
b¯: ____ ____ ____ ____
LSS:
____ A: HC
____
____ PAC
____
Motives:
m. 4
m. 8
? bb œ œ œ œ œ œ œ
œ
____
____
____
____
œ
œ œ
œ œœœœ œ œ
œ œ œ bœ œ œ
œ œ ˙
123
..
..
123
œœœœ
.
œ
.
..
B
œ œ œ œ œ œ Uœ
____
____
____
____
œ
œ
bb œ . œ œ œ ____
œ
œ
.
____
____
____
____
____
b
œ
œ
.
a'
a'
:/: e: PAC b
D: PAC œ
G: HC
PAC :/
& b
m. 8
m.
12
m.
16
m.
20
PAC
HC
PAC
rit.
m. 8
m. 12
m. poco
18
œ
œ
p A œ
œ
œ
U
œB œ
? b a œœ œ a' œœ œb
œ
c
d
:/
/: b b
:/:
24.9.3. diagram:
Answer.
Menuetto
A
____
____
/:
G: HC
m.A:
4 HC
m. 4
1594
RN:
____
Trio diagram:
HF:
____
a
TWO-REPRISE SECTIONAL
CONTINUOUS
A
ROUNDED BALANCED
B
/
A
a
: diagram:
Trio
B¯:
:/:
b
B
c
c'
IAC
G: HC F: PAC
D: PAC c: IAC
m. 4
TERNARY
A
24.9.4. Answer.
Menuetto diagram:
BINARY
m. 8
B¯:
e: PAC
m. 12
a
IAC
d
:/
G: HCIAC
m. 16
PAC
PAC
m. 20
HC
PAC
Two-Reprise Continuous Ternary, if looking at the proportion, or TwoReprise Continuous Rounded Binary, if you interpret the first two notes
E¯:
HC
PAC
HC
A: PAC
PAC
D: DC
HC
PAC
A: PAC
PAC
435
œ
U
œ
œ
œ
œ
b
œ
œ
œ
œ
œ
œ
œ 123
.
œ
b
œ
œ
œ
.
.
in bbar
13
as being built from
the first two notes in bar .1—and if you
are
œ
œ
b
.
. to compose
&considering that Mozart, as a Classical-era composer,
œ œ˙ isb œlikely
œ
œ that
#
œ
œ œ œBalanced
a rounded binary.
Two-Reprise
Continuous
Binary
is a label
˙
œ
œ
œœ poco
‰
n
œ
Πrit.
Π..
œ
œ
œ
œ
p
&the endings
describes that
of
the
halves
are
the
same,
but
doesn’t
take
into
œ
œ
œ
U
œœ material
œ in œbar 21. œ
?account
bb b œœthe returnœœ œof the opening
œ
p
.œ œ.
.œ œ.
.œ œ.
bœ nœ .
APPENDIX A. ANSWERS TO PRACTICE EXERCISES
1594
1621
?
A
œ
œ
24.9.5. Answer.
A
.
a
a'
b: IAC
A
PAC
œ
/:
a
/: Sectional
Ternary
œ.
a
a'
B¯:
IAC
A: PAC
PAC
:/:
:/:
F: PAC
a
IAC
b
PAC
Œ
:/
:/
a'
B
HC
HC
c
IAC
PAC
a'
HC
PAC
PAC
A: PAC
PAC
(final phrase could
be
:/
analyzed as two phrases)
B¯: IAC
c: IAC
Œ
a'
B
b
D: DC
œ
œ
A
b: HC
HC
PAC
œ
b'
D: IAC
a'
B¯: HC
Bœ
B
b
24.9.6. Answer.
E¯: HC A PAC
/:
œ
IAC
PAC
Two-Reprise
Menuetto
diagram: Sectional Rounded Binary (because the motives from the
first section are used in the construction of the melody of the second seca
b
c
a
a
tion)
Trio diagram:
a
a
G: HC
b
D: PAC
c
e: PAC
c'
m. 4
8
m. 12
25 · Sonata
andm.Rondo
Forms
25.6 · Practice Exercises
A: HC
25.6.1. Answer.
m. 4
PAC
m. 8
(a) Haydn: Expository
(b) Beethoven: Developmental
(c) Mozart K. 576: Transitional
(d) Mozart K. 550: Developmental
(e) Mozart K. 309: Expository
(f) Haydn: Terminative
(g) Mozart K. 309: Transitional
(h) Mozart K. 576: Terminative
(i) Mozart K. 310: Terminative
(j) Haydn: Transitional
(k) Mozart K. 457: Expository
(l) Mozart K. 550, IV: Developmental
25.6.2. Answer.
G: HC
m. a16
HC
m. 12
PAC
dm. 20
PAC
m. 18
..
? # ..
G: V65
I
0:30
0:48
1:36 2:07
2:24
IV
1:01
1:27
I
V7
3:13
vi
3:37
I6
V7
4
I
APPENDIX A. ANSWERS TO PRACTICE EXERCISES
DEVELOPMENT
EXPOSITION
transition
transition
In major:
0:08
0:00
I
modulating
In minor:
i
modulating
(2nd
time) 0:51
0:58
PT = Primary Theme
DEVELOPMENT
ST
ST
CT
(CT)
III
1:40
III
4:32
436
RECAPITULATION
RECAPITULATION
RetransitionPTPT transition
transition
Fragmentation &
sequencing
0:45
0:22
V
V
1:12
4:19
3:48
3:04
2:37
EXPOSITION
PT
PT
..
ST (CT)CT
ST
V modulations
V pedal
2:03I
2:11
tonicizations
2:31
I
I 2:54
III modulations
V pedal
i
tonicizations
i
i
1:35
ST = SecondaryTheme
CT = ClosingTheme
Figure A.0.1 Mozart, Piano Sonata K. 545, I.
EXPOSITION
PT
DEVELOPMENT
transition ST1
0:00
0:30
0:48
ST2
1:01
CT
1:27
RECAPITULATION
Retransition
3:13
3:37
PT
transition
3:48
4:19
ST1
ST2
CT
4:32
4:45
5:12
2:07
2:24 2:37 3:04
œœ
œœ
œœ
œ
œœ
œ
œœ
œœ
& œœ
œœ
œœ
œ
œ nachtmusik,
Figure
K.
& œœ A.0.2œœ Mozart,œœ Eine kleine
œ
œ 525, I.
?œ
œœ
œœœ
œœœ
œœœ
œœœ Leading
œ
26 ·
Triads
? Voice
&
œœ
œ
œ
œ6
œ6
6
6
C:
I
V
I
C:
IV
I
IV
4
4
26.13
· Practice
Exercises
6
C: I
V64
I6
C: IV
Iœ64
IV
œ
? œ Answer.
œ
œ
œ
26.13.1.
#
b
5th
5th6
œœ 5thRtRtI6 œœ 3rd
œœœ 3rd
C: bI b c œ
C: IV
I#64 c œ
IV6 œ Rt
&
œœ 3rd
Rt
bb c œœœ V5th
3rd4
3rd
5th
œ
œ
œœ 5th
œ 3rd
Rt
œ
# œœœ 5th
c
3rd
Rt
b
œ
œ
5th
3rd
Rt
Rt
5th
3rd
&
œœ 3rd
œœ 3rd
œ
Rt
3rd
5th
œ
œ 5th
œ 5th # œ 3rd œ 3rd
Rt
3rd
Rt
œ 5th
Rt
œ 3rd œ Rt œ 3rd
? b c œ 5thRt œ Rt œ 3rd œ 5th # c œ 5th œ 3rd œ Rt œ 5th
Rt
œœ RtRt # œœ 5thRt œœ 3rd5th
? bb bb cc œœœ 3rdRt œœ 5thRt œœ RtRt œœ 3rd
# cc œœ 3rd
&
Rt
Rt
Rt
5th
Rt
Rt
b
œ
œ
5th
3rd
Rt
Rt
3rd
Rt
œ Rt
Rt
3rd
œ RtRt
œ
E¯: I
vi
IV
ii
e: III 5th iv
œ 3rd œV Rt VI
œœ 5th
? b b cE¯: œI Rt viœ
# ce: III
(deceptive
IV
ii
iv
VI
Rt
œV Rt cadence)
Rt
b
œ Rt œ Rt
œ Rt œ Rt (deceptive
cadence)
#
3rd
b b Answer. œ Rt œ 5th œœ 3rd
26.13.2.
œ Rt Vœœ 3rd VIœœ Rt
Rt
# e:cc IIIœœ 3rd
& bb b b b E¯:cc I œœœ 5th
œœ 3rd iiœ 3rd
3rd
5th
Rt
Rt ivœ
viœ
Rt IVœ 5th
3rd
œ
œ
œœ 5thRt(deceptive
Rt
Rt
5th
& b
œ
œ
œœ 5thRt
3rd
œœ 5th œœ 5th œ 3rd œ Rt
œœ 3rdRt cadence)
Rt
œ
5th
Rt
5th
Rt
5th
3rd
œ
5th
3rd
œœ
œœ 5th œ 3rd
? bb c
#
3rd
œ
Rt
5th
œ
c
5th
Rt
3rd
3rd
3rd
œ
œ
œ
Rt
œœ 3rdRt œ RtRt # cc œ RtRt œ RtRt œœ 3rd5thRt œ 3rd
? bb bb b cc œœ 5thRtRt œœœ 5th
&
œ Rt œœ 5thRt
œ Rt œœ 5thRt œ RtRt œœ 5thRtRtRt
Rt
œœ Rt 3rd
b
f: i
iv
VII
III
G: vi 5th œii
V
3rd
œœ
œII 3rd
5th
œ
iv
VII
III
G:
vi
ii
V
? b b b cf: i
#
œ
Rt
c Rt œ
œ Rt œ Rt
Rt œ Rt
b
Rt
œœ
œœ Rt
œ
& bb cc œœ œ œœœ
œ
œ
œœ
œœ
œœ
œœ V
œœ
œœf: i œ iv œœVII III
&
G: vi œ ii
œ
œ
œ
œœ I
œ
œ
œ
œ
œ
26.13.3. Answer.
#
œ
œ
œ
œœ
œ
œ
œœ
?b c œ
œœ
# œœœ
œœœ
œœ
œœ
? b cc œœ
&
œ
œ
œœ
œœœ
œ˜
œ
œ
œ
œ
œœ
œœ
#____
œœV˜
iœ
VII
III
iv
VI
iv
œœ
____
____
____
____
____
____
œœi
? b d:d:c ____
œ
iœ
VII
III
iv
V
VI
iv
i
œ
(deceptive
cadence)
____
____
____
____
____
____
____
____
159
159
(2nd time) 1:36
#
& # cc
&
26.13.4.
?# c
? # cc
&
˜
(deceptive cadence)
œœ
œœ
œœ
œœœ
œ
œ
Answer.
œœ
œœœ
œœ
œ
i
d: ____
____
? # G:
I
G:c ____
œ
I
I
G: ____
VII
____
III
____
œœ
œœ
œ
œ
œœ
œ
œ
iv
____
œœœ
œœœ
œœœœ
V
VI
____
____
(deceptive cadence)
œœ
œœ
œ
œ
œœ
œIV
œœœ
œœœ
œœœœ
iv
____
˙˙
˙˙
˙
˙
˙˙
˙
V
vi
____
____
V
vi
____
____
(deceptive cadence)
(deceptive cadence)
iii
____
iii
____
œ
____
IV
____
œ
ii
____
ii
____
V
____
V
____
V
vi
____
____
(deceptive cadence)
iii
____
IV
____
ii
____
V
____
œ
œ
˙
i
____
159
4:45
5:12
i
d: ____
VII
____
III
____
V
VI
iv
____
____
____
(deceptive
cadence)
PRACTICE EXERCISES
APPENDIX A. ANSWERS TO
#
& c œœœ
?# c
œœ
œ
I
G: ____
160
œœ
œ
œœ
? # # c œœ
b œ
Rœœ
œœ
I
? b b cD:œœ ____ œ
œ
PRAC EX
## œœœ
Dom.
