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| Benson D. — Mathematics and music |
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| Предметный указатель |
Eclipse, ecliptic 200
Editors, sound 356
Effect, Mozart 362
Effective length 99
Effects unit 241
Eigenfunction 108 408
Eigenvalue stripping 412
Eigenvalues 107 108 407
Eitz's notation 156 213 329 330
Eitz, Carl (1848—1924) 0
Elasticity, longitudinal 114
Electric guitar 82
Electroencephalogram 9
Electromagnetic wave 2
Electronic music xi
Electronic Musician (magazine) xii 275 276
Electrophones 82
Elektra (Strauss) 280
Element 290
Elementary divisors 308
Eleventh harmonic 365
Elliptic orbit 59
Ellis, Alexander J. (1814—1890) 150 180 363
Elmore and Heald 425
End correction 99
Energy 406
Energy, density 68
Energy, potential 403
Enharmonic genus 182
Enharmonic notes 149
Ensoniq 358
entropy 227
Enumeration theorem, Polya's 314
Envelope 239 241 266 276
Epimoric 349
Epimorphism 297
Equal beating temperament 176
Equal temperament 173 179 193 363 372
Equal temperament, Cordier's, for piano 181
Equation, auxiliary 22
Equation, Bessel's 55
Equation, differential 13 14 54
Equation, Laplace's 398
Equation, partial differential 61 83 102 395 422
Equation, quadratic 22 199
Equation, Sturm — Liouville 110
Equation, wave 82 97 395 422
Equation, Webster's horn 110
Equilibrium position 14
EQUIVALENCE 217
Equivalence, octave 134 215 298
Equivalence, pitch class sets 311
Erlangen monochord 158
Erlich, Paul xii 192 214 219
Error, mean square 39 171
Escape (diesis) 155
Escher, Ascending and descending 144
Escher, Maurits Cornelius (1898—1972) 0
ethnomusicology 81
Euclid (ca. 330—275 B.C.) 0
Euclid's Algorithm 148 201 300
Euler phi function 301 316
Euler — Bernoulli beam equation 115
Euler's continued fraction for e 196
Euler's formula for eie 346
Euler's joke 233
Euler's monochord 162 218
Euler, Leonhard (1707—1783) 30 39
Even function 36
exercises, answers to 322
Expansion, Laurent 58
Exponential exp (CSound) 274
Exponential function exp(a;) 369
Exponential function, complex 45 346
Exponential interpolation 270
Extension 114
Extraduction 320
Fagius, Hans (1951— ) 178 390
Farey, John (1766—1826) 180
Fast Fourier Transform 237 274
Faux Bourdon 183
Fay, R. 9
Feedback 59 257
Fejer kernel 47
Fejer, Lipot (1880—1959) 39
Fenestra rotunda 5
Fibonacci (= Leonardo of Pisa, ca. 1180—1250) series 199
Fichet, Laurent 425
Fifteenth harmonic 365
Fifth Cordier's equal temperament 181
Fifth harmonic 152 364
Fifth, perfect 135 139 205 373
Fifths, circle/cycle of 148 149 301
Fifths, sequence of s 147
Fifths, spiral of s 149
Fifty-three tone scale 202
Filter 76 240
Filter, band pass 138
Filter, digital 76 233
Filter, low pass 224 231
Finale (software) 358
Finalis 377
Finality 166
Finite group 414
First isomorphism theorem 308
Fish, proving the existence of 70
Fisk organ, Wellesley 172
Fixed point 292
Flare parameter 111
Flat, double 149
Fletcher and Rossing 425
Fletcher-Munson curves 11 227
Flute 81 97 259
FM, instruments in CSound 269
FM, radio 248
FM, synthesis xi 51 59 250 252 261 267 344 422
FMusic (freeware) 361
Focus of ellipse 59
Focusing of sound 3
Fogliano's monochord 159
Fogliano, Lodovico (late 1400s—ca. 1539) 0
Fokker, AdriaanD. (1887—1972) 207 215
Folk music 165 360
Folk music, British 183
Foote, Edward (piano technician) 392
Force, shearing 113
Forced harmonic motion 25
FORM 303
Formants 77
FORMAT chunk 226
Formula, Cauchy's integral 58
Formula, double angle 19
Formula, Gauss' 396
Forte, Allen 311 425
Forty-Eight Preludes and Fugues (J.S. Bach) 173
Forty-three tone scale 189
Four group, Klein 304
Fourier coefficients 30 33
Fourier coefficients, bounded 41
Fourier coefficients, rapid decay of 41
Fourier series 16 29 49
Fourier transform 63
Fourier transform of  65
Fourier transform of a distribution 74
