Music Notation,
Music Representation,
AND
Intelligence
Donald Byrd
School of Music, Indiana University
3 February 2005
minor rev. 5 February
1
Overview
• Music representations: from abstract to concrete
(notation)
• Try to assume just the right things: e.g., no
knowledge of music or notation
• For motivation, focus on real-world content-based
music-IR situations
• Organization of the Talk
I. Motivation: Why is this Important and/or Interesting?
II. Representation and Semantics
III. Music Notation, Representation, and Intelligence
IV. Conclusions
2
You Are Here
I. Motivation: Why is this Important and/or
Interesting?
II. Representation and Semantics
III. Music Notation, Representation, and
Intelligence
IV. Conclusions
3
Audio-to-Audio Music “Retrieval”
• “Shazam - just hit 2580 on your mobile phone
and identify music”
• Query:
• Match:
• Fantastically impressive to many people
• Have they solved all the problems of music
IR? No, (almost) none!
• Reason: intended signal & match are identical
=> no time warping, let alone higher-level
problems (perception/cognition)
4
Similarity Scale for Content-Based Music IR
Relationship categories describing what’s in common between
items whose similarity is to be evaluated (from closest to most
distant)
• For material in notation form, distinctions among (1), (2),
and (3) don’t apply: it’s just “Same music, arrangement”
1. Same music, arrangement, performance, & recording (Shazam)
2. Same music, arrangement, performance; different recording
3. Same music, arrangement; different performance, recording
4. Same music, different arrangement; or different but closely-related
music, e.g., simpler variations (Mozart, etc.), minor revs. (OMRAS,
etc.)
5. Different & less closely-related music: freer variations (Schumann, etc.),
extensive revisions (AI)
6. Music in same genre, etc. (AI?)
7. Music influenced by other music (AI!)
5
OMRAS Polyphonic Audio Music IR: A Task
that Needs Note Representation
• Started with recordings of Bach preludes and fugues
• Did polyphonic (several notes at once) music recognition
• Polyphonic audio -> events is an open research problem
•Converted results to MIDI, used as queries against database of c.
3000 pieces in MIDI form
• One of worst-sounding cases: Prelude in G Major from WellTempered Clavier, Book I
•Outcome: the actual piece was ranked 1st!
• Models built from notation database, but note data only
• Query (audio -> MIDI -> audio)
• Match (original audio recording)
6
Basic Representations of Music & Audio
Digital Audio
Audio (e.g., CD, MP3):
like speech
Time-stamped
Time-stamped
Events Events
(e.g., MIDI file): like
unformatted text
Music
Notation
Music Notation
(sheet
music): like HTML text
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Basic Representations of Music & Audio
• MIDI = Musical Instrument Digital Interface: simple, very standard
low-bandwidth protocol (from early 1980’s)
Audio
Time-stamped Events Music Notation
Common examples
CD, MP3 file
Standard MIDI File
Sheet music
Unit
Sample
Event
Note, clef, lyric, etc.
Explicit structure
none
little (partial voicing
information)
much (complete
voicing information)
• Converting to form with less explicit structure (to left): moderately
difficult
• Converting to form with more explicit structure (to right): very
difficult
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Music-IR Problems that Needs More Structure
• Joan Public’s problem: find a song, given some of the
melody and some lyrics
– Needs notes and text (lyrics)
– Common question for music librarians, esp. in public libraries
• Musicologist’s problem: authorship/origin of works in
manuscripts
– Full symbolic data is important, even “insignificant” details of
notation (John Howard)
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You Are Here
I. Motivation: Why is this Important and/or
Interesting?
II. Representation and Semantics
III. Music Notation, Representation, and
Intelligence
IV. Conclusions
10
Representation, from Abstract to Concrete
• Cf. Basic Representations of Music & Audio
• Abstract: represention: semantics only
• Intermediate: syntax (mapping rules)?
• Concrete
– for use by computers: encoding
– for use by humans: if visual, notation (involves graphics
and/or typography)
• Analogous to knowledge representation vs. data
structure
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Semantics in Music
• Denotation (explicit, well-defined)...
