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Musical Analysis using statistical methods
20020030 권상일
Contents
1. Overview
2. MIDI
3. Theories
4. Samples
5. Results
6. Limits
7. Conclusion
8. Reference
1. Overview
What I want to do is… Analyze music with statistical approach. Search or define quantity that shows
characteristics of music. Find the factors that determine the BEAUTY of
famous songs.
2. MIDI (1)
Musical Instrument Digital Interface
Digitalized Score Time, channel, note, volume, instruments, and
various effects…
Table of few channel voice messagesChannel Voice Messages
StatusD7----D0
Data Byte(s)D7----D0
Description
1000nnnn0kkkkkkk0vvvvvvv
Note Off event.(kkkkkkk) is the key (note) number.
(vvvvvvv) is the velocity.
1001nnnn0kkkkkkk0vvvvvvv
Note On event.(kkkkkkk) is the key (note) number.
(vvvvvvv) is the velocity.
2. MIDI (2)
Table of MIDI Note Numbers
OctaveNumber
Note Numbers
C C# D D# E F F# G G# A A# B
-1 0 1 2 3 4 5 6 7 8 9 10 11
0 12 13 14 15 16 17 18 19 20 21 22 23
1 24 25 26 27 28 29 30 31 32 33 34 35
2 36 37 38 39 40 41 42 43 44 45 46 47
3 48 49 50 51 52 53 54 55 56 57 58 59
4 60 61 62 63 64 65 66 67 68 69 70 71
5 72 73 74 75 76 77 78 79 80 81 82 83
6 84 85 86 87 88 89 90 91 92 93 94 95
7 96 97 98 99 100 101 102 103 104 105 106 107
8 108 109 110 111 112 113 114 115 116 117 118 119
9 120 121 122 123 124 125 126 127
3. Theories (1)
1/f law (musical Zipf’s law) Almost every music have 1/f dependence. Frequency spectrum Pitch interval distribution
Scatter diagram It shows how strongly or weakly related one pi
ece of data is to the previous one. The x-axis is labeled n and the y-axis is n-1
3. Theories (2)
Fractal dimension Scatter Diagram’s
fractal dimension is given by
ln /
ln /
N nD
B b
3. Theories (3)
Entropy Treat each pitches as accessible states and the
number of appearance as probabilities. Then
High entropy : there are many chromatic notes…
Fractal dimension and entropy tells us Degree of correlation and ratio of chromatic scale
lnr rr
S P P
4. Samples (1)
Why many Beatles? Lennon and McCartney’s
songs have SIMPLE and VARIOUS style.
They are so FAMOUS!
Why Debussy? His melody line was very
UNUSUAL form for that time.
Why Bach? Many people says,
“Bach’s music has esthetical BEAUTY!”
Composer Title Tonic
J. S. Bach
Cello Suite No. 1 in G major - BWV 1007, Prelude 43 (G major)
Cello Suite No. 3 in C major - BWV 1009, Courante
48 (C major)
Cello Suite No. 6 in D major - BWV 1012, Courante
50 (D major)
The Art of Fugue - BWV 1080, Contrapunctus I 62 (D minor)
C. DebussyClair de lune 73 (C#
major)
Prelude a l'Apres-Midi d'un Faune 71 (B major)
J. Lennon(The
Beatles)
Across The Universe 74 (D major)
Girl 72 (C minor)
Julia 60 (C major)
Norwegian Wood 64 (E major)
Nowhere Man 64 (E major)
Strawberry Fields Forever70 (A#
major)
P. McCart
ney(The
Beatles)
And I Love Her68 (G#
minor)
Here, There And Everywhere 67 (G major)
In My Life 69 (A major)
Let It Be 72 (C major)
Michelle 62 (D minor)
Penny Lane 72 (Cmajor)
Yesterday 65 (F minor)
4. Samples (2)
4. Samples (3)
Programs Note counts Deviation Interval counts Interval distribution (scatter diagram) Pitch counts Fractal dimension Entropy
5. Results – Zipf’s Law (1)
Well-known factors satisfy Zifp’s law Frequency spectrum Pitch interval distribution Etc…
Bach – CS No. 1 in G major - BWV 1007, Prelude Debussy - Prelude a l'Apres-Midi d'un Faune
Lennon - Nowhere Man McCartney - Yesterday
Bach – CS No. 1 in G major - BWV 1007, Prelude Debussy - Prelude a l'Apres-Midi d'un Faune
Lennon - Nowhere Man McCartney - Yesterday
5. Results – Scatter Diagrams (1)
SD shows how close the notes are.
How can we know? Look at 1/f β ! 0 < β < 0.5 : white noise, nearly random 0.5 < β < 1 : pink noise, most songs are in here! 1.5 <β < 2 : brown noise, too correlated
Compare with y=x graph. Near : repetitious Far : varied
Debussy – Clair de lune (-1.3) Bach – AF BWV 1080 Contrapunctus I (2) (-1.6)
Lennon – Strawberry Field Forever (-1.2) McCartney – Yesterday (-1.3)
5. Results – Relative Pitch (1)
Relative Pitch shows… How chromatic a passage is?
Why we observe relative pitch? To calculate entropy Most of people recognize tonic, major third,
perfect fourth, and perfect fifth better than other pitches
To give the answer : What makes comfortable music be COMFORTABLE?
