Representation of Musical Information Donald Byrd School of Informatics & Jacobs School of Music Indiana University Updated 17 Oct. 2007 Copyright 2003-07, Donald Byrd 1 Review: Classification: Logician Generals Warning Classification is dangerous to your understanding Almost everything in the real world is messy, ill-defined Absolute correlations between characteristics are rare Example: some mammals lay eggs; some are naked Example: was the first real piano Cristofori's (ca. 1700), Broadwood's (ca. 1790), or another?
People say an X has characteristics A, B, C Usually mean an X has A, & usually B, C Leads to: People who know better claiming absolute correlations Is it this or that or that? questions that dont have an answer Don changing his mind But lack of classification is also dangerous to your understanding! 3 Oct. 07 2 Basic Representations of Music & Audio (1) Digital Audio Audio (e.g., CD, MP3): like speech Time-stamped Events Time-stamped Events (e.g., MIDI file): like
unformatted text Music Notation Music Notation: like text with complex formatting 27 Jan. 3 Basic Representations of Music & Audio (2) 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) Avg. rel. storage 2000
1 10 Convert to left - easy OK job: easy Convert to right 1 note: pretty easy OK job: fairly hard other: hard or very hard - Ideal for music bird/animal sounds
sound effects speech music music 27 Jan. 4 Basic Representations of Music & Audio (3) Audio: no (explicit) structure Events/MIDI: simple structure Notation: very complex structure 2 Oct. 07 5 Dimensions of Music Representations & Encodings (1)
Waveform Csound Expressive Completeness CMN MusicXML Notelist MIDI (SMF) Structural Generality (After Wiggins et al (1993). A Framework for the Evaluation of Music Representation Systems.) rev. 20 Feb. 07 6 Dimensions of Music Representations & Encodings (2) Expressive completeness
How much of all possible music can the representation express? Includes synthesized as well as acoustic sounds! Waveform (=audio) is truly complete Exception, sort of: conceptual music E.g., Tom Johnson: Celestial Music for Imaginary Trumpets (notes on 100 ledger lines), Cage: 4 33 (of silence), etc. Structural generality How much of structure in any piece of music can the representation express? Music notation with repeat signs, etc. still expresses nowhere near all possible structure rev. 31 Jan. 07 7 Representation vs. Encoding Representation: what information is conveyed? More abstract (conceptual) Basic = general type of info; specific = exact type Encoding: how is the information conveyed? More concrete: in computer (bits)or on paper
(atoms)! One representation can have many encodings Atoms example: music notation in printed or Braille form Bits example: any kind of text in ASCII vs. Unicode Bits example: formatted text in HTML, RTF, .doc 30 Jan. 06 8 Representation Example: a Bit of Mozart The first few measures of Variation 8 of the Twinkle Variations 27 Jan. 9 In Notation Form: Nightingale Notelist
%%Notelist-V2 file='MozartRepresentationEx' partstaves=2 0 startmeas=193 C stf=1 type=3 C stf=2 type=10 K stf=1 KS=3 b K stf=2 KS=3 b T stf=1 num=2 denom=4 T stf=2 num=2 denom=4 A v=1 npt=1 stf=1 S1 'Variation 8' D stf=1 dType=5 N t=0 v=1 npt=1 stf=1 dur=5 dots=0 nn=72 acc=0 eAcc=3 pDur=228 vel=55 ...... appear=1 R t=0 v=2 npt=1 stf=2 dur=-1 dots=0 ...... appear=1
[email protected]@.D1 [email protected]@../ 11 An Event Form: Standard MIDI File (interpreted) Header format=1 ntrks=3 division=480 Track #1 start t=0 Tempo microsec/MIDI-qtr=749760 t=0 Time sig=2/4 MIDI-clocks/click=24 32nd-notes/24-MIDI-clocks=8 t=2868 Meta event, end of track Track end
Track #2 start t=0 Meta Text, type=0x03 (Sequence/Track Name) leng=5 Text = t=0 NOn ch=1 num=72 vel=56 t=228 NOff ch=1 num=72 vel=64 t=240 NOn ch=1 num=74 vel=56 t=468 NOff ch=1 num=74 vel=64 (etc. File size: 193 bytes) 27 Jan. 12 Basic and Specific Representations vs. Encodings Basic and Specific Representations (above the line) Audio
Waveform Time-stamped Events Time-stamped MIDI SMF .WAV Red Book (CD) Csound score Music Notation Gamelan not. Time-stamped expMIDI Csound score expMIDI File Notelist Tablature
CMN Mensural not. MusicXML Finale ETF Encodings (below the line) rev. 15 Feb. 13 Time Domain & Frequency Domain (1) Time domain involves waveforms Frequency domain involves spectra Fouriers Theorem Any periodic signal can be described exactly as the sum of sine waves at integral multiples of its fundamental frequency (Fourier analysis) Fourier Transform takes time domain to frequency Inverse Fourier Transform takes freq. domain to time
Fourier synthesis is usual kind of additive synthesis Definite-pitched sounds are (more-or-less) periodic 8 Feb. 07 14 Time Domain & Frequency Domain (2) Sine waves in trigonometry Phase in degrees (0 to 360) Simple example of Fourier synthesis: perfect square wave = an infinite number of odd harmonics but only if theyre all in phase Demo: Fourier applet http://www.falstad.com/fourier/ 31 Jan. 07 15 Time Domain & Frequency Domain (3) But real-world sounds are almost never periodic!
