Sold Out
Book Categories |
Preface xi
Acknowledgements xiii
Introduction 1
Waves and harmonics 5
What is sound? 5
The human ear 7
Limitations of the ear 13
Why sine waves? 17
Harmonic motion 18
Vibrating strings 19
Sine waves and frequency spectrum 21
Trigonometric identities and beats 23
Superposition 26
Damped harmonic motion 28
Resonance 31
Fourier theory 36
Introduction 37
Fourier coefficients 38
Even and odd functions 44
Conditions for convergence 46
The Gibbs phenomenon 50
Complex coefficients 54
Proof of Fejer's theorem 55
Bessel functions 58
Properties of Bessel functions 61
Bessel's equation and power series 63
Fourier series for FM, feedback and planetary motion 68
Pulse streams 71
The Fourier transform 73
Proof of the inversion formula 77
Spectrum 80
The Poisson summation formula 81
The Dirac delta function 82
Convolution 86
Cepstrum 88
The Hilbert transform and instantaneous frequency 89
A mathematician's guide to the orchestra 91
Introduction 91
The wave equation for strings 92
Initial conditions 100
The bowed string 103
Wind instruments 107
The drum 112
Eigenvalues of the Laplace operator 117
The horn 120
Xylophones and tubular bells 122
Thembira 130
The gong 133
The bell 138
Acoustics 142
Consonance and dissonance 144
Harmonics 144
Simple integer ratios 145
History of consonance and dissonance 148
Critical bandwidth 151
Complex tones 152
Artificial spectra 153
Combination tones 155
Musical paradoxes 158
Scales and temperaments: the fivefold way 161
Introduction 162
Pythagorean scale 162
The cycle of fifths 164
Cents 165
Just intonation 167
Major and minor 168
The dominant seventh 170
Commas and schismas 171
Eitz's notation 172
Examples of just scales 174
Classical harmony 181
Meantone scale 185
Irregular temperaments 189
Equal temperament 198
Historical remarks 202
More scales and temperaments 210
Harry Partch's 43 tone and other just scales 210
Continued fractions 214
Fifty-three tone scale 223
Other equal tempered scales 227
Thirty-one tone scale 228
The scales of Wendy Carlos 231
The Bohlen-Pierce scale 233
Unison vectors and periodicity blocks 237
Septimal harmony 242
Digital music 245
Digital signals 245
Dithering 247
WAV and MP3 files 248
MIDI 251
Delta functions and sampling 251
Nyquist's theorem 254
The z-transform 256
Digital filters 257
The discrete Fourier transform 261
The fast Fourier transform 263
Synthesis 265
Introduction 265
Envelopes and LFOs 266
Additive synthesis / 268
Physical modelling 270
The Karplus-Strong algorithm 273
Filter analysis for the Karplus-Strong algorithm 275
Amplitude and frequency modulation 276
The Yamaha DX7 and FM synthesis 280
Feedback, or self-modulation 287
CSound 291
FM synthesis using CSound 298
Simple FM instruments 300
Further techniques in CSound 304
Other methods of synthesis 308
The phase vocoder 309
Chebyshev polynomials 309
Symmetry in music 312
Symmetries 312
The harp of the Nzakara 322
Sets and groups 324
Change ringing 329
Cayley's theorem 331
Clock arithmetic and octave equivalence 333
Generators 335
Tone rows 337
Cartesian products 339
Dihedral groups 340
Orbits and cosets 342
Normal subgroups and quotients 343
Burnside's lemma 345
Pitch class sets 348
Polya's enumeration theorem 353
The Mathieu group M12 358
Bessel functions 361
Equal tempered scales 365
Frequency and MIDI chart 367
Intervals 368
Just, equal and meantone scales compared 372
Music theory 374
Recordings 381
References 386
Bibliography 389
Index 393
Login|Complaints|Blog|Games|Digital Media|Souls|Obituary|Contact Us|FAQ
CAN'T FIND WHAT YOU'RE LOOKING FOR? CLICK HERE!!! X
You must be logged in to add to WishlistX
This item is in your Wish ListX
This item is in your CollectionMusic: A Mathematical Offering
X
This Item is in Your InventoryMusic: A Mathematical Offering
X
You must be logged in to review the productsX
X
X
Add Music: A Mathematical Offering, , Music: A Mathematical Offering to the inventory that you are selling on WonderClubX
X
Add Music: A Mathematical Offering, , Music: A Mathematical Offering to your collection on WonderClub |