musical analysis using statistical methods 20020030 권상일

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

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


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


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


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

musical analysis using statistical methods 20020030 권상일

Documents