True, but definite-pitched notes are close enough for Fourier analysis to be useful In reality, usually a series of short-term Fourier Transforms (STFTs) Look at spectra of individual notes (from Iowa samples, EBU arpeggios) This is mathematics & physics; perception (psychoacoustics) is different, subtle We perceive musical sound in both domains sometimes more one, sometimes more the other Phase affects waveform, but maybe not perception 25 Feb. 07 16 Time Domain & Frequency Domain (4) Summary Periodic waveforms: clearcut definite pitch With sharp corners: much high-freq. energy square wave; loud trumpet
Without sharp corners: little high-freq. energy sine wave; low, soft flute Almost-periodic piano waveforms: definite pitch Aperiodic waveforms: noisy, no definite pitch cymbal, bass drum 25 Feb. 07 17 Real-World Musical Sounds The Attack/Sustain/Release model for notes Attack, Sustain, Release modified from recordings Used in the Kurzweil 250 (1984), etc.
Original version had only 2 MB for all samples Piano had diff. samples for 2 loudness levels and diff. sound for every 4-6 semitones 1-2 sec. per sample for A+S+R How good did the K250 really sound? COUNTDOWN, by Christopher Yavelow An opera for the nuclear age the orchestral accompaniment is in reality a Kurzweil-250 digital sampler, synchronized to the baton of the conductor http://www.yavelow.com/docs/countdown.html 12 Feb. 07 18 Real-World Musical Sounds Nowadays, can afford unlimited sustain but also need diff. sounds for many (8?) diff. loudness levels (multisampling)
All Together Now, Electronic Musician, Jan. 2007 and diff. sound for every semitone or two W/ unlimited sustain, takes gigabytes just for piano! 19 Feb. 07 19 Scholars (and others) Beware! Plausible (at the time) assumptions Stomach ulcers cant be caused by organisms (20th century) Men have more teeth than women (ancient) What you expect & what you see Sponges, dinosaurs, etc.: discuss later What you expect & what you hear Don & the Kurzweil 250 flute sound Don, a famous musician, & K250 handclaps Huron on what he knew & learned R. Moog at Kurzweil & piano touch
rev. 20 Sep. 2006 20 Uncompressed Audio Files are Big 1 byte = 8 bits (nearly always) How much data on a CD? CD audio is 44,100 samples/channel/sec. * 2 bytes/sample * 2 channels = 176,400 bytes/sec., or 10.5 MByte/min. CD can store up to 74 min. (or 80) of music 10.5 MByte/min. * 74 min. = 777 MBytes Actually more: also index, error correction data, etc. 22 Sep. 2006 21 Compressed Audio: Lossless & Lossy Dont confuse data compression and dynamic-range compression (a.k.a. audio level compression, limiting) Codec = COmpressor/DECompressor Lossless compression Standard methods (LZW: .zip, etc.) dont do much for audio
Audio specific methods MLP used for DVD-Audio Apple & Microsoft Lossless Lossy compression Depends on psychoacoustics (perceptual coding) 16 Feb. 06 22 Lossless Compression of Text Lossless compression of a childrens nursery rhyme Pease porridge hot, Pease porridge cold, Pease porridge in the pot, Nine days old; Some like it hot, Some like it cold, Some like it in the pot, Nine days old.