____
œœ
œœœ
6
6
viio6
____
viio6
____
? ## c
&
b D: g:____
œ ____
& b HF:c ____
œ
? bb
#b#b#b ccœœ œ
?
&&b c œ œ
26.13.7.
b b Answer.
HW
b
HW
V6
____
?#b b# b
?
bb
6 chord
& type:
4
HF: ____
i
b: ____
? #b b
&&b #b
V6
A: I
6
4
____
V64
____
œ
w
w
ww
œœ
R
œœ
œœ
V
____
R
5
V
____
Pre-dom.
____
Dom.
____
˙
œ
˜
˜
œ œœ
œ
Ton. œ
____
I
____
I
œ
œ
IV6
œ ____ œ
œœ Rt œœœ Rt
5th
œ 5thRt
3rd
____
œ
6
6
œ
3rd
____
i6
____
3rd
____
____
iio6
____
œ
____
____
œ
œ
˙
˜
w
____w
œœ ww œ
________
œ
Pre-dom.
____ œ
œ
ii6
____
R
VI
____
VI
____
____
____
œœ œ
œ
œ
V
____
V
____
œœ
____
3
ww
w
ww
w
6
œœ
____
R
5
ii6
____
## œœ
œ
œœ
œœ
____
____
5
161
œ
œ
œ
œ
3
5
R
R
3
ww R
(one of several
o6 solutions)
vii
I
ww ii ____
possible
____
____
3
I6
œ____
œ
6
3
VI
____
œœ
R
˙
œ
5
˜
6
66
i6
____
i
____
6
c œ
œœ
œ
œœ
Ton.
____
œ
œœ
œ œœ
œ
c œ passing n œ
____
c: ____
V
____
I
____
Dom.
____
? #b b# c Answer. œ
26.13.8.
œ ____
g:
&#
Rt
#
3rd
c
œœ 5th
&
œ 3rd # œœœ Rt
5th
? ## c
b
?
#b#b cb œc
œ 5th
&
Rt
& b D: ____ ____
? ##
b
&b
PRAC EX
œœ
____
œ
œœ
____
I
# c____
? #b#B¯:
œ
Ton.
&?b HF:b ____
#
c œ
ii
____
œ
V6
____
c œ
bg: ____
i
i
g: ____
IV
____
IV
œ
____
26.13.6. Answer.
I
B¯: ____
iii
____
œ
5
œ
5
bb bb bcc Ton.
œœ
&
____
& HF:
& b cœœ
œ
?
? #b bb# cc œ
&?b bc œ
˙˙
˙
3
6
i6
____
viio6
____
&b c œ
œœœ
# œœ
œ
R6
437
œœ
œ
œ
b
& b c œœ
# œœ
26.13.5. Answer.
œ
œ
3
? b # #c c
&b œ œœ œ
i
____
œœœ
œ
V
vi
____
____
(deceptive cadence)
i
g: ____
PRAC EX
œœ
œ
œ
œ
˜
iv
____
œœ
œ
œ
____
____
œ
œ
œ
Dom.
____
____˙
I
____
# œœ
œ
Rt
5th
œ
3rd
5th
____
i46
____
3rd
Rt
5th
˜
6
4 ____
œ
V
____
cadential
____
w
œ
____
(one of several
possible solutions)
( )
V
____
V6
161
161
Rt
œ
œ
œ
( )
V
˙
˙
˙˙
˙
vi
3rd
5th
3rd
Rt
____
˙
____
VI
____
˙
Ω
6
____
œ
____
w
____
& ? b c
bb
?
?
APPENDIX
A. c:ANSWERS
EXERCISES
i
iv TOi64PRACTICE
iv6
iio6
i64
6
4
chord type:
____
c˜: V Answer.
i
26.13.9.
7
7
A: V7
A:comp.
V7
b b c comp.
œœ Rt
& b inc.
comp.
5th
œ
& ? b c œ 3rd
& bb
Rt
c˜: inc.
V
5th
œœ comp.
œœ
3rd
œ Rt œ
œ Rt œ
i
I
I
inc.
Rt
inc.
5th
3rd
5th
V
VI
438
____
œ
œ
œ
œ
5th
Rt
f: V7
i
E¯: V7
I
f:comp.
V7 comp.
i
E¯:comp.
V7
I
comp.
Rt
Rt
3rd
3rd
comp.
comp. comp.
5th comp. 5th
œœ
œ
œ
Rt
3rd
œœ
œ
œ
3rd
3rd
n œœ
œ
œ
3rd
5th
Rt
5th
Rt
œ
œ
œœ
5th
3rd
6
o6
c: i œ
iv
i64
i64
V
VI
?
&
œ iv œ ii œ cadential
œ
œ passing
?64 chordœœtype: œ
____ œ consec. 1st-inv.
œ ____ œ Dec. Cad.
œ
œ
œ
œ7
7
7
7
7
7
7
œ
œ7
7 œ
7Leading
7
7
7˜
27? · Voice
Chords
œ7
œ
œ Seventh
b c esc ____
œ
b: ____
____
____ n ____
____
____
____
œ
ant
˜
sus
b
#
&
____Practice
____
____ ____
____
____
____
27.6
Exercises
& b: c·
œ7 ____
7
7œ
7 œ
7
7 ˙
œœ7
œ
œ
#
#
œ
œ
27.6.1. Answer.
# # ˙____ ˙ ____ # ____œ ____œ ____
bbb ˙˙˙ ____˙˙
# ˙˙ dn ˙˙
& #?˙˙A:b b____
˙ p˙
csus˙˙ ____#ant
#
˙
˙˙
˙˙ œ ˙˙ œ b ˙˙
&
˙œ ˙ œ
? ## ˙˙˙c œœ ˙˙ œ
˙
˙
˙
œ
˙
#
˙
˙
œ ˙ œ
˙ œ
? #˙
# # ˙˙
˙ œ # # ˙˙
˙˙
˙
bb ˙
˙˙
?
##
# ˙
& ˙
p˙
˙
bb ˙
˙
˙
7
e:
____ D: V____
V7 ____ i
I ____
7
7
V
i
D:
V
I
inc.
comp.
comp. inc.
inc.
comp.
comp. inc.
?#
#
& # c
M6
M4
27.6.2. Answer.
# # G: I 5 IV 2
& #b œœ
œ
?
& bb b# bc œ œ œ
& bœ
œ
?
#
œ ____
b:
____
? b# œ
b
? bb b
b i7
iv7
____
& b:b c____
4
f: i
iv6
a:
a:
viiø65
œœ
œ
œ
œ____
œœ œ
œ
œ ____
œœ
œœ
œœ
œœ
171
7
e: V____
i ____ B¯: ____
V7
I
7
e: comp.
V7
i
B¯:
V
I
comp.
comp. comp.
comp. comp.
comp. comp.
iii4
vi56
ii4
œ
____
œ
œœ œ
œ ˜
œ ____
œœ
vi
œœ
œœ œ
2
2
œœ ˙
V56
# œ ____
œ
œœ
œ
œ
œœ
IV
œœ
œœ
I
œœ
œœ
œœ
ii42
V56
IM42
IM42
VII7
IIIM7
VIM7
iiø7
V7
i
____
____
____
____
____
____
4
M6
M4
ø
6
VII
III 5 or incomplete
VI 2 with complete)
ii 5
V42
i65
5
2
(alternate
complete
with2 incomplete,
27.6.3.
? Answer.
b# c
œœ
œœ F:
?#
#
& M6
&
G: I
I
5
œœ
œœ
vi
IVM42
IV
viiø65
V
iii42
vi65
# Voice Leading With Non-Chord Tones
28? ·
bb
& b b·
28.4
Practice Exercises
? bb b
# bc esc
&
œœ œ œœ # œ
28.4.1. Answer.
? # c œœ
i
e: ____
œ.
œ
sus 4 - 3
V
____
ant
n
œ n œ œœ œ
p
œ
œ œœ
œ œ
p
VI
____
iv
____
œœ
sus
4 - 3 ant
dn
œœ # œ œ ˙
˙
œ œ œ œ œ
œ
œ
i64
____
V7
____
˙
i
____
167
Rt
ant
sus
4 - 3
p
˙˙
œ
sus
4 - 3
sus
œ
œ PRACTICE
œA. ANSWERS
œ œ œ EXERCISES
œ
œœ # œ
APPENDIX
TO
? ## c œ
œ
œ
œ
œ
9 - 8
˜
28.4.2. Answer.
#
œœ
& # c œœ œ œœ œ œœ
sus
&b c
ant
4 - 3
p
œ
œ
œ
œ œ œ
? # # cc
œ
œ
œ
œ
b
n iv
i
b: ____
____
172
i I
F: ____
b:
iv
vi
____
i
____
i
IV
____
III
____
iv
____
œœ œ
9 - 8
sus
œ
œ
III
V____
˙˙
V
____
VI
____
œœ
˙˙
sus
4 - 3
œœ # œ
˜
ivvi
____
439
V
IV
____
˙˙
177
VI
I____
#
app
& œœ 7th œœ
n
sus 4 - 3
ant 3rd
&
œ
b
c
œ
œ
œ
œ
&
œœ œ œœ œ œœ .
œ
œ œ œ
œ œ˙˙
?
œœ
?#
#œ
n
sus 4 - 3
sus 4 - 3
œ
œ
œ
œ
C: viioœ7/ii
œ
œ
œ
? b&c œ
œ
œ
œ
œ
œ
˙ || 5ths
7th
7th
b
œ
œ
#?
œ
˙
œ
œ œ nœ
& F: I œ vi œ IV &Vœb b n œ 3rdvi n œ IV n œ 3rdI œ
doubled
3rd
unequal 5ths
7
7
7
7
29 · Voice Leading
Chromatic
Harmonies
(avoid on V)
(preferable)
Ω
Ω
Ω
b
& # · Practice Exercises œ
?
œ
29.5
A¯: ____
____
____
? ____ # œ ____n œœ ____ # œ ____ n œœ
28.4.3. Answer.
178
?b bb
& b b œœ
#
œ
&
&
? bb b
b œ
?#
I
? A¯: ____
29.5.1. Answer.
œœ
nœ
œ
n œœ
bœ
œ
V7/vi
____
V7/ii
____
comp.
viio7/ii
inc.
ii
29.5.2.
b Answer.
A: I
bbb
c:
b œœ viio7/V œœ
n
& b# b#b
& # c œœ œ n œœ
? bb
bb
œ
œ
? ### c
œ
#œ
A: I
viio7/ii
nœ
œ
V
œœ
œ
œ
ii
V24
n
vi
____
V65 /V
œœ œ # œœ . œ œ œœ
œ
œ
I6
œœ
V
sus 4
n
œ˙
œ œ ˙˙
#œ
V56 /V
V
˙˙
viio7/vi
____
ant
œ
œ
˙˙
viio7/V
n œœ
V7/V
V
____
____
free res.
comp
V42
I6
p
œœ
ii
-
3
œ
V
Notice that the chords on beats 5 and 6 are consecutive first inversion
chords (even though one is a 7th chord), therefore the third is doubled on
I6 &
to avoid parallel fifths.
?
29.5.3. Answer.
4
Ω3
Rom. num.: ____ ____
APPENDIX A. ANSWERS
E: ____
____
Harm. func.: ton.
dom.
&
&b
&
?
?b
?
180
6
____
____
ton.
œ
6
4+
3N6
6
4
viio7/V
____
____
____
____
¯6
6
Ω7
____
____
____
____
____
dom. ton. prol.
6
˜
6
5
˜
6
˙œ
œ œ
#œ œ
b˙œ¯7 œ ¯7 œœ
Ω
&
# Answer.
29.5.4.
&#
? # œ œ
&
œ œ
? # A¯: vi
? # # œœ b # œœ
&
6
4
3
#
?
&D:
Int:
œœ
œ
œ
b b b b œœ œœ œœ
Fr+6
I ___
Fr+6 ___
V
___
V7
œ n¯VI
œ œ
bb b b n œ b œ œ
6
6
5
3
6
4
#
b: i6
& 44& b b b b œœ œ œœ
## œ œ
œ # œ # œœ
œœ # œœ œœ
viio7/Vœ
# # œœ b œœ œ
vi
# # œœ œœ œœ
N6
V
+6 i6
IV6 Ger
f: ___
___ ___
G: V43/V EnGer+6 I64
4
b: i6
œœ œ œ
b ∫ œœ
n œœ
c.f.
