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Tuning, Timbre, Spectrum, Scale / Edition 1

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6.4 Summary In the pursuit of genuinely xenharmonic music that does not sacrifice con­ sonance or depth of timbral material, this chapter presented three concrete examples of related tunings and spectra. The tingshaw bell and the Chaco rock showed how to take the spectrum of an existing sound, draw the disso­ nance curve, find the related scale, and build a playable "instrument." The crystal section showed how to take an arbitrary complex spectrum and to realize it in sound via a related partial-based scale. Despite the odd timbres and scales, the resulting music gives an impres­ sion of tonality or key. It has the surface feeling of tonality, but is unlike 19 anything possible in 12-tet. McLaren comments The Chaco Canyon Rock bounces from one inharmonic "scale mem­ ber" to another, producing an astonishing sense of consonance. The effect isn't identical to traditional tonality-yet it produces many of tonality's effects. One is instantly aware of "right" and "wrong" pitches, and there is a sense of spectral "progression." We call such music xentonal.
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Product Details

  • ISBN-13: 9783540761730
  • Publisher: Springer-Verlag New York, LLC
  • Publication date: 11/26/1997
  • Edition description: BOOK & CD
  • Edition number: 1
  • Pages: 345
  • Product dimensions: 6.09 (w) x 9.17 (h) x 0.94 (d)

Table of Contents

Variables, Abbreviations, Definitions
1 The Octave is Dead... Long Live the Octave 1
2 The Science of Sound 11
3 Musical Scales 49
4 Consonance and Dissonance of Harmonic Sounds 73
5 Related Spectra and Scales 89
6 A Bell, A Rock, A Crystal 123
7 Adaptive Tunings 147
8 The Gamelan 165
9 Consonance-Based Musical Analysis 189
10 From Tuning to Spectrum 211
11 Spectral Mappings 235
12 A "Music Theory" for 10-tet 259
13 Speculation, Correlation, Interpretation, Conclusion 271
App. A Mathematics of Beats 283
App. B Ratios Make Cents 285
App. C Speaking of Spectra 287
App. D Additive Synthesis 297
App. E How to Draw Dissonance Curves 299
App. F Properties of Dissonance Curves 303
App. G Behavior of Adaptive Tunings 309
App. H Tables of Scales 313
App. I Classical Music of Thailand 319
Bibliography 321
Discography 333
Sound Examples 337
Index 341
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