Diagram from Witten, Moffat, & Bell, Managing Gigabytes, 2nd ed. 12 Feb. 07 23 Specs for Some Common Audio Formats 13 Feb. 06 24 Psychoacoustics & Perceptual Coding Pohlmann, Ken (2005). Principles of Digital Audio, 5th ed., Chapter 10: Perceptual Coding Rationale: much better data compression Based on physiology of ear and critical bands Not fixed frequency: any sound creates one or more critical bands Masking Depends on relative loudness & frequency
Noise is much better than pitched sounds Threshhold of hearing Depends greatly on frequency 22 Sep. 2006 25 Compressed Audio: Lossy Compression (1) General method 1. Divide signal into sub-bands by frequency 2. Take advantage of (e.g.): Masking (shadows), via amplitude within critical bands Threshhold of audibility (varies w/ frequency) Redundancy among channels MPEG-1 layers I thru III (MP1, 2, 3), AAC get better & better compression via more & more complex techniques There is probably no limit to the complexity of psychoacoustics. --Pohlmann, 5th ed. However, there probably is an asymptotic limit to compression! Implemented in hardware or software codecs
22 Feb. 06 26 Compressed Audio: Lossy Compression (2) Evaluation via critical listening is essential ITU 5-point scale 5 = imperceptible, 4 = perceptible but not annoying, 3 = slightly annoying, 2 = annoying, 1 = very annoying Careful tests: often double-blind, triple-stimulus, hidden reference E.g., ISO qualifying AAC with 31 expert listeners (cf. Hall article) Test materials chosen to stress codecs Common useful tests: glockenspiel, castanets, triangle, harpsichord, speech, trumpet Soulodres worst-case tracks: bass clarinet arpeggio, bowed double bass, harpsichord arpeggio, pitch pipe, muted trumpet References: Pohlmann Principles of Digital Audio (on reserve) 17 Feb. 06 27
Hybrid Representation & Compression (1) Events (with predefined timbre) take very little space Mozart fragment AIFF (CD-quality audio): 794,166 bytes Mozart fragment MIDI file: 193 bytes Timbre takes same amount of space, regardless of music length! Problem: dont have exact timbre for any performance CSound, CMusic, etc. have MIDI-like score and software synthesis def. of orchestra 17 Feb. 07 28 Hybrid Representation & Compression (2) Mike Hawleys approach: find structure in audio; create events & timbre definition Hawley, Michael J. (1990). The Personal Orchestra, or, Audio Data Compression by 10000:1. Usenix Computing Systems Journal 3(2), pp. 289329.
Could hybrid event/audio representation lead to his audio data compression by a factor of 10,000? Maybe, but no time soon! 17 Feb. 07 29 An Event Form: Standard MIDI File (file dump)
30 An Event Form: Standard MIDI File (interpreted) Header format=1 ntrks=3 division=480 Track #1 start t=0 Tempo microsec/MIDI-qtr=749760 t=0 Time sig=2/4 MIDI-clocks/click=24 32nd-notes/24-MIDI-clocks=8 t=2868 Meta event, end of track Track end
Track #2 start t=0 Meta Text, type=0x03 (Sequence/Track Name) leng=5 Text = t=0 NOn ch=1 num=72 vel=56 t=228 NOff ch=1 num=72 vel=64 t=240 NOn ch=1 num=74 vel=56 t=468 NOff ch=1 num=74 vel=64 (etc. File size: 193 bytes) 27 Jan. 31 MIDI (Musical Instrument Digital Interface) (1) Invented in early 1980s Dawn of personal computers Designed as simple (& cheap to implement) real-time protocol for communication between synthesizers Low bandwidth: 31.25 Kbps
Top bit of byte: 1 = status, 0 = data Numbers usually 7 bits (range 0-127); sometimes 14 or even 21 Message types Channel: Channel Voice, Channel Mode System: System Common, System Real-Time, System Exclusive 5 Feb. 06 32 MIDI (2) Important standard Events are mostly Channel Voice msgs Note On: channel (1-16), note number (0-127), on velocity Note Off: channel, note number, off velocity Can change voice (really patch!) any time with Program Change msg A way around the 16-channel limit: cables may or may not correspond to a physical cable each cable supports 16 channels independent of others Systems with 4 (=64 channels) or 8 cables (=128) are common MIDI Monitor allows watching MIDI in real time