A¯: vi
Fr+6
¯VI
V7
N6
viio7/V
__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __
c.f.
?#
V
vi
w
?4
8
Interval: ____
& 44
& 44
&
w
w
c.f.
œœ w
__ __ __ __ __
First4and Second Species Exercises
30.9.1. Answer.
V
__7
œ œ
œ
30 ·
w towCounterpoint
4 Introduction
&4 w w w
w w w w
30.9 ·esc,Practice
Exercises
4-3 sus, p, ant
&
It+6 V
œœ .
? 4? w#b œœ b n œœw b œœ w A b œœw œ w œ w b œ w œœ w
4 b bb w
œ
nœ
&
&
It+6 V
4/V
˜: i __ V__
V6
viio4/iv
IV6
Ger+6
N6
__ __ f __
2 __ __ __ __3 __ __ __ __ __ __ __ __ __
29.5.5.
? # Answer.
Int:
œ
œ
œ œœ œ
7
____
6 V7 VI
e: VI N____
G: V43/V EnGer+6 I64
f: ___ ___ ___
440
# œ nœ #œ œ
œ œ œ œœ
œ˙ œ
4
4
6 viio7/V
b¯:___
____
____
vi
iv____
V ____
i6 N
V
3 ___
F: ___
a: ___
___
___ 3___
G: ____
ii7 viio7 ____
I
D: ___ ___ ___
Ω5
TO PRACTICE EXERCISES
# œ œ
œœ œœ ˙œ œ œœ b œœ # œœ œœ # œ
œ œ
œ
œœ b œ
œ bœ œ ˙
œ œ œ œœ
œ
#
œ
œ œ œ ˙ 6 œ œn6œ# œ b œ ¯7
œ œΩ7 œ œ
bœ œ 4
4
Ω
7
3 6
¯
œ
#œ
w
3
____
6
____
w
6
____
w
3
____
6
____
8
____
w
w
w
w
w
w
w
w
w
w
4
&4
w
w
w
w
w
w
APPENDIX A. ANSWERS TO PRACTICE EXERCISES
w
c.f.
8
Interval: ____
c.f.
3
____
6
____
& 44 w
w
w
w
4
&4
w
w
6
3
____
____
w
w
w
w
6
____
6
____
w
w
w
w
6
3
____
____
w
w
w
#w
441
8
____
w
w
no more than 3 consecutive 6ths or 3rds
changed direction on B (avoid changing on Fn later)
w w w w w w w w #w w
& 44 w w w w
Int:
8
___
& 44 w
& c.f.
8
Int:
___
c.f.
8
Int: 4 ___
w8
Int:
c.f.
8
& 44 ___
Int:
___
w
c.f.
c.f.
w
&
44 w
&
&
& 444 w
&
44 w
&
& 4 ww
3
3
5 ___
8 ___
3 ___
6 ___
3
___
___
___
w w w w w w w w w w w
5
___
5
___
5
___
5
___
w
ww
w
6
___
6
___
6
___
6
___
6
___
6
___
6
___
6
___
w w
ww w
w ww
w ww w
ww ww www
1 ___
w2 ___5 ___6
Int:
___
c.f.
1
2
5 ___
6
Int:
___
___
___
30.9.2.
Answer.
w
4
w
1 ___
2
Int:
___
___
& 44 c.f.
w5 ___6
w
c.f.
& 44 w pt w
&
& 444 ˙ pt˙ ˙ ˙
& 44 ˙˙ pt˙ ˙ ˙
˙ ˙ ˙
&4
&
Int:
6 ___
6 ___
3 ___
3 ___
6 ___
8
___
8
__ __
3
___
3
___
3
___
3
___
w
ww
w
w
ww
w
3
___
3
___
3
___
3
___
w
ww
w
w
ww
w
8 ___
6
___
w
w
w
˙ ˙
˙ ˙
˙ ˙
8 ___
6
___
8 ___
6
___
5
___
5
___
5
___
5
___
w
ww
w
w
ww
w
8 ___
6 ___
3 ___
6
___
8
6
3
6
___ ___ ___ ___
8 ___
6 ___
3 ___
6
___
8 ___
6 ___
3 ___
6
___
w
ww
w
w
ww
w8
6 ___
___
w
w
w
˙ ˙
˙ ˙
˙ ˙
6 ___
8
___
6 ___
8
___
w
ww
w
w
ww
w
3 __
2 __
3 __
5 __
8 __
7 __
3 __
5 __
6 __
7
__
w
ww
w
w
ww
w
6 ___
8
___
w
w
w
˙ ˙
˙ ˙
˙ ˙
6 ___
8
___
6 ___
8
___
w
ww
w
w
ww
w
3
___
3
___
3
___
3
___
w
ww
w
w
ww
w
5 ___
3
___
w
w
w
˙ ˙
˙ ˙
˙ ˙
w w
3 ___
1
___
3
1
___ ___
3 ___
1
___
3 ___
1
___
5 ___
3
___
5 ___
3
___
w
ww
w
w
ww
w
1
___
w
ww
ww
ww
w
w
w
ww
w
w
1
___
1
___
6 __
3 __
6 __
3 __
5 __
6
__
8
__
8 __
3 __
2 __
3 __
5 __
8 __
7 __
3 __
5 __
6 __
__ __
˙6 ˙__3 __
˙6 ˙__3 __˙5 #__6˙ __8w
˙ ˙7__ __
& 444__Ó__˙˙ __˙ __˙ __˙ __˙ __˙˙__˙ __ ˙__˙˙ __ __
__
__
˙ ˙ ˙__ ˙__ __˙ # ˙__ w
˙
˙
˙
˙
˙
Ó
˙
˙
pt
pt
˙
&
& 44 Ó ˙ w˙ pt˙ ˙ ˙ ˙ ˙ w˙ ˙ ˙ ˙ ˙w ˙ ˙ ˙ ˙ # ˙ w
?
w
&4 w
w pt
w
w pt
w
pt w
w
w
w
? 444 c.f.
w
w
w
w
w
w
w
w
w
w
? 44 c.f.
w
w
w
w
w
w
w
&
Int:
Int:
Int:
c.f.
8 __
5 __
3 __
3 __
5 __
8 __
3 __
3 __
2 __
3 __
2 __
3 __
5 __
6 __
7 __
3 __
5 __
6 __
3 __
8
__ __
c.f.
__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __
w __ __
w __ __w __ __w __
& 444 __c.f.
w __ __
w__ __w__ __w__ __w__ __w__ __ __
c.f.
w
& 44 w
w pt w pt ˙w ww pt w w
w
w
˙
w
˙
& 4 Ów ˙ ˙w
?
˙ ˙w ˙ ˙w ˙ ˙w ˙ ˙ ˙ ˙ ˙w ˙ w˙ ˙
4
w
˙
˙
? 44 Ó ˙ ˙
˙ ˙˙ ˙˙ ˙˙ ˙˙ ˙˙ ˙˙ ˙˙
˙
˙
? 44 Ó ˙ ˙
˙ ˙˙ ˙˙ ˙˙ ˙˙ ˙˙ ˙˙ ˙˙
&
Int:
Int:
&
&
&
&
&
&
w
w
w
w
w
Intervals:
Intervals:
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__ __
__
__
4
&4
&4
APPENDIX
A. ANSWERS TO PRACTICE EXERCISES
?4
w
w
w Dayw Two
? 44 wCounterpoint:
Species
c.f.
c.f.
w
w
442
w
w
w
30.9.3. Answer.
__
œ
œ
œ
œ
œ
œ
œ
œ
œ œ œ œœœ œ œœœ œœ
œœ œ œ œœœ w
œ
pt
pt
pt
8 __
6 __
Int: __
__
__
__
__
__
__
__
__
__
__
__
__
__
__
__
__
__
__
__
__
__
__
__
__
88 __
22 __
33 __
8__
33 __
22 __
88 __
33 __
6__
55 __
33 __
44 __
33 __
44 __
55 __
66 __
33 __
33 __
55 __
66 __
66 __
77 __
88 __
66 __
88 __
77 __
55 __
66
Int:
__
__
& 44
pt
? 44
w
w
c.f.
c.f.
pt
pt
w
pt
pt
w
pt
pt
w
w
camb.
camb.
w
__
88
w
4
w
w
w
&4 w
w
w
w
w
c.f.
camb.
c.f.
pt
pt
pt
pt
pt
pt pt
? 44 œ œœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ # œ œ œ œ w
Int: __
__
__
__
__
__
__
__
__
__
__
__
__
__
__
__
__
__
__
__
__
__
__
__
__
__
__
__
__
8 __
7 __
6 __
5 __
3 __
4 __
6 __
5 __
3 __
8 __
2 __
3 __
3 __
2 __
8 __
7 __
5 __
5 __
tt __
3 __
3 __
8 __
2 __
3 __
3 __
5 __
4 __
3
Int:
8 __
2 __
3 __
5 __
6 __
5 __
3 __
4 __
3 __
2 __
1 __
7 __5 __
4 __
3 __
5 __
6 __
7 __
8 __
7
Int: __
8 __
2 __
3 __
5 __
6 __
5 __
3 __
4 __
3 __
2 __
1 __
7 __5 __
4 __
3 __
5 __
6 __
7 __
8 __
7
Int: __
5 __
4 __
3 __
5
__
5 __
4 __
3 __
5
__
6 __
5 __
3 __
4 __
3 __
2 __
1 __
7 __5 __
4 __
3 __
5 __
6 __
7 __
8 __
7
__
6 __
5 __
3 pt
4 __
3 pt
2 __
1 pt
7 __5 __
4pt __
3 __
5 __
6 __
7pt__
8 __
7
pt
__
__
__
__
5 __
4 __
3 __
5
__
5 __
4 __
3 __
5
pt
__
œœœœ
œœœœ
œwptœ œ œ
œ ptœ œ œ
wpt
w
w
__ __ __ __
6 __
5 __
4 __
3
__
44 œ œ œ œ
& Int:
& Int:
4 œ____88 ptœ____22 œ____33 œ____55
4 œ ptœ œ œ
&
444 wœ œ œ œ
?
&
? 4 w ptpt
4 w
? 4 c.f.
w__ __ __ __
? Int:
4 c.f.
4 c.f.
8 __
3 __
4 __
5
Int:
__
44 c.f.
œ
œ
& Int:
œ
& Int:
4 œœ____88 œ____33 œ____44 œ____55
4 œ ptœ œ
&
444 œw œ œ œ
?
&
? 4 œw ptpt
4
? 4 c.f.
w
? 4 c.f.
4 w
œœœœ
œœœœ
œ œ œ ptœ
œw œ œ œ
w ptpt
w __ __ __
__
w
6 __
7 __
8 __
2
__
œ__6 __œœ7 __œœ8 __œœ2
œ6 __7 __8 __2
__
œ ptœœ œœ ptœœ
œw pt
wptpt pt
w
w
30.9.4. c.f.
Answer.
&
&4
&4
&
?4
?
?4
? 44
c.f.
8
Intervals:
__
8
Intervals:
__
& 44
&4
?
? 4444
Ó ˙˙
Ó
w
w
c.f.
c.f.
Intervals:
Ó ˙
Ó ˙
ww
8
__
c.f.
c.f.
4 Ó
&
& 444 Ó ˙˙
? 44 w
c.f.
c.f.