Bach - Suite No. 1 in G major - BWV 1007, Prelude Debussy - Prelude a l'Apres-Midi d'un Faune
Lennon – Norwegian Wood McCartney – Let it be
5. Results – Dimension & Entropy (1)
Composer Title Dimension Entropy
J. S. Bach
Cello Suite No. 1 in G major - BWV 1007, Prelude 0.2737 2.163
Cello Suite No. 3 in C major - BWV 1009, Courante 0.2728 2.209
Cello Suite No. 6 in D major - BWV 1012, Courante 0.03714 2.098
The Art of Fugue - BWV 1080, Contrapunctus I (2) 0.2703 2.186
C. DebussyClair de lune 0.08722 2.160
Prelude a l'Apres-Midi d'un Faune 0.2680 2.207
J. Lennon(The Beatles)
Across The Universe 0.07342 1.793
Girl 0.2075 1.804
Julia 0.2328 1.695
Norwegian Wood 0.05774 2.042
Nowhere Man 0.09632 1.854
Strawberry Fields Forever 0.1757 1.943
P. McCartney(The Beatles)
And I Love Her 0.03356 1.893
Here, There And Everywhere 0.2127 2.029
In My Life 0.05774 1.748
Let It Be 0.07600 1.601
Michelle 0.2474 1.803
Penny Lane 0.2427 1.919
Yesterday 0.06015 1.937
5. Results – Dimension & Entropy (2)
Number Title Dimension
1 Bach - Cello Suite No. 1 in G major - BWV 1007, Prelude 0.2737
2 Bach - Cello Suite No. 3 in C major - BWV 1009, Courante 0.2728
3 Bach - The Art of Fugue - BWV 1080, Contrapunctus I (2) 0.2703
4 Debussy - Prelude a l'Apres-Midi d'un Faune 0.268
5 McCartney – Michelle 0.2474
6 McCartney - Penny Lane 0.2427
7 Lennon – Julia 0.2328
8 McCartney - Here, There And Everywhere 0.2127
9 Lennon – Girl 0.2075
10 Lennon - Strawberry Fields Forever 0.1757
11 Lennon - Nowhere Man 0.09632
12 Debussy - Clair de lune 0.08722
13 McCartney - Let It Be 0.076
14 Lennon - Across The Universe 0.07342
15 McCartney – Yesterday 0.06015
16 Lennon - Norwegian Wood 0.05774
17 McCartney - In My Life 0.05774
18 Bach - Cello Suite No. 6 in D major - BWV 1012, Courante 0.03714
19 McCartney - And I Love Her 0.03356
5. Results – Dimension & Entropy (3)
Number Title Entropy
1 Bach - Cello Suite No. 3 in C major - BWV 1009, Courante 2.209
2 Debussy - Prelude a l'Apres-Midi d'un Faune 2.207
3 Bach - The Art of Fugue - BWV 1080, Contrapunctus I (2) 2.186
4 Bach - Cello Suite No. 1 in G major - BWV 1007, Prelude 2.163
5 Debussy - Clair de lune 2.16
6 Bach - Cello Suite No. 6 in D major - BWV 1012, Courante 2.098
7 Lennon - Norwegian Wood 2.042
8 McCartney - Here, There And Everywhere 2.029
9 Lennon - Strawberry Fields Forever 1.943
10 McCartney - Yesterday 1.937
11 McCartney - Penny Lane 1.919
12 McCartney - And I Love Her 1.893
13 Lennon - Nowhere Man 1.854
14 Lennon - Girl 1.804
15 McCartney - Michelle 1.803
16 Lennon - Across The Universe 1.793
17 McCartney - In My Life 1.748
18 Lennon - Julia 1.695
19 McCartney - Let It Be 1.601
5. Results – Dimension & Entropy (4)
Composer Bach Debussy Lennon McCartney
Dimension 0.1527 0.1776 0.1406 0.1329
Entropy 2.164 2.184 1.855 1.847
The entropy of impressionist Debussy is higher than that of baroque composer Bach.
Easy-listening pop song has very low entropy It is a SONG. Bach and Debussy’s sample music is orchestra
pieces.
6. Limits (1)
Statistical approach Notes are NOT INDEPENDENT particles.
Complexity Changing key makes entropy higher. Polyphony music is pretty hard…
Dimension It’s not easy that consider other factors (such
as volume, rhythm, etc.)
Various composition goal There are so many genre! (such as rap)
6. Limits (2)
Catching the exact key is not so easy…
Example (McCartney – Yesterday)
7. Conclusion
Statistical approach can give us MOST OBJECTIVE data. So it can be a good music analysis in spite of many limits.Beauty of music is dependent on 1/f (of course!) Tonic, major third, perfect fourth, perfect fifth But they are just NECESSARY condition.
So, what can we do with that methods? Give a quantitative value of certain music Artificial compose
8. Reference
이석원 , 음악심리학 , 심설당 , 1994. Madden, C. "Fractals in Music: Introductory Mathematics for Musical Analysis", High Art Press, 1999.Manaris B., McCormick, C. and Purewal, T. "Can Beautiful Music be Recognized by Computers? Nature, Music, and the Zipf-Mandelbrot Law," Technical Report CoC/CS TR#2002-7-1, March 2002. http://www.midiox.com/ http://www.csw2.co.uk/tech/midi2.htm
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