Freeware and open source! 5 Feb. 06 33 MIDI Sequencers Record, edit, & play SMFs (Standard MIDI Files) Standard views Piano roll often with velocity, controllers, etc., in parallel Event list Other: Mixer, Music notation, etc. Standard editing Adding digital audio Personal computers & software-development tools have gotten more & more powerful => "digital audio sequencers: audio & MIDI (stored in hybrid encodings) Making results more musical: Humanize Timing, etc. isnt mechanicalbut not really musical (yet)
8 Feb. 06 34 Is a MIDI File a Score or a Performance? MIDI files are often used to encode music from notation but also often used to describe performances! Whats the difference? Timing Dynamics Realizing ornaments, etc. For scores, MIDI files are very limited Max. 16 explicit voices, no spelling info, no slurs, etc. though not as badly as many assume Can include time sig., key sig., text/lyrics, etc. Cf. Dimensions of Music Representations & Encodings graph 15 Feb. 07 35
Another Warning: Terminology (1) A perilous question: How many voices does this synthesizer have? Syllogism Careless and incorrect use of technical terms is dangerous to your learning much Experts very often use technical terms carelessly Beginners often use technical terms incorrectly Therefore, your learning much is in danger Somewhat exaggerated, but only somewhat 5 Feb. 06 36 Another Warning: Terminology (2) Not-too-serious case: system Confusion because both standard (common) computer term & standard (rare but useful) music term Serious case: patch, program, timbre, or voice Vocabulary def.: Patch: referring to event-based systems such as MIDI and most synthesizers (particularly hardware synthesizers), a setting that
produces a specific timbre, perhaps with additional features. The terms "voice", "timbre", and "program" are all used for the identical concept; all have the potential to cause substantial confusion and should be avoided as much as possible Patch is the only unambiguous term of the four but the official MIDI specification (& almost everything else) talks about voices (as in Channel Voice messages control the instruments 16 voices) and to change the voice, you use a program change! 6 Feb. 06 37 Another Warning: Terminology (3) Some terminology is just plain difficult Example: Representation vs. Encoding Distinction: 1st is more abstract, 2nd more concrete but what does that mean? Explaining milk to a blind person: a white liquid... Dons precision involves being very careful with terminology, difficult or not Vocabulary is important source
Cf. other sources Contributions are welcome 6 Feb. 06 38 Selfridge-Field on Describing Musical Information Cf. Selfridge-Field, E. (1997). Describing Musical Information. What is Music Representation? (informal use of term!) Codes in Common Use: solfegge (pitch only), CMN, etc. Representations for Computer Application: total, MIDI Parameters of Musical Information Contexts: sound, notation/graphical, analytic, semantic; gestural? Concentrates on 1st three Processing Order: horizontal or vertical priority Code Categories
Sound Related Codes: MIDI and other Music Notation Codes: DARMS, SCORE, Notelist, Braille!?, etc. Musical Data for Analysis: Plaine and Easie, Kern, MuseData, etc. Representations of Musical Patterns and Process Interchange Codes: SMDL, NIFF, etc.; almost obsolete! 30 Jan. 06 39 Review: The Four Parameters of Notes Four basic parameters of a definite-pitched musical note 1. pitch: how high or low the sound is: perceptual analog of frequency 2. duration: how long the note lasts 3. loudness: perceptual analog of amplitude 4. timbre or tone quality Above is decreasing order of importance for most Western music and decreasing order of explicitness in CMN!
