1 Representation of Musical Information Donald Byrd School of Music Indiana University Updated 20 February 2007 Copyright © 2003-07, Donald Byrd.

1

Representation of Musical Information

Donald Byrd

School of Music

Indiana University

Updated 20 February 2007

Copyright © 2003-07, Donald Byrd

31 Jan. 07 2

Classification: Logician General’s Warning

• Classification is dangerous to your understanding– Almost everything in the real world is messy– Absolute correlations between characteristics are rare– Example: some mammals lay eggs; some are “naked”– Example: is the piano a keyboard, a string, or a

percussion instrument?• 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– Arguments among experts over which characteristic is

most fundamental– Don changing his mind

rev. 20 Feb. 07 3

Dimensions of Music Representations & Encodings (1)

(After Wiggins et al (1993). A Framework for the Evaluation of Music Representation Systems.)

Structural Generality

• Waveform

• MIDI (SMF)

• Notelist• MusicXML

Expressive Completeness

• Csound

• CMN

rev. 31 Jan. 07 4

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

30 Jan. 06 5

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

27 Jan. 6

Basic Representations of Music & Audio

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

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

Music Notation: like text with complex formatting

Digital Audio

Time-stamped Events

Music Notation

27 Jan. 7

Basic Representations of Music & Audio

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 much (complete information) 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 music music bird/animal sounds sound effects speech

27 Jan. 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• N t=240 v=1 npt=1 stf=1 dur=5 dots=0 nn=74 acc=0 eAcc=3 pDur=228 vel=55 ...... appear=1• N t=480 v=1 npt=1 stf=1 dur=5 dots=0 nn=75 acc=0 eAcc=2 pDur=228 vel=55 ...... appear=1• N t=720 v=1 npt=1 stf=1 dur=5 dots=0 nn=77 acc=0 eAcc=3 pDur=228 vel=55 ...... appear=1• / t=960 type=1• N t=960 v=1 npt=1 stf=1 dur=4 dots=0 nn=79 acc=0 eAcc=3 pDur=456 vel=55 ...... appear=1• (etc. File size: 1862 bytes)

5 Feb. 10

An Event Form: Standard MIDI File (file dump)

• 0: 4D54 6864 0000 0006 0001 0003 01E0 4D54 MThd.........‡MT • 16: 726B 0000 0014 00FF 5103 0B70 C000 FF58 rk......Q..p¿..X • 32: 0402 0218 0896 34FF 2F00 4D54 726B 0000 .....ñ4./.MTrk.. • 48: 0055 00FF 0305 5069 616E 6F00 9048 3881 .U....Piano.êH8Å • 64: 6480 4840 0C90 4A38 8164 804A 400C 904B dÄH@.êJ8ÅdÄJ@.êK • 80: 3881 6480 4B40 0C90 4D38 8164 804D 400C 8ÅdÄK@.êM8ÅdÄM@. • 96: 904F 3883 4880 4F40 1890 4F38 8360 9050 êO8ÉHÄO@.êO8É`êP • 112: 3883 4880 4F40 1890 4D38 8330 8050 4018 8ÉHÄO@.êM8É0ÄP@. • 128: 804D 400D FF2F 004D 5472 6B00 0000 3200 ÄM@../.MTrk...2. • 144: FF03 0550 6961 6E6F 8F00 9041 2B81 6480 ...Pianoè.êA+ÅdÄ • 160: 4140 0C90 4330 8164 8043 400C 9044 3181 A@.êC0ÅdÄC@.êD1Å • 176: 6480 4440 0C90 4647 8164 8046 4001 FF2F dÄD@.êFGÅdÄF@../ • 192: 00 .

27 Jan. 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 = <Piano>• 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)

rev. 15 Feb. 12

Basic and Specific Representations vs. Encodings

Audio Time-stamped Events Music Notation

CMN Mensural not.

Gamelan not.

SMF

Csound score

NotelistMusicXML

FinaleETFexpMIDI File

Time-stamped MIDI

Time-stamped expMIDI

Csound score

Waveform

Red Book (CD)

Tablature

.WAV

Basic and Specific Representations (above the line)

Encodings (below the line)

8 Feb. 07 13

Time Domain & Frequency Domain (1)

• Time domain involves waveforms• Frequency domain involves spectra• Fourier’s 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

31 Jan. 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 they’re 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– 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

12 Feb. 07 16

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

19 Feb. 07 17

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!

rev. 20 Sep. 2006 18

Scholars (and others) Beware!

• Plausible (at the time) assumptions– Stomach ulcers can’t 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

22 Sep. 2006 19

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.

16 Feb. 06 20

Compressed Audio: Lossless & Lossy

• Don’t confuse data compression and dynamic-range compression (a.k.a. audio level compression, limiting)

• Codec = COmpressor/DECompressor

• Lossless compression– Standard methods (LZW: .zip, etc.) don’t do much for audio

– Audio specific methods

• MLP used for DVD-Audio

• Apple & Microsoft Lossless

• Lossy compression– Depends on psychoacoustics (“perceptual coding”)

12 Feb. 07 21

Lossless Compression of Text

• Lossless compression of a children’s nursery rhymePease 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.