• vs. Connotation (implicit, ill-defined)
• In text
– Two “definitions” of pig:
• 1. Ugh! Dirty, evil-smelling creatures, wallowing in filthy
sties! (Hayakawa)
• 2. Mammal with short legs, cloven hoofs, bristly hair, and a
cartilaginous snout used for digging (Amer. Heritage)
– Prose is “mostly” denotation
– Poetry is art => connotation much more important
• Music is always art, & only connotation!
• Major issue for content-based music IR
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From Representation to Notation
• Choosing a representation inevitably introduces bias
• Given a representation, choosing notation inevitably
introduces more bias
• Important to consider the purpose (R. Davis et al;
Wiggins et al)
• For huge body of important music, we have no choice:
notation is CMN (Conventional Music Notation)!
–
–
–
–
Really “CWMN” (W = Western)
Alternative for some music: tablature (guitar, lute, etc.)
CMN is among the most successful notations ever...
but enormously complex and subtle
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Notation Says Much about Representation
• CMN standard for Western music after c.1650
• Evolved for “classical” music, but heavily used
for very wide range (pop, jazz, folk, etc.)
• Composers/arrangers/transcribers have
pushed it hard => reveals things about music
representation in general
• Will concentrate on notation (CMN)
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You Are Here
I. Motivation: Why is this Important and/or
Interesting?
II. Representation and Semantics
III. Music Notation, Representation, and
Intelligence
IV. Conclusions
15
How to Read Music (CMN) Without Really
Trying: The Basics
• Four basic parameters of a musical note
1. Pitch: how high or low sound is
2. Duration: how long the note lasts
3. Loudness: perceptual analog of amplitude
4. Timbre or tone quality
• Above in decreasing order of importance for most Western music
• Principles of CMN (& e 1)
1. Pitch on vertical axis: clef gives offset (“zero”)
2a. Duration indicated by note/rest shapes
2b. Start times (sum of durations in the voice) on horizontal axis
3. Loudness indicated by signs like p , mf , etc.
4. Timbre indicated with words like “violin”, “horn”, “pizzicato”
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Why is Musical Information Hard to
Handle?
1. Units of meaning: not clear anything in music is
analogous to words (all representations)
2. Polyphony: “parallel” independent voices, something
like characters in a play (all representations)
3. Recognizing notes (audio only)
4. Other reasons
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Units of Meaning (Problem 1)
• Not clear anything in music is analogous to words
– No explicit delimiters (like Chinese)
– Experts don’t agree on “word” boundaries (unlike Chinese)
•
•
•
•
•
•
Are notes like words?
No. Relative, not absolute, pitch is important
Are pitch intervals like words?
No. They’re too low level: more like characters
Are pitch-interval sequences like words?
In some ways, but
– Ignores note durations
– Ignores relationships between voices (harmony)
– Probably little correlation with semantics
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Independent Voices in Music
(Problem 2) (& e 2)
J.S. Bach: “St. Anne” Fugue, beginning
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Independent Voices in Text
MARLENE. What I fancy is a rare steak. Gret?
ISABELLA. I am of course a member of the / Church of England.*
GRET. Potatoes.
MARLENE. *I haven’t been to church for years. / I like Christmas carols.
ISABELLA. Good works matter more than church attendance.
--Caryl Churchill: “Top Girls” (1982), Act 1, Scene 1
Performance (time goes from left to right):
M: What I fancy is a rare steak. Gret?
I:
G:
I haven’t been...
I am of course a member of the Church of England.
Potatoes.
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Complex Notation: Multiple Voices (&
e 3)
Multiple voices on a staff rapidly gets worse with
more than 2 (Telemann “Liebe, Liebe”):
• 2 voices in mm. 5-6: not bad: stem direction is enough
• 3 voices in m. 7: notes must move sideways
• 4 voices in m. 8: almost unreadable—without color!
• Still acceptable because specific voice is rarely important
21
Problems: Example 1 (superficial but
interesting)
•
•
•
•
Ravel work has slur with 7 inflection points
Impressive, but complexity is purely graphical
No big deal in terms of representation
…but influence of performance on notation is revealing
22
Duration and Higher-Level Concepts of
Time
• Schubert Impromptu (& e 4)
• Measures: everything between barlines
• Time signature: 3/4 = 3 quarter notes per
measure
• Triplets: 3 notes in the time normally used by 2
– General concept is tuplets
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Problems: Example 2 (Deep)
• Chopin Nocturne has nasty situation (& e 5)
• One notehead is triplet in one voice, but
normal duration in another
• “Semantics” (execution) well-defined, obvious
– Note starts 1/16 before barline…
– But also (2/3)*(1/16) before barline! How to play?