Fourier, Jean Baptiste Joseph, Baron de (1768—1830) 30
Fourth, perfect 139 146 152 182
frac (CSound) 274
Fractal music xii
Fractal Tune Smithy (free / shareware) 361
Fractal waveform 39
| Fractions 193
Fractions, continued 193 196 208 379 426
Fractions, partial 200 236
FractMus (freeware) 361
Frazer, J. 146
Frederick the Great 282
Fredholm alternative 401
Fredholm operator 401
Fredholm, Erik Ivar (1866—1927) 0
French horn 81 383
French Revolution 31
frequency 2 134 136 141
Frequency, chart 355
Frequency, cochlea 6
Frequency, collision 1
Frequency, combination tone 142
Frequency, combined 19
Frequency, Hertz 8
Frequency, instantaneous 78
Frequency, limit of discrimination 12
Frequency, missing fundamental 143
Frequency, modulation 248 384
Frequency, multiples of fundamental 30
Frequency, nominal 106
Frequency, Nyquist 230
Frequency, octave 15
Frequency, piano strings 19
Frequency, ratio 150
Frequency, resonant 13 27 28
Frequency, sine wave 16 17
Frequency, spectrum 10 69
Frequency, standard 17
Frick, Arthur 435
Friction 22 40
Frieze patterns 285
Fripertinger, Harald 386
Frobenius reciprocity 417
Frobenius, Ferdinand Georg (1849—1917) 0
Froberger, Johann Jakob (1616—1667) 178 393 394
Front page, CSound 357
ftp.ucsd.edu 358
Fubini solutions 61
Fubini, Eugene (1913—1997) 0
Fubini, Guido (1879—1943) 61
Function 296
Function,  64
Function,  399
Function, arctan 196
Function, Bessel 49—58 253 336 433
Function, complementary 25
Function, cosine 16
Function, Dirac delta 71 228
Function, Euler's phi 301 316
Function, even 36
Function, exponential 346 369
Function, generalized 73
Function, Green's 398
Function, Heaviside 75
Function, hyperbolic 347
Function, inverse 292 297
Function, kernel 74 401
Function, logarithm 150 363 368
Function, periodic 30 32 137
Function, rational 235
Function, sampling 228
Function, sawtooth 39 40 42
Function, sine 16
Function, square wave 33 39 42 61 240
Function, tangent 196
Function, test 73
Function, transfer 234
Function, triangular 41
Function, Weber 56
Fundamental 133 139
Fundamental domain 215
Fundamental theorem of calculus 368
Fundamental, missing 2 106 143
Furia and Scacciaferro 425
Gaffurius, Franchinus (1451—1522) 135 386
Galilei pitch and frequency 136
Galilei's principle 1
Galilei, Galileo (1564—1642) 0
gamelan 133 187
Gamma scale (Carlos) 211 364
Garland and Kahn 425
Gas 1
Gaudi (Rich) 393
Gauss' formula 396
Gauss, Johann Carl Friedrich (1777—1855) 49 198 199
Gaussian integers 201
GEN05 (CSound) 270
GEN07 (CSound) 267
GEN10 (CSound) 264
General linear group 415
Generalized function 73
Generalized keyboard harmonium 202
Generators for a group 299
Generators for a sublattice 217
Genevois and Orlarey 425
Genus 182
Geometric series 49
Geometry 136
Germain, Sophie (1776—1831) 122
Gestalt 428
Gibbs phenomenon 35 41
Gibbs, Josiah Willard (1839—1903) 0
Gibelius' monochord 170
Gilbert and Sullivan 29
Gitangi 289
Glareanus 378
Glide reflection 282
Global variables (CSound) 266
GNU 359
Gold and Morgan 425
Goldberg Variation 25 (J. S. Bach) 359
Golden ratio 196 199 260
Goldwave (shareware) 357
Gong 122 133
Gordon, Webb and Wolpert 109
Gotze and Wille 425
Gouk, Penelope 426
Gourd 120
Graff, Karl 426
Grains 276
Granular synthesis 261 276 432
graphicx xii
Gray's Anatomy 3
Great diesis 155 170 364
Greatest common divisor 148 300
Greek music 182
Greek scales 182
Green's function 398
Green's theorem 396
Green, George (1793—1841) 0
Griffith and Todd 426
Group 279 290 429
Group, abelian 291
Group, alternating 316
Group, cyclic 300
Group, dihedral 304
Group, finite 414
Group, general linear 415
Group, infinite cyclic 279
Group, infinite dihedral 284
Group, Klein four 304
Group, Mathieu,  319
Group, permutation 293
Group, simple 320
Group, sporadic 320
Group, symmetric 293
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