What is Music?: Solving a Scientific Mystery

Cover......Page 1
WHAT IS MUSIC?......Page 2
Copyright......Page 3
Half Title......Page 4
Dedication......Page 5
Contents......Page 7
Acknowledgements......Page 14
1.1.1 The Facts of Life......Page 15
1.1.2 The Mathematics of the Universe......Page 16
1.2 The Science and Mathematics of Music......Page 17
1.3 A First Breakthrough: 2D/3D......Page 18
1.4 A Second Breakthrough: Super-Stimulus......Page 19
1.5.2 The Super-Stimulus Theory......Page 20
1.5.3 Questions, Review and the Future......Page 22
2.1 Music is Something We Like......Page 24
2.2.1 Having More Grandchildren......Page 25
2.2.2 Charles Darwin and His Theory......Page 26
2.3 Explaining Purposeful Behaviour......Page 29
2.3.1 Incorrect or Apparently Incorrect Sub-Goals......Page 31
2.4 Proof of our Ignorance About Music......Page 33
2.4.1 Subjective and Objective......Page 34
2.4.2 The Martian Scientist......Page 35
2.4.3 The Incompleteness of Music Theory......Page 36
2.4.4 Musical Formulae......Page 38
2.4.5 The Economics of Musical Composition......Page 39
2.5 Universality......Page 41
2.6.1 Testability and Falsifiability......Page 44
2.6.2 Simplicity and Complexity......Page 47
3.1 Existing Literature......Page 50
3.2 The Origins of Music......Page 51
3.3 The Archaeology of Music......Page 52
3.4.1 The Evolutionary Assumption......Page 54
3.4.2 The Music Assumption......Page 55
3.4.3 The Communication Hypothesis......Page 56
3.4.4 The Social Assumption......Page 57
3.4.5 The “In the Past” Assumption......Page 58
3.4.7 The Cultural Assumption......Page 59
3.4.8 The Cortical Plasticity Assumption......Page 60
3.4.9 The Simultaneous Pitch Assumption......Page 61
3.4.10 Other Musical Aspect Assumptions......Page 63
3.5 Questions That Have to be Answered......Page 64
4.1.1 Vibrations Travelling Through a Medium......Page 69
4.1.2 Linearity, Frequency and Fourier Analysis......Page 70
4.2.1 Notes......Page 77
4.2.2 Intervals......Page 78
4.2.3 Scales......Page 79
4.2.4 Consonant Intervals......Page 81
4.2.5 Harmony and Chords......Page 82
4.2.6 Home Chords and Dominant Sevenths......Page 83
4.3 Musical Time......Page 84
4.4 Melody......Page 87
4.5.1 Harmonic Accompaniment......Page 89
4.6.1 Repetition......Page 90
4.6.2 Songs, Lyrics and Poetry......Page 91
4.6.3 Dance......Page 92
5.1 Three Different Vector Representations......Page 93
5.1.1 What is a Vector Space?......Page 94
5.1.2 1D Semitones Representation......Page 97
5.1.4 3D Consonant Interval Representation......Page 98
5.2 Bases and Linear Mappings......Page 100
5.2.1 2D to 1D Natural Mapping......Page 101
5.2.3 3D to 2D Natural Mapping......Page 105
5.2.4 Images and Kernels......Page 106
5.2.5 Visualising the Syntonic Comma......Page 109
5.3 The Harmonic Heptagon......Page 111
6.1 An Information Processing System......Page 113
6.1.1 Analogy with Computers......Page 114
6.2 The Neuron......Page 115
6.2.1 Comparison to Computer Components......Page 119
6.2.2 How Many Connections?......Page 120
6.3 Modularity in the Brain......Page 121
6.3.1 The Representation of Meaning......Page 124
6.3.2 Temporal Coding......Page 126
6.3.3 Localisation and Functional Maps......Page 128
6.4 Separation and Binding......Page 129
6.4.1 Colour Perception......Page 130
6.4.2 The Binding Problem......Page 131
6.5 Population Encoding......Page 133
7.1.1 Another Mapping from 2D to 1D......Page 137
7.1.2 Another Perceptual 3D to 2D Mapping......Page 138
7.2 The Looping Theory......Page 140
7.3 Outlook for the 2D/3D Theory......Page 141
8.1 Where is the Purpose?......Page 143
8.2 That Which is Like Music......Page 144
8.3 Corollaries to the Hypothesis......Page 148
8.3.1 What is Musicality?......Page 149
8.3.3 Subjective Awareness of Musicality......Page 150
8.3.4 Double Dissociation......Page 151
8.3.5 Differences in Melody and Rhythm......Page 152
8.3.6 Attributes Apparently Absent in Speech......Page 153
8.4 Explaining Musical Behaviours......Page 154
8.4.1 Dance......Page 156
9.1 Definition of Symmetry......Page 157
9.1.1 Symmetries of Physics......Page 159
9.2.1 Discrete and Continuous......Page 161
9.2.3 Stronger and Weaker Symmetries......Page 162
9.3 Musical Symmetries......Page 163
9.3.1 Pitch Translation Invariance......Page 164
9.3.2 Octave Translation Invariance......Page 166
9.3.3 Octave Translation and Pitch Translation......Page 167