7 __
6
__
7 __
6
__
œœœœ
œœœœ
œwptœ œ ptœ
œ ptœ œ ptœ
wpt pt
w
w__ __ __
__
5œ __
3 __
1 __
2
__
œ__5 __3œœ __1œœ __2œœ
5 __
__
œ 3œ __1œ __2œ
œ œ œ ptœ
w pt
w pt
w
w
5 __
6
__
5 __
6
__
œ œœ œœ œœ
œ
œwptœœ œœ ptœœ
œwpt pt
wpt pt
w
__ __ __ __
œœ œœ
œœ œœ
wœ ptœ œ œ
œw ptœ œ œ
w pt
w
__ __ __ __
6 __
8 7 6
__
œ œœ __œœ __œ
6œ __
8 __
7 __
œ66
__
6 __
8 __
7 __
__
œ
œ œ ptœœ œ
œw œ
w ptpt
w
w
3 __
5
__
3 __
5
__
˙ ˙ ˙ ˙ ˙ ˙˙
˙ ˙ ˙ ˙ ˙
sync.
sus.
sync.
sync.
sus.
sync.
w
w
w
w
w
w
œœœœ
œœœœ
wœ ptœ œ œ
œw ptœ œ œ
w pt
w
œœœœ
œ__66 œ__55 œ__44 œ__33
__ __ __ __
œ œ ptœ œ
œw œ œ œ
w ptpt
w
w
3 __
2 __
8 __
6
__
3 __
2 __
8 __
6
__
3 __
2 __
8 __
6
__
7
__
7
__
6
__
6
__
˙ ˙
˙ ˙
sus.
sus.
w
w
8 __
7 __
5 __
6
__
8 __
7 __
5 __
6
__
8
__
8
__
œ œ œ #œ
œ œ œ #œ
œwcamb.
œ œ #œ
œwcamb.
œ œ #œ
camb.
wcamb.
w
__ __ __ __
3 __tt __5 __6
__
œ__3 __œœtt __œœ5 œœ__6
œ3 __tt __5 __6
__
œwptœœ œœ œœ
œ
wpt
wpt
w
w__8
w__8
w
ww
w
w
__
__
w8
w8
__
__
w8
w
w
w
w
w
8 __
7 __
5 __
6
__
8 __
7 __
5 __
6
__
7 __
6
__
7 __
6
__
7 __
6
__
7 __
6
__
sus.
sus.
sus.
sus.
˙ ˙ ˙ ˙
˙ ˙ ˙ ˙
w
w
__
8
__
w
w
8
__
8
__
w
w
w
w
__ __ __ __ __ __ __ __ __ __
__
˙ ˙ ˙ ˙˙ ˙˙ ˙˙ ˙˙ ˙ ˙ ˙ ˙ # ˙ w
˙ ˙ ˙
˙ ˙ ˙ ˙ #˙ w
sus.
sync.
sync.
sync.
sync.
w sus.
w
w
ww
w
w
ww
ww
w
w
w
4 __
3
__
˙˙ ˙˙
w
8
5
˙˙ ˙˙
w
6
5
˙
˙˙ ˙
w
6
3
˙˙ ˙˙
w
5
6
˙˙ ˙
˙
w
7
6
˙˙ ## ˙˙
w
8
ww
w
&
˙˙ ˙ ˙ ## ˙˙
˙ ˙˙ ˙˙ ˙ ˙ ˙ ˙ ˙˙ sync.
& 44 Ó ˙ sus.
sus.
sync.
sync.
sync.
sus.
sus.
w
sync.
sync.
sync.
ww
sync.
w
w
w
?
4
w
w
w
w
w
?4
w
w
w EXERCISES
APPENDIX
TO PRACTICE
4 c.f. A. ANSWERS
w
ww
443
c.f.
44
&
&4
?
? 44
4
c.f.
c.f.
44
&
&4
?
? 444
ÓÓ ˙˙ ˙˙ ˙ ˙ ˙ ˙ ˙˙ ˙˙ ˙˙ ˙˙ ˙˙ ˙˙ ##˙˙ ww
˙ ˙ ˙ ˙
sus.
sus.
sync.
sync.
sus.
ww
sync.
ww
ww
ww
ww
ww
ww
ww
c.f.
8 __
4 __
3
__
8 __
4 __
3
__
Intervals:
Intervals:
ÓÓ ˙
˙
ww
Intervals:
3
__4 __
3
__4 __
˙˙ ˙
sus. ˙
ww
sus.
˙˙ ˙
˙
sus.
sus.
ww
8 __
6 __
3
__
5 __
3
__
5 __
3
__
4 __
3
__
4 __
3
__
˙ ˙
˙˙ ˙ ˙ ˙˙
sus.
sync.
sus.
sync.
ww
ww
4 __
3
__
5 __
8
__
4
__
3
__
8 __
6
__
8 __
6
__
7 __
6
__
7 __
6
__
8
__
8
__
˙˙ ˙ ˙ # ˙
˙ sus.
˙ #˙
sync.
sus.
ww
sync.
ww
6 __
8
__
ww
ww
7 __
6
__
8
__
c.f.
Invention Expositions
30.9.5. Answer.
œ parts
(downbeats restricted to chord tones; non-chord tones occur on
œ
. weakest
. ofœ beats)
& 433 œ œ œ . œ œ œ œ œ œ . œ œ œœ œ . œ œœ œ # œ œ . œ œœ œ œœ œœ œœ . œ œœ œ œœ . œ œ
œ
& 4 œ œ œ œ . œ œ œ œ œ œ . œ œ œ . œ œ # œnn œ . œpp œ
œ Intervals:
n 8 p2
3
3
3
8
7
3
4
3
3
3
8
7
3
5
3
Intervals: 3 3 3 8 7 3 4 3 3 3 8 7 8 2
3 5 3 33 8877 33 44 33 33 33
Intervals: 3 3 3 8 7 3 4 3 3 3 8 7 8 2
3œ 5 3 3 8 7œ 3œ 4œ 3œ œ
œ # œ œ . œ œ œ œ œ3 3œœ
?3
œ œœ
œ
œ
œ
œ
∑
œ
œ
Œ
œ
œ
.
œ #œ œ.
? 43
œ œ œœ œ . œp œ œ œ œ
œ Œ
∑
4
pp nn alteration
p n
œ
p n
p n alteration
(downbeats
(downbeats restricted
restricted to
to chord
chord tones;
tones; non-chord
non-chord tones
tones occur
occur on
on weakest
weakest parts
parts of
of beats)
beats)
192
192
192
C:
C: II
C: I
n
II
I
V
V
V
V
V
V
II
I
œœœœœœœœœœ # œ œœœ#(##œœœnn)œœœ # œ œ œ œ œ œ# œ œ # œ œœ œ
# œ #œ œ
œ
& # œ œ # œ œ œœ œ œœ œœœ œœœœ œœ œ œ œ œ œ ## œœ ( ) œœœ ##œœ œœ œ œ ##œœ œœ œ ##œœ œœ œ
& œ
œ œ
œœœ
Intervals: 3 3 4 3 3 8 6 6 5
Intervals: 3 3 4 3 3 8 6 6 5
?#
?#
œ œ
œœ œœ###œœœ œœ œœœœœœœœœ
œ nn œ œ œ
∑∑
∑
e: i
e: i
#
& ###
&
? ##
? ##
i
i
? bb
?b
##
&
&
?#
3 8 7 (8)
3 8 7 (8)
œœ ŒŒŒ
œ œœ
œ
V
œ #œ œ
Œ Œ # œ# œ œœ((##œœ))œœ œ # œ œ œœ œœ
Œ #œ
œ #œ œ
n
3 3 43 38 6 3 3
3 3 43 38 6 3 3
V
V
V
422 œ œ œ œ œ œ œ . œ œ œœ
4 œ œ œ œ œ œ œ. œ œ
œ œ œ œ œ œ œ.
œ œ œ œ œ œ œ.
D: I
V
422
4
43
4
43
e: i
3
∑
∑
8 3 3
I
∑
∑
3 5
(ii)
8
3 8
œ
œ
7
œ œ.
œ
œ.
œ œ . œœ ## œœ œ œœ nn œœ œœ # œ œœ œœ ## œœ .. œœ œ .
#œ
œ œ. œ #œ œ œ nœ œ œ œ #œ. œ œ.
#œ
œ
n œ œœ .. œœ
nœ
nœ œ. œ
I
œ
œ
œ
tritone is harmonically
supported in V7 chord
‰ Jœ œœ œœ œ # œ œ œœ œœ œ
‰ J œ#œœ
œ
‰ œJ œ œ œ # œ œ œ œ œ
i
œ
œ œœ œ
œ
i
adjustment
V
"microharmony"
œ . œœ œœ ..
œ.
œ .œœ œ .
alteration
alteration
i
n
3 8 3 3 3 tt 3
œ œœ œ œœ œœ œœ œœ
œ œ
œ
œ œœ œ œœ œœ œœ œ œ Œ
œ œ
œ Œ
Intervals:
j
433 ‰‰ œœj œ œ œ œ œ
4 j œ œ œ ## œœ œ œ
43 ‰ œ œ œ œ # œ œ œ
? 3
∑
& bb
&
&b
melodic minor
melodic minor
V
Œ
Œ
Œ
#œ nœ
œ œ
‰ œJJ # œ n œ œœ ## œœ œœ œ œ
‰ œ #œ nœ
œ#œœ œ œ
‰J
V
i
D: I
I
V
(ii)
7
V
"microharmony"
I
tritone is harmonically
supported in V7 chord
APPENDIX A. ANSWERS TO PRACTICE EXERCISES
3 j
& b 4 ‰ œ œ œ œ #œ œ œ œ. œ œ.
p
?
3
b 4
Intervals:
∑
d: i
Fugue Analysis
30.9.6. Answer.
melodic minor
œ œ. œ #œ œ œ nœ
œ
œ #œ œ œ #œ. œ .
p
œ
‰ J œ œ œ #œ œ œ
673 4 5 3 3 6
i
p
444
œ
n
3 5 3 2 8 7 (8)
alteration
V
œ
Œ
‰
V
nœ œ. œ
p
6œ 7 3
œ
4 5 3 3 83 3
#
œ
n
œ
œ #œ œ œ œ
J
p
alteration
i
APPENDIX A. ANSWERS TO PRACTICE EXERCISES
445
Table A.0.3 Mass in B Minor: Fugue Analysis Table
FORM
SOPRANO
ALTO
TENOR
BASS
KEY
Meas.
Exposition 1
Subject
F4m
1
Subject
Sub.
2
3
Subject
Countersubject
C4 m
4
l
FORM
SOPRANO
ALTO
TENOR
BASS
KEY
Meas.
(Bridge)
Subject
Countersubject
5
Bridge Mot. A
Bridge Mot. B
Bridge Mot. A
Bridge Mot. B
Bridge Mot. A
Bridge Mot. B
7
8
6
l
FORM
SOPRANO
ALTO
TENOR
BASS
KEY
Meas.
Exposition 1 (continues until 4th voice has subject)
Subject
Subject
Subject
Sub.
Countersubject
Countersubject Countersubject
C.S.
Ctrpt
Ctrpt
Ctrpt
Ctrpt
Ctrpt
4
Fm
C4 m
9
10
11
12
l
FORM
SOPRANO
ALTO
TENOR
BASS
KEY
Meas.
Subject
Countersubject
Ctrpt
Ctrpt
13
Episode 1
Bridge Mot. A
Bridge Mot. B
Ctrpt
Mot. B
Ctrpt
14
15
Bridge Mot. A
Ctrpt Ctrpt
Ctrpt
16
l
FORM
SOPRANO
ALTO
TENOR
BASS
KEY
Meas.
Exposition 2
Ctrpt
Ctrpt
Subject Subject
Ctrpt
Ctrpt
Cadential
Cadential
Cadential
Ctrpt
Subject
Ctrpt
F4m
17
18
31 · Introduction to Jazz Theory
31.12 · Practice Exercises
31.12.1. Answer.
19
20
&
2. B7(˜5)
1. G9sus
4. C˜m11
¯9
5. D7 ¯5
¯5
&
APPENDIX
A. ANSWERS TO PRACTICE EXERCISES
6. GmΔ9
7. A¯Δ9(˜11)
8. D¯69
9. E¯Δ9(˜5)
6. GmΔ9
7. A¯Δ9(˜11)
8. D¯69
9. E¯
# wΔ9(˜5)
? wAwww7 # 95
? c w˙ ww
& ˙w
9
w
# wwww
b ˙# ww
#
76
E b 7(# 9)
2. B7(˜5)
2. B7(˜5)
1. G sus
1. G9sus
? c # ˙˙w
? # ˙ww
? bb # www
wΔ9
6. Gm
2. 6. GmΔ9
79
3. Em9(¯5)
446
# # ww #
F # 9sus
#
w
## ## wwww C m
b # www
# w#w
˙ b www # ˙
3. Em9(¯5)
4. C˜m11
G 9(13)
b #bb wwww
b # ww
w
10.