• Reason: musical necessity
• Solution for performer: “rubato”
• Solution for music IR program: ?
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Problems: Example 3 (Medium)
• Bach: time signature change in middle of measure
•
(& e 6)
• “Semantics” well-defined and obvious
– Measure has duration of 18 16ths…
– But not until the middle of the measure!
• How does this make sense?
• Triplets express same relationship as equivalent
simple/compound meter
• Invisible (unmarked) triplets
• Cf. Bach Prelude: two time signatures at once (&
• Reason: avoid clutter
e 7)
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Problem 4 (Medium)
•
•
•
•
•
Brahms Capriccio (& e 8)
Time signature 6/8 => measure lasts 12 16ths
A dotted half note always lasts 12 16ths…
but here it clearly lasts only 11 16ths!
Reason: avoid clutter
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Two Ways to Have Two Clefs at Once
• Clef gives vertical offset to determine pitch
• Debussy (& e 9)
– Bizarrely obvious something odd involving clefs
• Ravel (&
e 10)
– Only comparing time signature (3/8) and note
durations makes it clear both clefs affect whole
measure
• Reason: save space (by avoiding a 3rd staff)
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Surprise: Music Notation has MetaPrinciples! (1)
1. Maximize readability (intelligibility)
–
–
–
–
Avoid clutter = “Omit Needless Symbols”
Try to assume just the right things for audience
Audience for CMN is (primarily) performers
General principle of any communication
• Applies to talks as well as music notation!
– Examples: Schubert, Bach, Brahms
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Surprise: Music Notation has MetaPrinciples! (2)
2. Minimize space used
– Save space => fewer page turns (helps performer);
also cheaper to print (helps publisher)
– Squeezing much music into little space is a major
factor in complexity of CMN
– Especially important for music: real-time, hands full
– Examples: Telemann, Debussy, Ravel
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The “Rules” of Music Notation
• Tempting to assume that rules of such an elaborate &
successful system as CMN work (self-consistent, reasonably
unambiguous, etc.) in every case
• But (a) “rules” evolved, with no established authority; (b) many
of the “rules” are very nebulous
• In common cases, there's no problem
• If you try to make every rule as precise as possible, result is
certainly not self-consistent
• Trying to save space makes rules interact; something has to
give!
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Music Notation Software and Intelligence
• Despite odd notation, really nothing strange going on
in almost all of these examples
– Ravel slur, Debussy & Ravel 2 simultaneous clefs, Bach &
Schubert invisible triplets, Brahms “short” dotted-half note,
Telemann 4 voices/staff are all simple situations
– Chopin Nocturne is complex
• Programmers try to help users by having programs
do things “automatically”
• A good idea if software knows enough to do the right
thing “almost all” the time—but no program does!
• Notation programs convert CMN to performance
(MIDI) and vice-versa => requires shallow
“semantics”; makes things much harder
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You Are Here
I. Motivation: Why is this Important and/or
Interesting?
II. Representation and Semantics
III. Music Notation, Representation, and
Intelligence
IV. Conclusions
32
Conclusions: Review (1)
•
•
•
•
Representations express Semantics
Semantics of Music; Denotation & Connotation
Principles of CMN
Meta-Principles of CMN
1. Maximize readability; Omit Needless Symbols
• Try to assume just the right things for audience
• General principle of any communication
2. Minimize space used
• Save space => fewer page turns, less paper
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Conclusions: Review (2)
• We need CMN or equivalent to solve spectrum
of music-IR (and other music-IT) problems
–
–
–
–
–
But CMN can’t represent everything we want
Even when it can, may not, at least explicitly
Need high-level intelligence to interpret
Solution: unknown
Likely to require major funding :-)
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Conclusions: Why is this really Important
and/or Interesting?
• Some problems directly related to other areas
of informatics
– Example: Approximate string matching in
bioinformatics
• Encourages progress on real semantics
– Connotation is an important part of meaning in
everything
– Can often ignore, but any semantics in arts forces
you to deal with connotation
– Music is at least as quantifiable as any art, so likely
to be more tractable than others!
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You Are Here
The End
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