13 Feb. 06 22

Specs for Some Common Audio Formats

22 Sep. 2006 23

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 Feb. 06 24

Compressed Audio: Lossy Compression

• General method1. 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

5 Feb. 25

An Event Form: Standard MIDI File (file dump)

• 0: 4D54 6864 0000 0006 0001 0003 01E0 4D54 MThd.........‡MT • 16: 726B 0000 0014 00FF 5103 0B70 C000 FF58 rk......Q..p¿..X • 32: 0402 0218 0896 34FF 2F00 4D54 726B 0000 .....ñ4./.MTrk.. • 48: 0055 00FF 0305 5069 616E 6F00 9048 3881 .U....Piano.êH8Å • 64: 6480 4840 0C90 4A38 8164 804A 400C 904B dÄH@.êJ8ÅdÄJ@.êK • 80: 3881 6480 4B40 0C90 4D38 8164 804D 400C 8ÅdÄK@.êM8ÅdÄM@. • 96: 904F 3883 4880 4F40 1890 4F38 8360 9050 êO8ÉHÄO@.êO8É`êP • 112: 3883 4880 4F40 1890 4D38 8330 8050 4018 8ÉHÄO@.êM8É0ÄP@. • 128: 804D 400D FF2F 004D 5472 6B00 0000 3200 ÄM@../.MTrk...2. • 144: FF03 0550 6961 6E6F 8F00 9041 2B81 6480 ...Pianoè.êA+ÅdÄ • 160: 4140 0C90 4330 8164 8043 400C 9044 3181 A@.êC0ÅdÄC@.êD1Å • 176: 6480 4440 0C90 4647 8164 8046 4001 FF2F dÄD@.êFGÅdÄF@../ • 192: 00 .

27 Jan. 26

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 = <Piano>• 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)

5 Feb. 06 27

MIDI (Musical Instrument Digital Interface) (1)

• Invented in early 1980’s– 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 28

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!

8 Feb. 06 29

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. isn’t mechanical—but not really musical (yet)

15 Feb. 07 30

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!• What’s 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

5 Feb. 06 31

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

6 Feb. 06 32

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 instrument’s 16 voices”)

– …and to change the “voice”, you use a “program change”!

6 Feb. 06 33

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...”

• Don’s precision involves being very careful with terminology, difficult or not– Vocabulary is important source– Cf. other sources– Contributions are welcome

30 Jan. 06 34

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!

35

Review: The Four Parameters of Notes

• Four basic parameters of a definite-pitched musical note1. 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!

36

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.

10 Feb. 37

Complex Notation (Selfridge-Field’s 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!

rev. 12 Feb. 38

Complex Notation (Selfridge-Field’s 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 unreadable—without color!

• Acceptable because exact voice is rarely important

1 Feb. 06 39

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 1980’s) pioneered three domains:– Logical: “ note is a qtr note” (= ESF(Selfridge-Field)’s “notation”)– Performance: “ note sounds for 456/480ths of a quarter” (= ESF’s “sound”; also

called gestural)– Graphic: “ notehead is diamond shaped” (= ESF’s “ notation”)– Nightingale and other programs followed

• SMDL added fourth domain– Analytic: for Roman numerals, Schenkerian level, etc. (= ESF’s “analytic”)

20 Feb. 07 40

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 41

Representing Basic Parameters in MIDI Files Vs. Notation

MIDI File Music Notation

Timing (incl. duration)

Metric or time-code-based timeMetric: ticks per quarter note (e.g., 480, 1024)Time-code-based: can be SMPTE or millisec.Encoding as delta time, to save space

Metric. Relative duration via notehead shape, aug. dots, tuplets, fermatas, etc.; relative time from alignment. Tempo & metronome marks

Pitch Note number = piano key, plus (global) pitchbendNo 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.

10 Feb. 42

Different Classifications of Music Encodings

Selfridge-Field ByrdSound-related codes (1): MIDI Time-stamped MIDI

Sound-related codes (2): Other Codes forRepresentation and Control

Time-stamped Events + Audio

Musical Notation Codes (1): DARMS CMN (domains L, G)

Musical Notation Codes (2): Other ASCIIRepresentations

CMN (domains L, G)

Musical Notation Codes (3): Graphical-objectDescriptions

CMN (domains L, P, G)

Musical Notation Codes (4): Braille CMN: non-computerrepresentation!

Codes for Data Management and Analysis (1):Monophonic Representations

CMN (emphasizes domain A)

Codes for Data Management and Analysis (2):

Polyphonic Representations

CMN (emphasizes domain A)

Representations of Musical Patterns and

Processes

“CMN” (abstracted; emphasizes

A)Interchange Codes CMN (domains L, P, G, A)

43

Mozart: Variations for piano, K. 265, on “Ah, vous dirais-je, Maman”, a.k.a. Twinkle