Music Theory and Notation
Music theory is the study and analysis of the written and heard elements of music. It is closely
tied to musical notation, the system of recording music in written form.
The Staff
Music usually is notated on a five-line staff. The staff includes notes, rests, and
instructions about key, rhythm, and other musical elements.
Clefs
A clef is a notation that assigns specific pitch values to the lines and spaces on the staff.
Because the instruments of the orchestra possess widely varying registers (pitch
ranges),composers use different clefs for different instruments to avoid having to use too
many ledger lines (small line segments that extend the staff above or below the
standard five lines).
The treble clef (G clef) is used for higher-pitched instruments like the flute or
violin.
The bass clef (F clef) is used for lower-pitched instruments like the tuba or
cello.
The C clef is movable, and its name depends on where it is aligned on the staff.
The following staves show where the same pitch (middle C) appears on different clefs:
Music for instruments with a wide range (such as the piano) is notated on the grand
staff, which combines the treble clef and the bass clef:
Rhythm, Notes, and Rests
Rhythm refers to the arrangement of beats in a piece of music. Rhythm is expressed
graphically with notes and rests (durations of silence in which no notes are played).
Notes are named based on their duration. The longest note in conventional use is the
whole note; the shortest in conventional use is the 128th note:
Rests are named in a manner similar to notes:
Adding a dot to a note or rest increases the duration of that note or rest by one half:
A tie over two or more notes of the same pitch indicates that the notes under it should
be held or sustained:
Sometimes, composers break rhythms into three equal parts called a triplet. There are
also quintuplets, septuplets, and other groupings, collectively called tuplets.
Meter and Time Signature
Meter is the organization of rhythm into equal groups called measures or bars. Meter
organizes the rhythm of a piece of music in the context of a regular pulse or beat.
The composer uses two numbers called the time signature to indicate the meter of a
piece of music. The top number tells the number of beats per measure; the bottom
number indicates the time value of each beat in the measure. For example, in 6/8 time,
there are six beats per measure, and each beat is an eighth note.
The following are some standard time signatures:
Two of the frequently used standard time signatures are abbreviated with symbols:
Most time signatures in Western music are duple (the number of beats per measure are
divisible by two) or triple (the number of beats per measure are divisible by three).
Some time signatures are irregular and cannot be described as duple or triple. Two
common irregular time signatures are 5/4 time and 7/8 time:
Pitch
Pitch refers to the sound frequency of a note (i.e., whether the note is high or low). In
Western music, there are 12 named pitches, which together are called the chromatic
scale.
Some pitches have two names—for example, C and D are the same pitch. Such pitches
are called enharmonic equivalents. The name given to an enharmonic pitch depends on
notation and key.
The space between two adjacent pitches in the chromatic scale is called a half step (also
known as a semitone). Two semitones equal one whole step or whole tone.
Accidentals are symbols used in musical notation to raise or lower the pitch of specific
notes:
A sharp raises a note a half step.
A flat lowers a note a half step.
A double sharp raises a note two half steps.
A double flat lowers a note two half steps.
A natural cancels any of the above accidentals and returns a note to its “natural”
pitch.
The space between a given pitch and the next pitch with the same letter name (for
example, from C to C or from F to F) is called an octave.
Scales
A scale is an ascending or descending series of pitches.
The pitches that make up a scale are called degrees, and each is assigned a
name and number. From lowest to highest, the scale degrees are called the tonic
(I), supertonic (II), mediant (III), subdominant (IV), dominant (V),
submediant (VI), and leading tone (VII).
The name of a scale is determined by its starting pitch and its key signature.
Most Western scales consist of a series of whole steps and half steps in a specific order.
The two most common Western scales are the major scale and the minor scale.
There are three types of minor scales:
Natural minor: The basic form of a minor scale (the c minor scale above is
natural minor).
Harmonic minor: A minor scale with the seventh degree elevated a half step.
Melodic minor: A minor scale with the sixth and seventh degrees elevated a half
step each.
Other types of scales have been used throughout the history of Western music:
Pentatonic scale: A five-tone scale widely used in indigenous folk music around
the world.
Whole-tone scale: A six-tone scale with a whole step between adjacent notes.
Debussy and other Impressionist composers explored uses of this scale in the late
1800s.
Octatonic scale: An eight-tone scale composed of alternating whole steps and
half steps between adjacent notes. The octatonic scale came into widespread use
in the 20th century.
Key and Key Signature
In Western music, most pieces are written in a key—a specific pitch that provides a tonal
center or point of focus for the piece. A single piece of music may switch, or modulate,
among several keys over its course. Often, a piece will make several modulations and
then finish in the key in which it started.
The key signature is a visual indication of key, placed on the staff at the beginning of a
piece of music that shows which notes on the staff are sharp or flat for the duration of
the piece. The composer may override the key signature by placing accidentals in front of
individual notes.
Each major key has a relative minor key that shares the same key signature, just as
each minor key has a relative major key that shares the same key signature. For
example, F major has one flat, as does its relative minor, d minor.
A diagram called the circle of fifths displays these relationships among the keys in
visual form:
Intervals
An interval is the space between any two pitches. Intervals are described with a
numerical measure that counts the number of semitones that each interval spans
(counting both the top and bottom pitches). Numerically, an interval may be described as
a second, third, fourth, fifth, sixth, seventh, eighth (octave), and so on.
Intervals also are described in terms of quality. An interval may be:
Perfect (P): An interval whose constituent pitches appear in both the major and
minor form of a given scale. For example, the interval between C and G is called a
perfect fifth because the pitches C and G appear in both the C major and c minor
scales. The only intervals that may be perfect are the fourth, fifth, and eighth
(octave).
Major (M): An interval whose constituent pitches appear in the major form of a
given scale. Seconds, thirds, sixths, and sevenths may be major.
Minor (m): An interval whose constituent pitches appear in the minor form of a
given scale. Seconds, thirds, sixths, and sevenths may be minor.
Diminished (d or °): A perfect or minor interval that has been reduced by a
semitone.
Augmented (A or +): A perfect or major interval that has been increased by a
semitone.
The same interval may have different names depending on the context in which it
appears. For example, the tritone is a special interval that spans three whole tones. The
tritone maybe described as either an augmented fourth (A4) or diminished fifth (d5).
The following staves show the intervals from a minor second to a major ninth:
Harmony and Dissonance
Intervals are an integral part of harmony, a broad concept that relates to the use of
simultaneous pitches in music and the way such relationships are organized over time.
Whereas melody refers to the “horizontal” aspects of music (i.e., notes played in
sequence), harmony refers to the “vertical” aspects (i.e., notes played together).
Certain intervals, such as the major third, perfect fourth, and perfect fifth, sound
“pleasant” or “stable” to the ear. These intervals form the basis of much traditional
Western harmony.
Other intervals, such as the tritone and major seventh, create a harshness or discordance
referred to as dissonance. The use of dissonance in Western music has become
gradually greater over the course of history.
Chords
A chord is a group of three or more pitches that sound simultaneously.
The intervals between the notes within a chord determine the chord quality. Chords,
like intervals, may be:
M
major
m
minor
°
diminished
+
augmented
In addition, certain types of chords may be:
Mm
major-minor
half-diminished
A triad is a chord that contains three pitches separated by major or minor thirds. A chord
with four pitches separated by major or minor thirds is called a seventh chord. Triads
and seventh chords form the basis of harmony for the vast majority of traditional
Western music.
The following staff shows several chords built on the note C. The notations in blue
indicate the intervals between the notes within each chord:
Tempo
The tempo of musical composition is the speed at which it is played.
Tempo and meter are closely connected. Tempo establishes the relationship between
meter and actual time and thus affects how the meter and time signature of a
composition sound to the ear. If a piece in 6/8 time is played at a slow tempo, the ear
tends to perceive six beats per measure; if played at a fast tempo, the ear tends to
perceive only two beats per measure.
Musicians often use a device called a metronome to keep track of tempo. A metronome
marks time by making a regular ticking or beeping sound a specified number of beats per
minute.
Often, tempo is described in terms of metronome number or metronome
mark (M.M.), i.e., the number of ticks or beats per minute. Use of metronome
marks enables the musician to determine tempo accurately with a metronome.
Alternatively, a composer may allow more casual interpretation of tempo by using
only suggested ranges of beats per minute.
The composer can use tempo marks to change tempo throughout the course of
a musical composition. These marks often take the form of descriptive terms from
Italian, including:

Largo: very slow (M.M.=40–60)

Larghetto: very slow, but faster than largo (M.M.=60–66)

Adagio: slow (M.M.=66–76)

Andante: somewhat slow; a leisurely walking tempo (M.M.=76–108)

Moderato: medium tempo; not particularly fast or slow (M.M.=108–120)

Allegro: fast (M.M.=120–168)

Presto: very fast (M.M.=168–208)

Prestissimo: as fast as possible (M.M.>208)
Dynamics
Dynamics are directions, written in a piece of music, that indicate the volume at which a
note or musical passage should be played. Composers typically indicate dynamics using
abbreviations for a number of Italian terms:
piano-pianissimo: extremely soft
pianissimo: very soft
piano: soft
mezzo piano: moderately soft
mezzo forte: moderately loud
forte: loud
fortissimo: very loud
forte-fortissimo: extremely loud
Expression and Articulation
Expression marks are symbols or words placed in written music to provide further
information about how the composition should be played. Expressions often are written in
Italian, although composers sometimes use their native languages as well.
Some common expressions include:

Cantabile (cant.): singing, flowing, melodic

Dolce: sweetly or gently

Espressivo (espr.): expressive; “play out”

Legato (leg.): evenly; notes should be fluid and continuous, and without
accent

Marcato (marc.): notes should be heavily accented and percussively
attacked

Staccato (stacc.): notes should be short and abbreviated

Tenuto (ten.): notes should be sustained and slightly attacked
The above expressions sometimes are modified with additional terms from Italian:

Molto: very

Moltissimo (moltiss.): extremely

Poco: a little

Pochissimo (pochiss.): a tiny amount
Articulation marks provide information about attack and decay —the beginning and
dying away of the sound of a note or a group of notes. Common articulation marks
include:
Themes, Motifs, and Structures
Most compositions are structured around recurring melodic or rhythmic passages called
themes or subjects. A composition may also feature a number of recurring motifs —
shorter fragments of melody or rhythm, often derived from the composition’s themes.
The composer usually does not notate themes and motifs explicitly in a piece of written
music.
Music scholars analyze the structure of a piece by labeling each distinct musical passage
or theme with a letter. For instance, a piece that begins with a theme (A); then moves to
another, different, theme (B); and then returns to the initial theme (A) is said to be in
ABA form.
Two common structures in Western music are the rondo form and the sonata form.
Rondo form: A structure that starts with a primary theme that returns between
contrasting sections. A rondo with two contrasting sections has ABACA form; one
with three sections has ABACADA form. A rondo may have any number of
contrasting sections.
Sonata form: A form that became the standard form for the first movements of
pieces in the Classical and Romantic eras. The sonata form typically includes four
sections:

Exposition: An opening section that generally presents two themes;

Development: A section that expands upon and evolves the themes of
the exposition;

Recapitulation: A section that repeats the themes of the exposition
unaltered; and

Coda: A concluding section that lends resolution or a sense of finality.