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Music Notation,Music Representation,

AND

Intelligence

Donald ByrdSchool of Music, Indiana University

3 February 2005minor rev. 5 February

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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 TalkI. Motivation: Why is this Important and/or

Interesting?II. Representation and SemanticsIII. Music Notation, Representation, and IntelligenceIV. Conclusions

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You Are Here

I. Motivation: Why is this Important and/or Interesting?

II. Representation and SemanticsIII. Music Notation, Representation, and

IntelligenceIV. Conclusions

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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)

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Similarity Scale for Content-Based Music IR

1. Same music, arrangement, performance, & recording (Shazam)2. Same music, arrangement, performance; different recording3. Same music, arrangement; different performance, recording4. 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!)

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”

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OMRAS Polyphonic Audio Music IR: A Task that Needs Note Representation

• Query (audio -> MIDI -> audio)

• Match (original audio recording)

• 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 Well-Tempered Clavier, Book I•Outcome: the actual piece was ranked 1st!

• Models built from notation database, but note data only

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Basic Representations of Music & Audio

Audio (e.g., CD, MP3): like speech

Time-stamped Events (e.g., MIDI file): like unformatted text

Music Notation (sheet music): like HTML text

Digital Audio

Time-stamped Events

Music Notation

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Basic Representations of Music & Audio

Audio Time-stamped EventsMusic Notation

Common examples CD, MP3 file Standard MIDI FileSheet music

Unit Sample Event Note, clef, lyric, etc.

Explicit structure none little (partial voicing much (complete

information) voicing information)

• Converting to form with less explicit structure (to left): moderately difficult

• Converting to form with more explicit structure (to right): very difficult

• MIDI = Musical Instrument Digital Interface: simple, very standard low-bandwidth protocol (from early 1980’s)

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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 SemanticsIII. Music Notation, Representation, and

IntelligenceIV. Conclusions

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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 SemanticsIII. Music Notation, Representation,

and IntelligenceIV. Conclusions

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How to Read Music (CMN) Without Really Trying: The Basics

• Four basic parameters of a musical note1. 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

M: What I fancy is a rare steak. Gret? I haven’t been...

I: I am of course a member of the Church of England.

G: Potatoes.

Performance (time goes from left to right):

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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

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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

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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

(& e 7)• Reason: avoid clutter

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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 Meta-Principles! (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 Meta-Principles! (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 SemanticsIII. Music Notation, Representation, and

IntelligenceIV. Conclusions

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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