9.3.5 Time Translation Invariance......Page 168
9.3.6 Amplitude Scaling Invariance......Page 169
9.3.7 Pitch Reflection Invariance......Page 170
9.4 Invariant Characterisations......Page 171
9.4.1 Application to Biology......Page 173
9.4.3 Complete and Incomplete Representations......Page 175
10.1 Cortical Plasticity......Page 178
10.1.1 Plasticity and Theories of Music......Page 182
10.2 Musicality in Cortical Maps......Page 183
10.3 The Regular Beat Cortical Map......Page 184
10.3.1 Symmetries of Regular Beat Perception......Page 188
10.4 The Harmonic Cortical Map......Page 189
10.4.3 Intensity Invariance......Page 193
10.5 The Bass Cortical Map......Page 194
10.6 The Scale Cortical Map......Page 195
10.7 The Home Chord Cortical Map......Page 199
10.7.2 Alternative Theory: The Dominant 7th......Page 202
10.7.3 The Evolution of Cortical Maps......Page 203
10.8 The Note Duration Cortical Map......Page 204
10.9 The Melodic Contour Cortical Map......Page 205
11.1 Octave Translation Invariant Aspects of Music......Page 206
11.3 Digital versus Analogue......Page 207
11.4 Digital Representations in the Brain......Page 209
11.5 Split Representation of Pitch......Page 211
11.6 Octaves and Consonant Intervals......Page 215
12.1 A Four-Way Relationship......Page 216
12.2 Making Measurement Accurate......Page 217
12.2.1 Interpolation......Page 219
12.2.3 Arithmetic......Page 220
12.2.4 Not Measuring Non-Harmonic Intervals......Page 221
12.3 Calibration Experiments......Page 223
12.4 Temporal Coding......Page 224
12.5.2 Calibrating Ratios of Durations......Page 225
12.5.3 Calibrating Against Regular Beats......Page 226
13.1 Repetition as a Super-Stimulus......Page 228
13.2 Reasons for Perception of Repetition......Page 230
13.3 Perceptual State Machines......Page 231
13.4 The Flow Model......Page 232
13.4.2 Almost Exact Repetitions......Page 234
13.4.3 Faking n Dimensions in 2-Dimensional Maps......Page 235
13.5 Non-Free Repetition: Summary......Page 237
13.6 Free Repetition and Home Chords......Page 238
13.7 Reduplication......Page 240
14.1 The Story So Far......Page 241
14.2 So What is Musicality?......Page 242
14.2.2 Musicality is an Attribute of Speech......Page 243
14.2.3 The Emotional Effect of Music......Page 244
14.2.4 Different Aspects and Genres......Page 245
14.2.5 Constant Activity Patterns......Page 246
14.3 The Musicality Neuron......Page 248
14.4 Discount Factors......Page 252
14.5 The Meaning of Musicality......Page 254
14.5.1 The Conscious Arousal Hypothesis......Page 255
14.5.2 Arousal, Emotion and Emphasis......Page 258
14.6 Other Cortical Maps......Page 259
14.7 Implication of Identified CAP......Page 260
14.9 Constraints......Page 261
14.9.1 The Implications of Constraint......Page 264
14.10 Compromises and Rule-Breaking......Page 266
14.11 Aspectual Cross-Talk......Page 268
14.12 Music/Speech Specialisation......Page 269
14.12.2 The Implied Importance of Musicality......Page 271
15.1 Questions Answered by the Theory......Page 273
15.2.1 The Effect of Loudness......Page 275
15.2.4 Timbre......Page 276
15.3.1 Brain Studies......Page 280
15.3.3 Constant Activity Patterns......Page 281
15.3.5 Symmetries......Page 282
15.3.8 Musicality......Page 283
15.3.9 Non-Typical Musical Aspects......Page 284
Untitled......Page 285
15.4.3 Variation in Musicality Perception......Page 286
15.4.5 Dependence on Exposure to Music......Page 288
15.4.7 Why Language Makes Little Difference......Page 290
15.5 Intensity/Position Conversion......Page 291
15.6 Choruses and Verses......Page 292
15.7 The Pleasure of Music......Page 294
16.1.1 Information Processing......Page 295
16.1.2 The Importance of Musicality......Page 296
16.1.4 Musicality of Speech......Page 297
16.1.5 Music is a Super-Stimulus......Page 298
16.1.8 Musicality is Not Emotion-Specific......Page 299
16.1.9 Musical Cortical Maps......Page 300
16.1.10 Symmetries......Page 301
16.2.2 Harmonic Map......Page 304
16.2.3 Home Chord Map......Page 305
16.4.1 General Principle of Music......Page 306
16.4.4 Constant Activity Patterns......Page 307
17.1 Music as a Commercial Enterprise......Page 309
17.1.1 Composition Technology......Page 311
17.1.2 Profiting from a Complete Theory......Page 312
17.2 A Post-Music-Theory World......Page 313
17.2.1 Music Junkies?......Page 316
17.2.2 The Future......Page 317
Books......Page 318
Web Sites......Page 319
Index......Page 320