10.
6
9
3. Em9(¯5)
4. C˜m11
5. D7 ¯9
¯9
5. D7 ¯5
¯5
8. D¯9
8. D¯69
9. E¯Δ9(˜5)
9. 4.E¯Δ9(˜5)
10. FΔ7(¯5)
10.
5. FΔ7(¯5)
b ww
www
b
b
b
w
˙
b ˙ bb bb www
b b bbb wwwww # ˙
bΔ9(ww 11)
6
7. A¯ ˜
7. A¯Δ9(˜11)
3.
FΔ7(¯5)
FΔ7(¯5)
ww
b wwww# w
bw
w
www
ww
C 7( b 5)
C 7( 5)
C 7( b 9)
C 7( 9)
C7 _
C 7( b13) or C7(˜5)
+5
#
?
bw
? b w D b b w C 7 # 95 b b ww F 13susb b ww B 13sus b b ww ¯5E¯maj9(13)
9
bw
b
w
b
w
&
www ˙ n www # ˙
31.12.2.
ww ˙
ww
˜5
˙˙˙
& cb n bwwwb Answer.
#
w
#
w
w
b
˙
9
b
w
respell 5 to agree with ¯7 wrespell ˜9 to agree
wwwith ¯7 b #wwww˜
# wwwpreferred
?? b b b wwww˜ ∑
# www
n
w
w
∑
w
w
#
w
w
b ww
w
ww∑
? c b˙#
#
&
˙
˙
9
& A 7E¯m
#5 6
E b 7(# 9)
G˙
9(13)
F # 9sus
Cw# m
Gm7(11)
A9(˜11)
F˜m9(¯5)
B13sus¯9
1. _____9
2. _____
3. _____
4. _____
5. _____
˙
c
b
˙
ww
& ˙
#˙ w
#w
nw ˙
w
w
b
w
w
ww b n ww
?& # ##9#wwwww
# ww
b
wwb # ww
b
w
w
b
n
w
#
w
b
w
w F #9susb w
A 7##˙5 w
E b 7(# 9) w
G 9(13)
C #m
w
˙
? c˙ # w
w
bw #w
b˙
2
6
9
#
#
+_ 9
6
9
6
76
82
11
79
85
15
82
& ˙ ˙ww b ˙ b ˙ # w ˙˙ ˙
?
w
b ˙ D7˜¯59 ˙
#6.˙˙ _____
EmΔ9(13) ˙ 7. _____
?
w
b b b www˙˙w
& ˙ # www b ˙
w
b w
Db 9
& c Dbbb ˙˙b˙w
b˙
& b b ˙˙˙ ww
&?
? cb ˙ b ˙ w
9. _____
? b˙
&
& # 9b # www
? A7 #5 w
& ˙˙ w
6
9
13. _____
&? # ˙˙
19
&
85
˙
#9
9
˙˙
#˙
E sus
8. _____
ww# # ww
˜
ww 9. _____
F ˜# w
˜
ww # ww
w
ww
b
w
b b b www
11
7 9
5
#9
C7 #5
6
9
31.12.5. Answer.
&
o7
C
10. _____
C7 #5
6
9
#9
Db
C7 #5
F 13sus
B 13sus
E maj9(13)
4 Diminished-Whole Tone
31.12.4.
Answer.
1.
G
&?
&2. b Fb ˙˙4˙Octatonic
b ˙˙˙˙ (Half-Whole)
b ˙˙˙˙
n # # ˙˙˙˙
# # ## wwww
b˙
b
4
3. F Locrian 2
?4. Cb ˙2Whole-Tone
˙
˙
5. A Lydian-Dominant
˙
w
6. C Locrian
&
w
w
B 13sus
E maj9(13)
# ww
n ww F 13sus
wwww
w
w
˙
˙
#˙
#
w
F 13sus
B 13sus
E maj9(13)
b www
b w˙
˙
bw
#
˙
b ˙˙˙
n # ˙˙˙
# # ## wwww
bbbw˙˙˙
˙ 10. _____
˙ _____
11.
˙
w 12. _____
˙
˙ w
˙
w
b ww
b www
#
w
n
w
# w
ww
E b 7(# 9)
F # 9sus
C #m
# wG 9(13)
b b www
#
w
w˙
b b ˙˙
# ˙˙
#
w
˙
# w
14. _____
15. _____
16. _____
b˙
˙˙
˙˙
# ww
˙
#
w
˙
#˙
b˙
31.12.3.
Answer.
&
w
6
w # ˙˙ # ˙
w
6
9
203
199
47
203
&
1. E¯7(˜ ); Scale: ____________________________
&
&
&3. F Diminished-Whole Tone
4. E¯ Octatonic (Whole-Half)
5
APPENDIX
ANSWERS
TO PRACTICE EXERCISES
2. B¯7˜9;A.
Scale:
____________________________
?
?
?
œ œ
&
? œ #œ #œ #œ œ #œ
447
˜9; Scale: ____________________________
2. B¯7¯5
9; Scale: ____________________________
˜¯5
2. B¯7¯5
˜9; Scale: ____________________________
2. B¯7¯5
œ bœ bœ
bœ bœ bœ bœ œ
7(¯5); Scale: ____________________________
3.1.Fm
E Lydian-Dominant
2. B¯ Phrygian-Dorian
7(¯5); Scale: ____________________________
3. Fm7(¯5)
3. Fm
; Scale: ____________________________
3. Fm7(¯5); Scale: ____________________________
&
?
&
bœ bœ bœ œ
&
∫
œ
b
œ
b
œ
&œ
œ bœ bœ
bœ nœ #œ œ œ bœ
˜5); Scale: ____________________________
4.3.A¯FΔ7(
Diminished-Whole
Tone
4. E¯ Octatonic (Whole-Half)
Δ7(
˜5); Scale: ____________________________
4. A¯Δ7(
5)
˜
4. A¯
; Scale: ____________________________
4. A¯Δ7(˜5); Scale: ____________________________
?
?
?
&
?
31.12.6.
Answer.
E¯ Whole Tone
˜5); Scale: ____________________________
1. E¯7(
E¯ Whole Tone
1. E¯7(7(˜55)); Scale: ____________________________
E¯
Whole Tone
˜
1. E¯
; Scale: ____________________________
E¯ Whole Tone
1. E¯7(˜5); Scale: ____________________________
&
& bb ˙˙
& bRoot
˙
& bRoot
˙7 9
Root
˙˙
˙
3rd
3rd
˙
3rd
œœ
œ
œ
œœ
œ
œ
˙˙
˙
˙5th
˜5th
˜
B¯ Diminished-Whole
Tone ˜5th
˜ ; Scale: ____________________________
2. B¯
3rd
7¯5
Root
B¯ Diminished-Whole
Tone 5th
˜9; Scale: ____________________________
2. B¯
¯5
B¯ Diminished-Whole Tone ˜
˜9; Scale: ____________________________
2. B¯7¯5
B¯ Diminished-Whole Tone
˜9; Scale: ____________________________
2. B¯7¯5
?
? ˙
b˙
? bRoot
˙
? bRoot
bRoot
˙
h
Root h
bb œœ
bœ
bœ
w
w
w
w
bb ˙˙
b˜9th
˙
b˜9th
˙
˜9th
˜9th
h
h
h
h
Locrian
nn ˙˙
n3rd
˙
n3rd
˙
˙˙
˙
¯5th
˙
¯5th
3rd ww ¯5th
3rd w ¯5th
w
w
w
w
## œœ
#œ
#œ
bb œœ
bœ
bœ
bb ˙˙
b˙
b˙
¯7th
¯7th
¯7th
¯7th
bb ˙˙
b˙
¯7th
b˙
¯7th
w ¯7th
w
w ¯7th
w
w
w
w
w
bb œœ
bœ
bœ
w
&
F
(or F Locrian ˜2)
3. Fm7(¯5); Scale: ____________________________
&
F Locrian (or F Locrian ˜2)
3. Fm7(¯5); Scale: ____________________________
b˙ œ
b˙ œ
b
& ˙ b œ bb ˙˙ bb œœ b ˙˙ bb œœ b ˙ œ ˙ œ bb ˙˙ bb œœ bb ˙˙ bb œœ b ˙ œ
& ˙ bœ
˙ œ
(whole
step
between
E¯
and
F
and between A¯ and B¯
?
(whole
step
between
E¯
and
F
andbetween
betweenF A¯
?
permit whole step or half step
andand
G) B¯
h
h
permit whole step or half step between F and G)
A¯ Lydian-Augmented
?4. A¯ ˜ ; Scale: ____________________________
˙ C G b7/Bœ C
?
C
F C
F˙ C
Gœ7/D C/E ˙
D m/F œ
G7
?
b
œ
bc˙
?
& Root
œœœ .. œœœ œœœ œœ3rd œœ œ œœ 5th œ œ œœ 7thœœ œœ œœœ
œ
.
œ œ œœ œ ˜ œ
œ œ
Δ7( 5)
123
32 · Impressionism and Extended Tonality
? c œ. œ œ
œ œ œ
œ œ œ
œ
32.5 · Practice
œ Exercises
œ
32.5.1. Answer.
Cm
___
LSS:
125
b
& b b c œœ ..
œ.
? b c œ.
bb
i
___
RN:
b
&bb
127
? bb
b
ø7
Fm Cm
Fm Cm
Cm
___
___ ___
___ G___/D¯ ___
œœ œœ œ œ œ œ
œ œ œœ œœ œœ œœ
œ œ
œ
œ bœ œ
iv ___
i ___
iv ___
i ___
vø43 ___
i6
___
D¯/F
___
Gø7
___
ø7/B¯ Cm
Cm G___
___
___
b œœ œ b œœœ
œœ œœ œœœ
œ œ
œ
œ œ œ
œ
N6
___
vø7
___
i ___
vø65 ___
i
___
207
&c
LSS:
___
___
___
œ
? c œœ
___
___
___
APPENDIX
? A. ANSWERS TO PRACTICE EXERCISES
c
RN:
___
___
32.5.2. Answer.
LSS:
128
149
139
144
154
156
LSS: ____
bw
& b www w
& ww
bw
?bw w
? b w ww
___
G9
F9
___
___
___
E¯9
___
D9
___
(2) in 4ths
& c (1)b œœin 3rds
œœ œœ b œœ n œœ
œ œ œ
? c œœ œœ œœ b b œœœ # œœœ
32.5.3. Answer.
D¯11
E¯(1)
+ in 3rds
B¯
___
__
__
Dm
LSS: ____
C¯
D¯
ww E¯
w
&
wb œœw
c
& b b b b œœœœ
ww
?
w
?c
œ
32.5.4. Answer.
D
¯
E
¯+
__
___
C¯
D¯
b œœ
& c b b b b œœœœ
?c
F9
b œœœ
œ
b b œœ
www
wœ
nb
b
B
__¯
E¯
n œœœ
œœ
œ
448
___
E¯9
___
ww
b œ ww
ww
Cm
___
A
b œœ
œ
n # n œœœ
(lower chords can be any inversion)
___ ___ ___
209
F9
___
___
œœ b œœ
(3) in 5ths
(4) in 2nds
œœ n œœœ
œ
Cmin 4ths __
D (3) in __
C
¯
___
(2)
5ths
A
___ ___ ___
wF
ww b œ
B¯
œ
ww
w
C¯
__
D
__
B¯
œ
# b n œœœœœ
F
Dmin 2nds
___
(4)
˙ wwwwww
Gm
Dm
___
Gm
˙˙
bœ
b bn n œœœœ n ˙˙˙
œ b ˙
33 · Set Theory
33.9158· Practice Exercises
& Answer.
33.9.1.
(a) Normal form is [0, 2, 7]. Prime form is (027).