40 Review: How to Read Music Without Really Trying CMN shows at least six aspects of music: NP1. Pitches (how high or low): on vertical axis NP2. Durations (how long): indicated by note/rest shapes NP3. Loudness: indicated by signs like p , mf , etc. NP4. Timbre (tone quality): indicated with words like violin, pizzicato, etc. Start times: on horizontal axis Voicing: mostly indicated by staff; in complex cases also shown by stem direction, beams, etc. See Essentials of Music Reading musical example. 41 Complex Notation (Selfridge-Fields Fig. 1-4)
Complications on staff 2: Editorial additions (small notes) Instruments sharing notes only some of the time Mixed durations in double stops Multiple voices (divisi notation) Rapidly gets worse with more than 2! 10 Feb. 42 Complex Notation (Selfridge-Fields Fig. 1-4) Multiple voices rapidly gets worse with more than 2 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 unreadablewithout color! Acceptable because exact voice is rarely important rev. 12 Feb. 43 Domains of Musical Information
Independent graphic and performance info common Cadenzas (classical), swing (jazz), rubato passages (all music) CMN counterexamples show importance of independent graphic and logical info Debussy: bass clef below the staff Chopin: noteheads are normal 16ths in one voice, triplets in another Mockingbird (early 1980s) pioneered three domains: Logical: note is a qtr note (= ESF(Selfridge-Field)s notation) Performance: note sounds for 456/480ths of a quarter (= ESFs sound; also called gestural) Graphic: notehead is diamond shaped (= ESFs notation) Nightingale and other programs followed SMDL added fourth domain Analytic: for Roman numerals, Schenkerian level, etc. (= ESFs analytic)
1 Feb. 06 44 Representing Voicing in MIDI Files vs. Notation MIDI File Music Notation Explicit via tracks (max. of 16) Mostly explicit via staves, stem direction, voice-leading lines Implicit via patch, etc. Mostly implicit via stem direction, beaming, slurs, alignment, etc. 20 Feb. 07
45 Representing Basic Parameters in MIDI Files Vs. Notation Timing (incl. duration) MIDI File Music Notation Metric or time-code-based time Metric. Relative duration via notehead shape, aug. dots, tuplets, fermatas, etc.; relative time from alignment. Tempo & metronome marks Metric: ticks per quarter note (e.g., 480, 1024) Time-code-based: can be
SMPTE or millisec. Encoding as delta time, to save space Pitch Note number = piano key, plus (global) pitchbend No distinction between spellings Spelling with accidentals, including double & (very rarely) triple Dynamics Velocity: on (attack) & off (release) pppp to ffff, hairpins, text markings, accents, etc. Timbre Patch no., aftertouch, off velocity Instrument name, text markings,
symbols, etc. 20 Feb. 07 46 Communicating about Music Basic principle of communicating with people: say just whats necessary Strunk & White: Omit needless words Applies to a lecture or a notation 22 Feb. 07 47 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 48 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! What is a musical idea? Major issue for content-based music IR 49 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 50 Review: How People Find Text Information Query Database
understanding understanding Database concepts Query concepts matching Results What user wants is almost always concepts But computer can only recognize words 51 Review: How Computers Find Text Information Query (no understanding) Database
Stemming, stopping, query expansion, etc. (no understanding) matching Results Stemming, stopping, query expansion are all tricks to increase precision & recall (avoid false negatives & false positives) due to synonyms, variant forms of words, etc. 52 Notation Says Much about Representation CMN standard for Western music after ca.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) 53
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 54 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 55 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: ? 56 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) 57 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 58 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) 59
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 60 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 61 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! 62 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 timebut no program does! Notation programs convert CMN to performance (MIDI) and vice-versa => requires shallow semantics; makes things much harder 63 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 64 Conclusions: Review (2) We need CMN or equivalent to solve spectrum of music-IR (and other music-IT) problems But CMN cant represent everything we want Even when it can, actually may not (esp. explicitly) Need high-level intelligence to interpret Solution: unknown Likely to require major funding :-) 65 Why Music-IR Research is Important (Outside of Music) 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! 66 Different Classifications of Music Encodings Selfridge-Field Sound-related codes (1): MIDI Sound-related codes (2): Other Codes for Representation and Control Musical Notation Codes (1): DARMS Musical Notation Codes (2): Other ASCII Representations Musical Notation Codes (3): Graphical-object Descriptions Musical Notation Codes (4): Braille Codes for Data Management and Analysis (1): Monophonic Representations
Codes for Data Management and Analysis (2): Polyphonic Representations Representations of Musical Patterns and Processes Interchange Codes 10 Feb. Byrd Time-stamped MIDI Time-stamped Events + Audio CMN (domains L, G) CMN (domains L, G) CMN (domains L, P, G) CMN: non-computer representation! CMN (emphasizes domain A) CMN (emphasizes domain A) CMN (abstracted; emphasizes A) CMN (domains L, P, G, A) 67 Mozart: Variations for piano, K. 265, on
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