Connectionist Representations of Tonal Music

Discovering Musical Patterns by Interpreting Artifical Neural Networks

Ebook

Connectionist Representations of Tonal Music

Previously, artificial neural networks have been used to capture only the informal properties of music. However, cognitive scientist Michael Dawson found that by training artificial neural networks to make basic judgments concerning tonal music, such as identifying the tonic of a scale or the quality of a musical chord, the networks revealed formal musical properties that differ dramatically from those typically presented in music theory. For example, where Western music theory identifies twelve distinct notes or pitch-classes, trained artificial neural networks treat notes as if they belong to only three or four pitch-classes, a wildly different interpretation of the components of tonal music.

Intended to introduce readers to the use of artificial neural networks in the study of music, this volume contains numerous case studies and research findings that address problems related to identifying scales, keys, classifying musical chords, and learning jazz chord progressions. A detailed analysis of the internal structure of trained networks could yield important contributions to the field of music cognition.

Table of Contents

Table of Contents
Cover 1
Half Title 2
Title 4
Copyright 5
Contents 6
List of Figures 10
List of Tables 14
Acknowledgements 16
Overture: Alien Music 20
Chapter 1: Science, Music, and Cognitivism 26
1.1 Mechanical Philosophy, Mathematics, and Music 26
1.2 Mechanical Philosophy and Tuning 27
1.3 Psychophysics of Music 30
1.4 From Rationalism to Classical Cognitive Science 32
1.5 Musical Cognitivism 34
1.6 Summary 43
Chapter 2: Artificial Neural Networks and Music 46
2.1 Some Connectionist Basics 46
2.2 Romanticism and Connectionism 53
2.3 Against Connectionist Romanticism 55
2.4 The Value Unit Architecture 59
2.5 Summary and Implications 62
Chapter 3: The Scale Tonic Perceptron 66
3.1 Pitch-Class Representations of Scales 66
3.2 Identifying the Tonics of Musical Scales 73
3.3 Interpreting the Scale Tonic Perceptron 75
3.4 Summary and Implications 83
Chapter 4: The Scale Mode Network 86
4.1 The Multilayer Perceptron 86
4.2 Identifying Scale Mode 89
4.3 Interpreting the Scale Mode Network 91
4.4 Tritone Imbalance and Key Mode 96
4.5 Further Network Analysis 97
4.6 Summary and Implications 106
Chapter 5: Networks for Key-Finding 108
5.1 Key-Finding 108
5.2 Key-Finding with Multilayered Perceptrons 110
5.3 Interpreting the Network 112
5.4 Coarse Codes for Key-Finding 115
5.5 Key-Finding with Perceptrons 121
5.6 Network Interpretation 129
5.7 Summary and Implications 132
6.1 Four Types of Triads 136
Chapter 6: Classifying Chords with Strange Circles 136
6.2 Triad Classification Networks 138
6.3 Interval Cycles and Strange Circles 145
6.4 Added Note Tetrachords 160
6.5 Classifying Tetrachords 163
6.6 Interpreting the Tetrachord Network 165
6.7 Summary and Implications 182
Chapter 7: Classifying Extended Tetrachords 186
7.1 Extended Tetrachords 186
7.2 Classifying Extended Tetrachords 190
7.3 Interpreting the Extended Tetrachord Network 192
7.4 Bands and Coarse Coding 217
7.5 Summary and Implications 223
Chapter 8: Jazz Progression Networks 226
8.1 The ii-V-I Progression 226
8.2 The Importance of Encodings 229
8.3 Four Encodings of the ii-V-I Problem 230
8.4 Complexity, Encoding, and Training Time 236
8.5 Interpreting a Pitch-class Perceptron 239
8.6 The Coltrane Changes 249
8.7 Learning the Coltrane Changes 254
8.8 Interpreting a Coltrane Perceptron 257
8.9 Strange Circles and Coltrane Changes 261
8.10 Summary and Implications 265
Chapter 9: Connectionist Reflections 268
9.1 A Less Romantic Connectionism 268
9.2 Synthetic Psychology of Music 271
9.3 Musical Implications 278
9.4 Implications for Musical Cognition 284
9.5 Future Directions 288
References 290
F 310
E 310
D 310
C 310
B 310
A 310
Index 310
R 311
P 311
O 311
N 311
M 311
L 311
K 311
J 311
I 311
H 311
G 311
S 312
T 312
V 312
W 312