? Normal form is [1, 3, 6, 8]. Prime form is (0257).
(b)
(c) Normal form is [6, 10, 11, 1]. Prime form is (0237).
(d) Normal form is [7, 8, 0, 3]. Prime form is (0158).
(e) Normal form is [11, 0, 1, 4, 6]. Prime form is (01257).
(f) Normal form is [6, 7, 10, 11, 2]. Prime form is (01457).
(g) Normal form is [9, 10, 0, 1, 4, 6]. Prime form is (013479).
33.9.2. Answer.
APPENDIX A. ANSWERS TO PRACTICE EXERCISES
449
Table A.0.4
Set
Normal Form
1
[11, 1, 3, 5, 6]
2
[5, 8, 10, 0]
3
[9, 0, 1, 4, 5]
4 P0
[3, 5, 6, 10]
5
[2, 3, 6, 7, 9, 10]
6
[2, 3, 5, 6, 9, 10]
Prime Form Forte Number
(01357)
5–24
(0247)
4–22
(01458)
5–21
(0237)
4–14
R0
(013478)
6–Z19
(013478)
6–Z19
Interval Vector
131221
021120
202420
111120
313431
313431
bœ nœ œ nœ œ bœ
œ bœ bœ œ
bœ œ nœ #œ #œ nœ nœ bœ bœ nœ œ œ
& œ bœ
œ œ #œ #œ nœ
œ bœ bœ œ œ #œ nœ nœ
&(a)œ[5,n œ 8,# œ9]n œ œ b œ b œ n œ œ # œ # œ
I0
RI0
33.9.3. Answer.
(b) [9, 11, 3, 4]
I (begins on pitch class 9)
& œ #œ #œ nœ œ nœ œ #œ œ #œ #œ #œ
(c) 9[10, 11, 1, 4, 7]
33.9.4. Answer.
(a) [1, 2, 5]
œ #œ #œ nœ œ bœ bœ
œ bœ nœ nœ nœ
&
(b)RI[0,
2, 4] on pitch class 5)
5 (ends
(c) [10, 11, 3, 5]
33.9.5. Answer.
(a) T10 I
&
P7: 7 10 8 2 1 5 3 4 6 0 9 11
R7
(b) T11 I
(c) T5 I
I
34 · 7Serialism
& · Practice Exercises
34.7
RI7
34.7.1. Answer.
œ bœ nœ #œ nœ nœ œ œ #œ œ bœ nœ #œ œ bœ
nœ
œ
bœ œ
& œ bœ bœ œ #œ
P7: 7 10 8 2 1 5 3 4
6 0 9 11
R7
RI7
œ7 œ # œ œ b œ
n
œ
b
œ
b
œ œ œ bœ nœ bœ œ #œ nœ œ
n
œ
œ
b
œ
œ
b
œ
bœ
nœ
&
I
62
62
PP11
& #œ
&
(a)
(b)
œ
?
& #œ #œ
R4
R
4
8
bœ
II8
&
œ
10
? bœ bœ
& bœ bœ
RI10
RI
œ bœ
œ
œ bœ bœ
œ #œ
œ
œ
œ bœ
bœ
œ
œ nœ bœ nœ
nœ nœ
œ
œ #œ #œ
œ
œ nœ bœ
œ bœ nœ nœ
œ #œ
œ #œ
œ nœ
œ nœ
œ b œ nn œœ n œ bb œœ
nœ
œ bœ
61
?
R
R44
bœ bœ
œ nœ bœ nœ nœ nœ
bœ nœ
# œ ANSWERS
# œ œ TO PRACTICE EXERCISES
APPENDIX A.
(c)
&
b œ8
II8
œ #œ
œ
? bœ bœ
RI
RI10
10
(d)
œ
#œ
œ #œ
œ bœ nœ nœ
450
œ
bœ
œ bœ nœ nœ
œ nœ
œ #œ
œ
34.7.2. Answer.
&
(a) RI10
(b) I1
(c) R5
34.7.3. Answer.
Table A.0.5 Twelve-Tone Matrix
I3 ↓
E2
B
G
F
D2
G2
E
A2
P3 →
P11 →
P7 →
P5 →
P1 →
P6 →
P4 →
P8 →
P0 →
P2 →
P10 →
P9 →
I7 ↓
G
D4
I11 ↓
B
G
D4
C4
B
A
F
B2
G4
C
E
F4
D
C4
C
D
B2
A
↑RI3
↑RI7
A
D
C
E
A2
A4
G2
F
↑RI11
I1 ↓
C4
A
F
E2
B
E
D
G2
B2
C
A2
G
↑RI1
I5 ↓
F
C4
I0 ↓
C
G4
A
G
E2
A2
G2
B2
E
D
B2
E2
D2
D
E
C
B
↑RI5
I2 ↓
D
A4
F4
E
C
F
E2
F
A
B
G
F4
G
B
D2
A
A2
↑RI0
↑RI2
I10 ↓
B2
F4
D
C
A2
D2
B
E2
G
A
F
E
↑RI10
I6 ↓
G2
D
B2
A2
I4 ↓
E
C
A2
G2
E
A
G
B
E2
F
D2
C
↑RI6
D
G
F
A
D2
E2
B
B2
œ. . .
. > RI5
.
b
œ
.
œ
#
œ
#
œ # œ n œœ b œœ.
b
œ
n
œ
b
œ
.
œ
nœ œ. bœ œ
& c ‰ œ bœ œ #œ
w
>
p 1 2 3 4 5 6 7 8 9 10 11 12
34.7.4. Answer.
184
P5
P10
# œ.
>
n œœ # œ. 4 n n œœ. 9 >12
. n œ. n œ. w
.
b
œ
œ
.
#
œ
œ
b
œ
œ
b
œ
‰ J œ 65 œ 8 b œ œ b œ œ
n œ. œ b œ
#œ
1
?c Œ
187
2 3
4 5/6
7
8/9 10/11 12
2
3
1
RI3
34.7.5. Answer.
In phase
7
10
11
1 23 4
5 6 7 8 9 10 11
Out of phase
12
In phase
(a) Set 1: 3, 7, 11. Normal form: [3, 7, 11] Prime form: (048) Interval
œ. .
œ. .
œ. .
œ. .
œ .
œ .
.. œ œ000300
& 85vector:
œ œ . . œ œ œ œ . . œ œ œ œ . . œ œ œ œ . . œ œ œ œ . œœœœ .
12345
12345
12345
12345
12345
12345
(b) Set 2:1 2 1,
5, 0. 2Normal
form:
[0, 1, 5]
Prime form:
(015)1 Interval
345
3451
34512
45123
51234
2345
vector: 100110
& 85 .. œ œ œ œ œ .. .. œ œ œ œ œ .. .. œ œ œ œ œ .. .. œ œ œ œ œ .. .. œ œ œ œ œ .. œ œ œ œ œ ..
(c) Set 3: 2, 10, 6. Normal form: [2, 6, 10] Prime form: (048) Interval
vector: 000300
193
& b b www
? ww
first
rotation
# # # wwww
b ww
second
rotation
third
rotation
# www
b www
fourth
rotation
bw
b ww
bw
213
↑RI4
I8 ↓
G4
E
C
B2
G2
B
A
D2
F
G
D4
D
↑RI8
I9 ↓
A
F
D2
B
G
C
B2
D
G2
A2
E
E2
↑RI9
←R
←R
←R
←R
←R
←R
←R
←R
←R
←R
←R
←R
APPENDIX A. ANSWERS TO PRACTICE EXERCISES
451
(d) Set 4: 4, 8, 9. Normal form: [4, 8, 9] Prime form: (015) Interval
vector: 100110
Appendix B
GNU Free Documentation License
Version 1.3, 3 November 2008
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APPENDIX B. GNU FREE DOCUMENTATION LICENSE
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APPENDIX B. GNU FREE DOCUMENTATION LICENSE
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Index
6
9
Crucifixus, 232
Kyrie II, 362
Well-Tempered Clavier, Book
I
Fugue 2 in C minor, BWV
846, 354
Fugue 3 in C-sharp major,
BWV 848, 343
Prelude 1 in C major, 72,
94
Brandenburg Concerto No. 2
in F Major, BWV 1047,
I., 56
Chorale 103, “Nun ruhen alle
Wälder”, BWV 392, 317
Chorale 106, “Jesu Leiden,
Pein und Tod”, BWV
245/28, 317
Chorale 153, “Alle Menschen
müssen sterben”, BWV
262, 316
Chorale 204, “Wer weiß, wie
nahe mir”, BWV 166,
318
Chorale 237, “Gott lebel
noch”, BWV 320, 316
Chorale 323, “Allein Gott in
der Höh’ sei Erh”’, BWV
104, 330
Chorale 323, “Wie schön
leuchtet der
Morgenstern”, BWV 172,
330
Chorale 328, “Liebster Jesu,
wir sind hier,” BWV 373,
97
Chorale 342, “Lobt Gott, ihr
Christen, allzugleich”,
BWV 376, 329
Chorale 4, “Es ist das Heil
chords, 365
11th chords, 365
13th chords, 365
1950s progression, 75
3–2 son clave, 164
8ve, 2
accidentals, 3
afterbeats, 160
altered chords
definition of, 366
alto clef, 2
Amazing Grace, 44
antecedent
definition of, 128
antecedent group, 132
anticipation, 92
appoggiatura, 89
atonal music
definition of, 392
augmentation, 107
augmented intervals, 30
augmented sixth chord types
French augmented sixth
chord, 224
German augmented sixth
chord, 224
Italian augmented sixth
chord, 224
augmented sixth chords, 224
authentic cadence
definition of, 42
musical examples, 43
Bach, J.S.
Herz und Mund und Tat und
Leben BWV 147, X.
“Jesus bleibet Freude”
(“Jesu, Joy of Man’s
Desiring”), 202
Mass in B minor, BWV 232
459
INDEX
uns kommen her”, 244
Chorale 8, “Freuet euch, ihr
Christen”, BWV 40, 244
English Suite No 3 in G
minor, BWV 808
Gavotte I., 281
English Suite No. 4 in F
Major, BWV 809,
Sarabande, 240, 242, 243,
245
French Suite No. 1 in D
Minor, BWV 812,
Sarabande, 97, 218
Invention No. 1 in C Major,
BWV 772, 106, 107, 111,
350, 353
Invention No. 7 in E Minor,
BWV 778, 350
Invention No. 8 in F major,
BWV 779, 276
Barber, Samuel
Adagio for Strings, 96, 143
Bartók, Béla
Piano Concerto No. 2, II., 388
bass clef, 1
beat, 20
beats per minute, 20
Beethoven
Moonlight Sonata, Op. 27,
No. 2, I, 146, 221
Moonlight Sonata, Op. 27,
No. 2, III
Terminative function in
Closing Theme, 300
32 Variations in C minor,
WoO 80, 233
Bagatelle in A minor, WoO
59, “Für Elise”
period form, 128
Eleven Bagatelles, Op. 119,
No. 9, 286
Minuet in G, WoO 10, No. 2,
89
Pathétique Sonata, Op. 13, I,
269
Pathétique Sonata, Op. 13, I,
closing theme, 75
Pathétique Sonata, Op. 13, I,
Introduction, 109
Pathétique Sonata, Op. 13,
II, 323
Pathétique Sonata, Op. 13,
III, 301
Piano Sonata in C minor, Op.
460
13, (Pathétique), II, 130
Piano Sonata Op. 10, No. 1,
II (double period), 133
Piano Sonata Op. 110, I, 247
Piano Sonata Op. 2, No. 1, I
sentence structure in, 124
Piano Sonata Op. 2, No. 1,
III., 255
Piano Sonata Op. 2, No. 1,
IV, 160
Piano Sonata Op. 2, No. 3,
I., 69
Piano Sonata Op. 53, I, 199
Piano Sonata Op. 53, I
(repeated period), 135
Sonatina in F, Anh. 5 No. 2,
II. Rondo (phrase chain),
138
Symphony No. 1, Op. 21, I,
103
Symphony No. 2, Op. 36, I.,
252
Symphony No. 5, Op. 67, I,
226
Symphony No. 5, Op. 67, I.
