Transcript Representation of Musical Information

Representation of Musical
Information
Donald Byrd
School of Music
Indiana University
Updated 20 February 2007
Copyright © 2003-07, Donald Byrd
1
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
31 Jan. 07
2
Dimensions of Music Representations &
Encodings (1)
• Waveform
• Csound
Expressive
Completeness
• CMN
• M usicXML
• Notelist
• M IDI (SM F)
Structural Generality
(After Wiggins et al (1993). A Framework for the Evaluation of Music
Representation Systems.)
rev. 20 Feb. 07
3
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
4
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
5
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
Musiclike
Notation
Music Notation:
text with complex
formatting
27 Jan.
6
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
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.
7
Representation Example: a Bit of Mozart
The first few measures of Variation 8 of the “Twinkle” Variations
27 Jan.
8
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)
27 Jan.
9
An Event Form: Standard MIDI File (file dump)
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•
•
•
•
•
•
•
•
•
•
•
•
0:
16:
32:
48:
64:
80:
96:
112:
128:
144:
160:
176:
192:
4D54 6864
726B 0000
0402 0218
0055 00FF
6480 4840
3881 6480
904F 3883
3883 4880
804D 400D
FF03 0550
4140 0C90
6480 4440
00 .
0000
0014
0896
0305
0C90
4B40
4880
4F40
FF2F
6961
4330
0C90
0006
00FF
34FF
5069
4A38
0C90
4F40
1890
004D
6E6F
8164
4647
0001
5103
2F00
616E
8164
4D38
1890
4D38
5472
8F00
8043
8164
0003
0B70
4D54
6F00
804A
8164
4F38
8330
6B00
9041
400C
8046
01E0
C000
726B
9048
400C
804D
8360
8050
0000
2B81
9044
4001
4D54
FF58
0000
3881
904B
400C
9050
4018
3200
6480
3181
FF2F
5 Feb.
MThd.........‡MT
rk......Q..p¿..X
.....ñ4./.MTrk..
.U....Piano.êH8Å
dÄH@.êJ8ÅdÄJ@.êK
8ÅdÄK@.êM8ÅdÄM@.
êO8ÉHÄO@.êO8É`êP
8ÉHÄO@.êM8É0ÄP@.
ÄM@../.MTrk...2.
...Pianoè.êA+ÅdÄ
A@.êC0ÅdÄC@.êD1Å
dÄD@.êFGÅdÄF@../
10
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)
27 Jan.
11
Basic and Specific Representations vs. Encodings
Basic and Specific Representations (above the line)
Audio
Time-stamped Events
Waveform
Time-stamped MIDI
Csound score
Time-stamped expM IDI
.WAV
Red Book (CD)
SMF
Csound score
Music Notation
Gamelan not.
Notelist
expM IDI File
Tablature
CM N
M ensural not.
M usicXM L
Finale
ETF
Encodings (below the line)
rev. 15 Feb.
12
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
8 Feb. 07
13
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
14
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
31 Jan. 07
15
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
16
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
17
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
rev. 20 Sep. 2006
18
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
19
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”)
16 Feb. 06
20
Lossless Compression of Text
• Lossless compression of a
children’s 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
21
Specs for Some Common Audio Formats
Format
Encoding Type
Details
Fidelity
“Red Book” (CD)
Uncompressed,
linear
44.1KHz, 16 bit s/sample,
st ereo
Very high
Bandwidth
(Kbps)
ca. 1400
Early game audio
Uncompressed,
linear
22.05KHz, 8 bit s/sample,
mono
Low
176
MLP, Apple
Lossless
Compression, etc.
MP2 (Variat ions1)
Lossless comp.
compression ca. 2:1
Very high
ca. 700
Lossy comp.
compression ca. 3:1
High
ca. 400
MP3 (Variations2),
AAC, WMA
Lossy comp.
compression ca. 7:1 to
over 10:1
High t o
very high
ca. 128-192
compression more than
20:1
Medium
ca. 28-64
AAC (Variations2), Lossy comp.
WMA
13 Feb. 06
22
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
23
Compressed Audio: Lossy Compression
• 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
24
An Event Form: Standard MIDI File (file dump)
•
•
•
•
•
•
•
•
•
•
•
•
•
0:
16:
32:
48:
64:
80:
96:
112:
128:
144:
160:
176:
192:
4D54 6864
726B 0000
0402 0218
0055 00FF
6480 4840
3881 6480
904F 3883
3883 4880
804D 400D
FF03 0550
4140 0C90
6480 4440
00 .
0000
0014
0896
0305
0C90
4B40
4880
4F40
FF2F
6961
4330
0C90
0006
00FF
34FF
5069
4A38
0C90
4F40
1890
004D
6E6F
8164
4647
0001
5103
2F00
616E
8164
4D38
1890
4D38
5472
8F00
8043
8164
0003
0B70
4D54
6F00
804A
8164
4F38
8330
6B00
9041
400C
8046
01E0
C000
726B
9048
400C
804D
8360
8050
0000
2B81
9044
4001
4D54
FF58
0000
3881
904B
400C
9050
4018
3200
6480
3181
FF2F
5 Feb.
MThd.........‡MT
rk......Q..p¿..X
.....ñ4./.MTrk..
.U....Piano.êH8Å
dÄH@.êJ8ÅdÄJ@.êK
8ÅdÄK@.êM8ÅdÄM@.
êO8ÉHÄO@.êO8É`êP
8ÉHÄO@.êM8É0ÄP@.
ÄM@../.MTrk...2.
...Pianoè.êA+ÅdÄ
A@.êC0ÅdÄC@.êD1Å
dÄD@.êFGÅdÄF@../
25
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)
27 Jan.
26
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
27
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
28
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)
8 Feb. 06
29
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
15 Feb. 07
30
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
31
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
32
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
6 Feb. 06
33
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
34
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!
35
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.
36
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!
10 Feb.
37
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
rev. 12 Feb.
38
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”)
1 Feb. 06
39
Representing Voicing in MIDI Files vs. Notation
MIDI File
Music Notation
Explicit via tracks (max. of Mostly explicit via
16)
staves, stem direction,
voice-leading lines
Implicit via patch, etc.
Mostly implicit via stem
direction, beaming, slurs,
alignment, etc.
20 Feb. 07
40
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
41
Different Classifications of Music Encodings
Selfridge -Field
Sound -related codes (1): M IDI
Sound -related codes (2): Other Codes for
Representation and Control
Musical Notation Codes (1): D ARMS
Musical Notation Codes (2): O ther ASCII
Representations
Musical Notation Codes (3): G raphical-obje ct
Descriptions
Musical Notation Codes (4): B raille
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)
42
Mozart: Variations for piano, K. 265, on
“Ah, vous dirais-je, Maman”, a.k.a. Twinkle
Theme
2 œ œ
&4
2
? 4 œ
œ
Variation 2
&
?
`
œ
œ
œ œ
œ œ
œ œ
œ œ
œ œ
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