CONTENTS
Prelude = xi
Acknowledgements = xv
Variables, Abbreviations, Definitions = xvii
1. The Octave is Dead... Long Live the Octave = 1
1.1 A Challenge = 1
1.2 A Dissonance Meter = 3
1.3 New Perspectives = 5
1.4 Overview = 8
2. The Science of Sound = 11
2.1 What is Sound? = 11
2.2 Spectrum and Timbre = 13
2.3 Frequency and Pitch = 32
2.4 Pairs of Sines = 37
2.5 Summary = 46
2.6 For Further Investigation = 47
3. Musical Scales = 49
3.1 Why Use Scales? = 49
3.2 Pythagoras and the Spiral of Fifths = 50
3.3 Equal Temperaments = 54
3.4 Just Intonations = 58
3.5 Partch = 61
3.6 Meantone and Well Temperaments = 61
3.7 Overtone Scales = 65
3.8 Real Tunings = 67
3.9 Gamelan Tunings = 68
3.10 My Tuning Is Better Than Yours = 69
3.11 A Better Scale? = 70
4. Consonance and Dissonance of Harmonic Sounds = 73
4.1 A Brief History = 73
4.2 Explanations of Consonance and Dissonance = 76
4.3 Harmonic Dissonance Curves = 80
4.4 A Simple Experiment = 87
4.5 Summary = 88
4.6 For Further Investigation = 88
5. Related Spectra and Scales = 89
5.1 Dissonance Curves and Spectrum = 89
5.2 Drawing Dissonance Curves = 91
5.3 A Consonant Tritone = 93
5.4 Past Explorations = 96
5.5 Found Sounds = 104
5.6 Properties of Dissonance Curves = 112
5.7 Dissonance Curves for Multiple Spectra = 117
5.8 Dissonance "Surfaces" = 119
5.9 Summary = 122
6. A Bell, A Rock, A Crystal = 123
6.1 Tingshaw : A Simple Bell = 123
6.2 Chaco Canyon Rock = 131
6.3 Sounds of Crystals = 137
6.4 Summary = 145
7. Adaptive Tunings = 147
7.1 Fixed vs. Variable Scales = 147
7.2 Algorithm Statement = 148
7.3 Behavior of the Algorithm = 150
7.4 The Sound of Adaptive Tunings = 159
7.5 Implementations and Variations = 162
7.6 Summary = 163
8. The Gamelan = 165
8.1 A Living Tradition = 165
8.2 An Unwitting Ethnomusicologist = 167
8.3 The Instruments = 168
8.4 Tuning the Gamelan = 178
8.5 Spectrum and Tuning = 183
8.6 Summary = 187
9. Consonance-Based Musical Analysis = 189
9.1 A Dissonance "Score" = 189
9.2 Reconstruction of Historical Tunings = 200
9.3 What's Wrong With This Picture? = 209
10. From Tuning to Spectrum = 211
10.1 Looking for Spectra = 211
10.2 Spectrum Selection as an Optimization Problem = 211
10.3 Spectra for Equal Temperaments = 213
10.4 Solving the Optimization Problem = 218
10.5 Spectra for Simple Scales = 221
10.6 Summary = 232
11. Spectral Mappings = 235
11.1 The Goal : Life-like Nonharmonic Sounds = 235
11.2 Mappings Between Spectra = 237
11.3 Examples = 245
11.4 Discussion = 251
11.5 Summary = 256
12. A "Music Theory" for 10-tet = 259
12.1 What is 10-tet? = 259
12.2 10-tet Keyboard = 260
12.3 Spectra for 10-tet = 261
12.4 10-tet Chords = 263
12.5 10-tet Scales = 268
12.6 A Progression = 269
12.7 Summary = 270
13. Speculation, Correlation, Interpretation, Conclusion = 271
13.1 The Zen of Xentonality = 271
13.2 Coevolution of Tunings and Instruments = 272
13.3 To Boldly Listen = 274
13.4 New Musical Instruments? = 276
13.5 Silence Hath No Beats = 278
13.6 Coda = 279
Appendix A. Mathematics of Beats = 283
Appendix B. Ratios Make Cents = 285
Appendix C. Speaking of Spectra = 287
C.1 Spectrum of a Sine Wave = 288
C.2 Steady State Analysis = 291
C.3 Analysis of the Attack = 293
C.4 Pads and Windows = 294
C.5 Finding Spectral Peaks = 295
Appendix D. Additive Synthesis = 297
Appendix E. How to Draw Dissonance Curves = 299
Appendix F. Properties of Dissonance Curves = 303
Appendix G. Behavior of Adaptive Tunings = 309
Appendix H. Tables of Scales = 313
Appendix I. Classical Music of Thailand = 319
Bibliography = 321
Discography = 333
Sound Examples = 337
Index = 341