(opening), 59
Symphony No. 5, Op. 67, II,
266, 270
Symphony No. 7, Op. 92, I,
220
binary
balanced, 276
rounded, 278
simple, 281
binary principle, 282
Bizet, Georges
Carmen, Habanera (“L’amour
est un oiseau rebelle”),
168
Bo Diddley beat, 165
borrowed chords
definition of, 207
bpm, 20
Brahms, Johannes
Fünf Lieder, Op. 49
“Wiegenlied”, 274
Symphony No. 3 in F major,
Op. 90, III. Poco
Allegretto, 212
cadence
authentic, 42
deceptive, 42
definition of, 42
INDEX
half, 42
plagal, 42
cadential six-four (cadential 64 ),
184
Calloway, Reggie, “Casanova”, 166
Chopin, Frédéric
Nocturne in E-flat major, Op.
9, No. 2, 219
Prelude Op. 28, No. 20, in C
minor, 132
Waltz in A-flat major, Op. 34
No. 1, 74
chord, 32
chromatic mediants, 253
circle of fifths, 7
circle of fifths (harmonic
progression)
diagram, 57
example (Bach), 56
example (Fly Me to the
Moon), 59
example (Handel), 56
example (I Will Survive), 59
example (Love You Like a
Love Song), 59
example (Mozart), 58
example (Wagner), 58
circle of fifths (major key
signatures)
diagram, 8
circle of fifths (minor key
signatures)
diagram, 12
clef, 1
closely related keys
definition of, 241
Coltrane, John
“Mr. P.C.”, 229
Columbia, the Gem of the Ocean,
50
common-tone modulation, 251
complement
definition of, 401
compound meter, 20
consequent
definition of, 128
consequent group, 132
continuous
definition of, 275
contrasting period, 129
contrasting verse-chorus form, 119
Copland, Aaron
Appalachian Spring, 387, 390
counterpoint
461
definition of, 343
Couperin, Franéois
5 Pièces de Clavecin, 4. Le
Petit-Rien (Ordre XIV,
8) (phrase group), 137
Davis, Miles
“Tune-Up”, 62
Debussy, Claude
Danses, II. Danse profane, 383
Préludes, Book II, No. 3, La
Puerto del Vino, 384
Prelude to the Afternoon of a
Faun, 385, 386
Suite bergamasque, III. Clair
de lune, 384
String Quartet in G minor,
Op. 10, I., 382
deceptive cadence
definition of, 42
musical examples, 45, 47
developmental function
definition of, 299
diatonic
definition of, 40
diatonic common chord
modulation, 242
diminished intervals, 30
diminution, 107
direct modulation, 248
distantly related keys, 241
dot, 19
double flat, 3
double neighbor, 91
double period
definition of, 132
double sharp, 3
duplet, 21
durational symbols, 18
elision, 138
Ellington, Duke
“It Don’t Mean A Thing (If It
Ain’t Got That Swing)”,
227
“Take the ‘A’ Train”, 61
enharmonic, 4
enharmonic equivalence, 393
enharmonic modulation, 262
escape tone, 90
expository function
definition of, 296
figured bass
chromatic alterations to, 187
INDEX
definition of, 181
for seventh chords, 183
for triads, 183
first inversion, 34
flat, 3
foreign keys, 241
Forte number, 401
Forte, Allen
The Structure of Atonal
Music, 392
fragment, 110
fugue
answer
definition of, 353
bridge
definition of, 354
countersubject
definition of, 354
definition of, 353
episode
definition of, 353
exposition
definition of, 353
subject
definition of, 353
Giacchino, Michael
Star Trek, “End Credits”, 222
Giordani, Giuseppe
Caro mio ben, 327
Glass, Philip
Einstein on the Beach
Act 1, Scene 1, “Train”, 418
Music in Fifths, 418
Two Pages, 418
Metamorphosis Two, 84
grand staff, 2
Gretchaninoff, Alexander
Children’s Book, Op.98
No. 13 “After the Ball”,
291
guide tones, 371
half cadence
definition of, 42
Handel, George Frideric
Rinaldo, “Lascia ch’io
pianga”, 93
Xerxes, “Ombra mai fu”, 158
Gavotte, HWV 491, 288
Recorder Sonata in A minor,
HWV 362, I. Larghetto,
182
Suite in G minor, Passacaglia,
56
462
Suite No. 2 in D Major, HWV
349: II. All Hornpipe, 96
harmonic flowchart
in major, 68
in minor, 68
harmonic function
definition of, 67
harmonic rhythm
definition of, 60
harmonic sequence, 59
harmony, 32
Haydn
Piano Sonata in D major, H.
XVI:37, III, 304
String Quartet in E-flat
major, Op. 33, No. 2, IV,
305
Symphony No. 104 in D
major, Hob. I:104, IV,
305
Haydn, Joseph
Piano Sonata in C major,
Hob. XVI:35, I, 297
Piano Sonata in C Major,
Hob. XVI:35, III, 91
Piano Sonata in F Major,
Hob. XVI:9, III
period form, 127
Symphony No. 94 in G
major, Hob. I:94, II, 275
Holst, Gustav
The Planets, “Uranus”, 108
imperfect authentic cadence
definition of, 123
Impressionism, 382
incomplete chords, 48
interval class
definition of, 399
interval vector
definition of, 399
intervallic change, 107
intervals
augmented, 30
definition of, 26
diminished, 30
harmonic, 26
how to identify, 27
how to write, 29
inversion of, 29
major, 27
melodic, 26
minor, 27
perfect, 27
INDEX
inversion, 106
inverted chord, 34
inverted triad, 34
key change, 237
key signature, 6
Kirkland, Kenny
Dienda, 23
Kuhlau, Friedrich
Sonatina in C Major, Op. 55,
No. 1, I, 92
Lassus, Orlande de
Expectatio Justorum, 349
lead-sheet symbols, 32
ledger lines, 1
Ligeti, György
Trio for Violin, Horn, and
Piano, II, 168
Loesser, Frank
Hans Christian Andersen,
“Inchworm”, 213
M.M. (Maelzel’s Metronome), 20
Maelzel’s Metronome, 20
Mancini, Henry
“The Pink Panther Theme”,
229
melodic bass six-four, 186
meter, 20
compound, 20
duple, 20
quadruple, 20
simple, 20
triple, 20
middle C, 2
minor
parallel, 11
relative, 11
Miranda, Lin-Manuel
“First Burn”, 23
mode mixture
definition of, 207
modes
Aeolian, 376
Dorian, 376
Ionian, 376
Locrian, 376
Locrian 42, 376
Lydian, 376
Lydian-Augmented, 376
Lydian-Dominant, 376
Mixolydian, 376
Mixolydian-26̂ , 376
Phrygian, 376
463
Phrygian-Dorian, 376
modulation
borrowed common chord, 246
common-tone, 251
definition of, 237
diatonic common chord, 242
direct, 248
enharmonic pivot chord, 262
Neapolitan common chord,
247
secondary common chord, 245
sequential, 255
Monk, Thelonious
“Blue Monk”, 88
motion, types of
contrary motion, 311
oblique motion, 311
parallel motion, 311
similar motion, 311
motive
definition of, 103
Mozart, W.A.
Don Giovanni, K. 527, “Mi
tradi quell’alma ingrata”,
257
Eine kleine Nachtmusik, K.
525, I., 47
Eine kleine Nachtmusik, K.
525, I. (elision), 139
Eine kleine Nachtmusik, K.
525, II., 176
Marriage of Figaro, “Voi che
sapete”, 45
Andante in E-flat major, K.
15mm, 283
Ave verum corpus, K. 618, 47
Oboe Concerto in C major,
K. 314, III., 256
Piano Sonata in C Major, K.
545, II, 113
Piano Sonata in D major, K.
284, III., 279
Piano Sonata K. 279, III, 161
Piano Sonata K. 283, I., 69
Piano Sonata K. 310, I, 155
Piano Sonata K. 331, I, 289,
324
antecendent and consequent
in, 129
period form, 126, 184
sentence structure in, 124
Piano Sonata K. 333, I, 92
Piano Sonata K. 545, I, 149
INDEX
Piano Sonata K. 545, I.,
primary theme, 54
Piano Sonata K. 545, I.,
secondary theme, 58
Piano Sonata K. 545, II, 98
Piano Sonata, K. 284, I, 298
Piano Sonata, K. 333, I, 296
sentence structure in, 125
String Quartet K. 425, IV,
305
String Quartet K. 428, IV,
144
String Quartet K. 465, IV,
305
Symphony No. 39 K.543, IV,
305
Symphony No. 40, K. 550, I.
harmonic function in
primary theme, 72
Symphony No. 40, K. 550, I.
(opening melody), 60
Symphony No. 40, K. 550, II,
90
Symphony No. 40, K. 550,
III, 113
Symphony No. 41, K. 551, I.
Terminative function in
Closing Theme, 300
natural, 3
Neapolitan
definition of, 220
neighbor group, 91
neighbor tone, 88
ninth chords, 364
non-chord tones
definition of, 87
normal form
definition of, 395
octave, 2
octave equivalence, 393
octave registers, 2
offbeats, 161
order of flats, 7
order of sharps, 7
ornamentation, 109
pandiatonicism, 386
parallel minor, 11
parallel period, 129
passing six-four, 185
passing tone, 87
pedal point, 93
pedal six-four, 186
464
Perfect Authentic Cadence, 123
period
definition of, 125
phrase
definition of, 111
phrase chain
definition of, 137
phrase group
definition of, 136
pitch, 1
pitch class, 393
plagal cadence
definition of, 42
musical examples, 43
polychord
definition of, 388
prime form
definition of, 396
Puccini, Giacomo
Gianni Schicchi, “O mio
babbino caro”, 99
pulse, 20
Purcell, Henry
Dido and Aeneas, Z. 636
“When I am laid in earth”
(Dido’s Lament), 232
quadruplet, 21
quartal harmony
definition of, 387
quintal harmony
definition of, 387
quintuplet, 21
Rachmaninoff, Sergei
Prelude in C-sharp minor,
Op. 3 No. 2, 284
Rahn, John
Basic Atonal Theory, 392
Ravel, Maurice
Pavane pour une infante
défunte, 385
Piano Trio, I., 383
Reich, Steve
Clapping Music, 418
Piano Phase, 419
Three Movements, II., 420
relative minor, 11
repeated period, 134
retardation, 98
retrograde, 110
rhythmic change, 108
rondo form, 301
root, 32
INDEX
root position, 34
Rossini, Gioachino
William Tell Overture, 228
Saint-Georges, Joseph Bologne,
Chevalier de
Violin Concerto No. 9 in G
major, Op. 8, III., 304
scale degree names, 14
scales
Altered, 376
bebop dominant, 375
bebop major scale, 378
Blues scale, 375
diminished scale, 376
Diminished-Whole Tone, 376
Octatonic (Half-Whole), 376
Octatonic (Whole-Half), 376
Whole Tone, 376
Schönberg, Claude-Michel
Les Miserables
“One My Own”, 267
Schoenberg, Arnold
Chamber Symphony No. 1,
Op. 9, 388
Suite for Piano, Op. 25, 408
Schubert
Schwanegesang, D. 957
“Abschied”, 237, 246
“Der Atlas”, 271
“Frühlingssehnsucht”, 248
“Kriegers Ahnung”, 250
“Liebesbotschaft”, 249
Winterreise, D. 911
“Der Wegweiser”, 227
“Die Nebensonnen”, 145
“Frühlingstraum”, 324
“Gute Nacht”, 156
20 Minuets, D. 41
No. 18 in F major, 280
Piano Trio No. 1 in B-flat
major, D. 898, I., 253
Schumann, Clara
Op. 13, No. 2, “Sie liebten
sich beide”, 94
Schumann, Robert
Album for the Young, Op. 68,
No. 16, “First Loss”, 117
Dichterliebe, Op. 48
“Am leuchtenden
Sommermorgen”, 231
“Ich grolle nicht”, 156
“Im wunderschönen Monat
Mai”, 101
465
Album for the Young, Op. 68,
No. 17, “Little Morning
Wanderer”, 131, 241
second inversion, 34
second line drumming, 166
secondary diminished chord, 201
sectional
definition of, 274
secundal harmony
definition of, 387
segmentation
definition of, 398
semitone, 393
sentence
definition of, 123
sentence structure
example of, 124
sequence
definition of, 59
sequential modulation, 255
set theory, 392
seventh chord
definition of, 51
example of 5 types, 51
sharp, 3
simple meter, 20
simple verse-chorus form, 119
slash chord, 34
slur, 19
sonata form, 294
sonatina form, 295
songs (popular)
CHiPs Theme, 388
Jeopardy
Theme, 388
“(Sittin’ On) The Dock of the
Bay” (Otis Redding), 198
“All About That Bass”
(Meghan Trainor), 73
“All I Do Is Win” (DJ
Khaled), 83
“All My Ex’s Live in Texas”
(George Strait), 71
“All of Me” (John Legend),
76, 167
“All the Things You Are”, 63
“Another One Bites the
Dust” (Queen), 173
“Are You Gonna Be My Girl”
(Jet), 155
“As Time Goes By” (from the
motion picture
Casablanca), 62, 88
INDEX
“Baby Love” (The Supremes),
197
“Back in Black” (AC/DC),
174
“Back in the New York
Groove” (Ace Frehley),
165
“Barbara Ann” (Beach Boys),
154
“Barbie Girl” (Aqua), 63
“Beautiful Day” (U2), 170
“Beautiful” (Christina
Aguilera), 209
“Best of You” (Foo Fighters),
168
“Beyond The Sea”, 64
“Blackbird” (The Beatles),
207
“Blue Moon”, 64
“Born to Run” (Springsteen),
89
“Call Me” (Blondie), 93
“Can You Tell Me How to Get
to Sesame Street?”, 158
“Clocks” (Coldplay), 168
“Cold As Ice” (Foreigner), 159
“Cold” (Maroon 5), 170
“Colour My World”
(Chicago), 147
“Could You Be Loved” (Bob
Marley), 50, 162
“Creep” (Radiohead), 211
“Criminal” (Fiona Apple),
230
“Day Tripper” (Beatles), 172
“Dem Bow” (Shabba Ranks),
169
“Desire” (U2), 79, 165
“Despacito” (Luis Fonsi
featuring Daddy Yankee),
169
“Disclosure” (Latch featuring
Sam Smith), 23
“Don’t Know Why” (Norah
Jones), 190
“Don’t Stop Believin”’
(Journey), 115
“Don’t Stop” (Fleetwood
Mac), 114
“Don’t You (Forget About
Me)” (Simple Minds), 79,
151
“Downtown” (Macklemore
and Ryan Lewis), 173
466
“Dream On” (Aerosmith), 234
“Earth Angel” (The
Penguins), 75
“Eye of the Tiger” (Survivor),
166
“Faith” (George Michael), 165
“Fancy” (Iggy Azalea
featuring Charli XCX),
173
“Final Song” (MØ), 169
“Flashdance... What A
Feeling” (Irene Cara), 77
“Fly Me to the Moon”, 59
“Forget You” (CeeLo Green),
191, 196
“Friend Like Me” (from
Aladdin), 230
“Friends in Low Places”
(Garth Brooks), 203
“Ghostbusters” (Ray Parker
Jr.), 171
“Girl on Fire” (Alicia Keys),
33
“Girls Just Want to Have
Fun” (Cyndi Lauper),
167
“Good Times” (Chic), 173
“Greatest Love of All”
(Whitney Houston), 66
“Hard to Say I’m Sorry”
(Chicago), 37
“Haven’t Met You Yet”
(Michael Buble), 159
“Heart and Soul”, 75
“Heartbreaker” (Pat
Benatar), 157
“Hello” (Adele), 81
“Hey Jude” (Beatles), 70, 78
“Hold My Hand” (Jess
Glynne), 170
“Hotel California” (The
Eagles), 77
“I Got Rhythm” (Gershwin),
120
“I Want Candy” (The
Strangeloves), 165
“I Want You to Want Me”
(Cheap Trick), 190, 196,
202
“I Want to Hold Your Hand”
(Beatles), 43
“I Will Always Love You”
(Whitney Houston), 76
“I Will Survive”, 59
INDEX
“I’ll Be There For You” (The
Rembrandts), 74
“I’m Yours” (Jason Mraz),
164
“I’m Every Woman” (Chaka
Khan), 112
“I’m Not In Love” (10cc), 107
“If I Ain’t Got You” (Alicia
Keys), 146
“Imagine” (John Lennon), 198
“Immigrant Song” (Led
Zeppelin), 173
“Interstate Love Song” (Stone
Temple Pilots), 234
“Irreplaceable” (Beyoncé),
112
“It’s the Hard Knock Life”
(from Annie), 157
“Jar of Hearts” (Christina
Perri), 235
“Johnny B. Goode” (Chuck
Berry), 121
“Joy to the World” (Three
Dog Night), 210
“Just Give Me a Reason”
(Pink), 44
“Just the Way You Are”
(Billy Joel), 202
“Let’s Get It On” (Marvin
Gaye), 150
“Let’s Stay Together (Al
Green)”, 23
“Lithium” (Nirvana), 211
“Little Brown Jug” (Glenn
Miller), 172
“Livin’ on a Prayer” (Bon
Jovi), 237
“London Bridge is Falling
Down” (Count Basie),
379
“Love Song” (Sara Bareilles),
37, 160
“Love You Like A Love
Song”, 59
“Love Yourself” (Justin
Bieber), 49, 153
“Love on Top” (Beyoncé), 237
“Love on the Brain”
(Rihanna), 147
“Maneater” (Hall and Oates),
154
“My Girl” (The
Temptations), 112
“My Heart Will Go On” (from
467
Titanic), 89, 237, 251
“Never Gonna Give You Up”
(Rick Astley), 67
“Never” (Heart), 151
“No Scrubs” (TLC), 54, 148
“O-o-h Child” (The Five
Stairsteps), 52
“One Dance” (Drake), 169
“One Day I’ll Fly Away”, 214
“Part of Your World” (from
The Little Mermaid), 210
“Party Rock Anthem”
(LMFAO), 114, 171
“Pipeline” (The Chantays),
149
“Pompeii” (Bastille), 61
“Pretty Thing” (Bo Diddley),
165
“Problem” (Ariana Grande),
172
“Push It” (Salt-n-Pepa), 108
“Raise Your Glass” (Pink),
171
“Red Red Wine” (UB40), 163
“Reelin’ in the Years” (Steely
Dan), 79
“Rock ‘n’ Roll High School”
(The Ramones), 76
“Rolling In The Deep”
(Adele), 83
“Roxanne” (The Police), 159
“Rude” (by MAGIC
), 76, 164, 168
“Saturday in the Park”
(Chicago), 190
“Say You Won’t Let Go”
(James Arthur), 153
“Secrets” (One Republic), 148
“See You Again (Wiz Khalifa
ft. Charlie Puth)”, 116
“See You Again” (Wiz Khalifa
ft. Charlie Puth), 152
“September” (Earth, Wind,
and Fire), 66
“Shape of You” (Ed Sheeran),
168
“She’s Got a Way” (Billy
Joel), 158
“She’s Out of My Life”
(Michael Jackson), 122
“Silly Love Songs” (Wings),
91
“Sir Duke” (Stevie Wonder),
109
INDEX
“Smells Like Teen Spirit”
(Nirvana), 119
“Smoke on the Water” (Deep
Purple), 155
“Some Nights” (fun.), 145
“Someday My Prince Will
Come”, 120
“Someone Like You” (Adele),
80, 148
“Sorry” (Justin Bieber), 169
“Stairway to Heaven” (Led
Zeppelin), 82, 233
“Star Dust” (Hoagy
Carmichael), 121
“Starships” (Nicki Minaj), 172
“Stop
In the Name of Love” (The
Supremes), 101
“Stranger in Paradise”, 65
“Sunshine of Your Love”
(Cream), 375
“Superfreak” (Rick James),
173
“Take Me to Church”
(Hozier), 45
“Take the ‘A’ Train”, 61
“That’s What I Like” (Bruno
Mars), 152
“The Long and Winding
Road” (The Beatles), 53
“The Very Thought of You”,
107, 115
“Theme from New York, New
York” (Liza Minnelli), 73
“Thinking Out Loud” (Ed
Sheeran), 48, 150
“Tik Tok” (Kesha), 152, 172
“Toxic” (Britney Spears), 110
“Treat You Better” (Shawn
Mendes), 167
“True Colors” (Cyndi
Lauper), 46
“Umbrella” (Rihanna), 82
“Under Pressure” (Queen and
David Bowie), 173
“Underneath It All” (No
Doubt), 163
“Walk This Way”
(Aerosmith), 174
“Walking On Sunshine”
(Katrina and the Waves),
154
“Walking on the Moon” (The
Police), 162
468
“Want to Want Me” (Jason
Derulo), 88
“Warriors” (Too Many Zooz),
171
“We Are The World”, 118
“We Are Young” (fun.), 157
“We Are the Champions”
(Queen), 205
“When I Fall In Love”, 120
“While My Guitar Gently
Weeps” (The Beatles),
233
“White Christmas”, 120
“Why Do Fools Fall in Love”,
65
“Yesterday” (The Beatles),
189, 195
“You Can’t Hurry Love” (The
Supremes), 154
“You Know You Like It”
(Aluna George, DJ Snake
Remix), 170
“You Really Got Me” (The
Kinks), 173
spacing error, 312
species counterpoint
definition of, 343
staff, 1
Star-Spangled Banner, 67, 145,
185
musical example, 43, 90, 216,
217
Straus, Joseph
Introduction to Post-Tonal
Theory, 392
Strauss, Richard
Also Sprach Zarathustra,
Op.30, 208
Stravinsky, Igor
Petrushka, Fourth Tableau:
The Shrovetide Fair
(Toward Evening), 386,
390
Rite of Spring, “Dance of the
Adolescents”, 389
Septet, 414
subtonic triad
definition of, 42
in popular music in the major
mode, 78
tonicization of, 194
sus2 chord, 36
sus4 chord, 36
sus9 chord, 36
INDEX
suspension, 95
syncopation, 22
Tchaikovsky
The Nutcracker
“Miniature Overture”, 191,
295
“Waltz of the Flowers”,
214, 265
tempo, 20
tendency tones, 312
tenor clef, 2
terminative function
definition of, 300
ternary form, 283
compound, 285
tetrachord, 5
texture, 143
thoroughbass, See figured bass
tie, 19
time signature, 17
tonicization
definition of, 191
transitional function
definition of, 297
transposition
definition of, 39
treble clef, 1
triad
augmented, 32
definition of, 32
diminished, 32
inverted, 34
major, 32
minor, 32
triplet, 21
tuplet, 21
duplet, 21
quadruplet, 21
quintuplet, 21
triplet, 21
turnaround, 373
twelve-tone technique
inversion, 409
prime form, 409
469
retrograde, 409
retrograde inversion, 409
two-reprise
definition of, 276
unequal fifths
definition of, 325
Vejvoda, Jaromír
“Beer Barrel Polka”, 161
Verdi
Rigoletto, “La donna è
mobile”, 69, 191
Verse-Chorus form, 118
Vivaldi
Concerto for Two Violins and
Cello in D minor, RV
565, V., 325
voice leading
definition of, 310
Wagner, Richard
Das Rheingold, Scene 3, 254
Die Meistersinger, Act II,
Scene 6, 58
Tristan und Isolde, Prelude to
Act I, 46, 382
Webern, Anton
5 movements for string
quartet
No. 3. Sehr bewegt, 392
Williams, John
Raiders of the Lost Ark,
“Raiders March”, 222
Star Wars: Return of the
Jedi, “Main Title (The
Story Continues)”, 254
The Phantom Menace, “Duel
of the Fates”, 255
Zimmer, Hans and Antonius Tom
Holkenborg
Batman v Superman: Dawn
of Justice, “The Red
Capes are Coming”, 223
Colophon
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