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© in This Web Service Cambridge University Cambridge University Press 978-0-521-61999-8 - Music: A Mathematical Offering Dave Benson Index More information Index Bold page numbers indicate a main entry. = 1 2π θ θ θ am π 0 cos(m ) f ( )d ,40 amplifier, 14, 268 AAC, 250 response, 53 Aaron, Pietro (ca. 1480–1550) amplitude, 6, 7, 17, 25, 26, 27 meantone temperament, 186 instantaneous, 90 abelian group, 325 modulation, 276 abs (CSound), 307 peak, 21, 25 absolute RMS, 25 integrability, 74 AMSLATEX, xiii value, 49 analogue acceleration, 19 modelling synthesizer, 71 acoustic signal, 245 law, Ohm’s, 11 synthesizer, 71, 268, 385 pressure, 107, 119, 142 angular velocity ω = 2πν, 21, 33 acoustics, 117, 137, 142 animals, hearing range of, 13 nonlinear, 71 antanairesis, 163 additive synthesis, 268 anvil, 8 ADSR envelope, 266 apical, 9 adufe, 117 apotom¯e, Pythagorean, 164, 181, 369 Aeolian, 379 approximation aeolsklavier, 91 rational, 214–223 aerophones, 91 Archytas of Tarentum (428–365 bce), 203 Africa, 131 arctan function, 218 Agamemnon, 313 area Agricola, Martin (1486–1556) density, 112, 133 monochord, 175 in polar coordinates, 75 AIFF sound file, 249, 291 Aristotle (384–322 bce), 4 air, 5 Aristoxenus (ca. 364–304 bce), 208 bulk modulus, 108, 142 arithmetic, clock, 333 algorithm Aron, see Aaron DX7, 285, 288 artifacts, 255 Euclid’s, 163, 223, 336 Ascending and Descending (Escher), 158 inductive, 215 ascending node, 222 Karplus–Strong, 273, 291 ascii, 292, 295 aliasing, 254 associative law, 87, 325 alpha scale (Carlos), 207, 232, astronomy, 147, 148 369 atonal music, 205, 348 alternating group, 355 attack, 266 aluminium, 129 AU sound file, 249 Alves, Bill, 381 auditory canal, 7 AM radio, 276 augmented triad, 342 amplification, 258 aulos, 171 393 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-61999-8 - Music: A Mathematical Offering Dave Benson Index More information 394 Index auricle, 7 Berg, Alban (1885–1935), 320, 348 authentic mode, 379 Bernoulli, Daniel (1700–1782), 37, 126 auxiliary equation, 28 solution of wave equation, 98 AVI movie file, 248 Bessel, F. W. (1784–1846) equation, 64 = 1 2π θ θ θ function, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, bm π 0 sin(m ) f ( )d ,40 Babbitt, Milton, 348 69, 282, 361 Bach, J. S. (1685–1750) computation of, 363 Italian Concerto, etc. (Rousset), 198, 381 graph of, 60 Jesu, der du meine Seele, 184 hyperbolic, 134 Musical Offering, 314 Neumann’s, 65 Organ Music (Fagius), 198, 381 power series for, 65 Partitia no. 5, Gigue, 183 zeros of, 114, 361 Toccata and Fugue in D, 312 horn, 121 Toccata in F minor, 192 beta scale (Carlos), 207, 232, 369 Well Tempered Clavier, 189 Bewitched, The (Partch), 385 Bach, P. D. Q. (1807–1742)?, 322, 360 Biber, Heinrich Ignaz Franz von (1644–1704), 381 Badings, Henk, 229 bifurcation, 288 bagel, 226 bijective function, 332 bagpipe tuning, 212 binary representation, 245 balafon, 91 birnd (CSound), 307 balance, 8 Blackwood, Easley (1933–), 228, 381 Balinese gamelan, 207 Blake, William (1757–1827), 319 bamboo marimba (Partch), 210 blend factor, 274 band pass filter, 151 block bandwidth, 35 diagram (DX7), 282 critical, 150, 151 periodicity, 237, 240, 344 Barca, Alessandro, 194 Bˆocher, Maxime (1867–1918), 53 Barker, Andrew, 208 Boethius, Anicius Manlius Severinus Barlow, Clarence, 228, 381 (ca. 480–524 ce), 171 Barnes, John, 196 Bohlen–Pierce scale, 162, 233, 368 baroque music, 181 Bologna State Museum, 230 Bart´ok, B´ela (1881–1945) Bombelli, Rafael (1526–1572), 215 Fifth String Quartet, 312 Boo I (Partch), 210 Music for Strings, Percussion and Celeste, 319 Bosanquet, Robert H. M. (1841–1912), 224 basal end of cochlea, 9 bottle, plucked, 275 base of natural logarithms, 218 Boulanger, Nadia (1887–1979), 233 basilar membrane, 9, 19, 151 Boulanger, Richard Charles (1956–), 236, 308 basis for a lattice, 238 boundary conditions, 96 bass bowed string, 49, 103 clef, 367, 375 parabolic envelope, 104 singer, 15 BP intervals, 234, 235 bassoon, 304 BP-just scale, 235 baud rate, MIDI, 251 brass, 120, 288 bc -l, 364 brightness, 268 beam equation, Euler–Bernoulli, 126 Brombaugh, John (organ builder), 189 beat, dead, 29 Brouncker, William (1620–1684), 218 beats, 23, 200, 368 Brown, Colin, 180 Beauty in the Beast (Carlos), 207 brown noise, 81 Beethoven, Ludwig van (1770–1827), 205, 312, 384 Brownian motion, 47, 81 B´ek´esy, Georg von (1899–1972), 11 Brun, Viggo (1885–1978), 223 bel (= 10 dB), 14 bulk modulus, 108, 142 bell, 138 bullroarer, 91 (FM & CSound), 300 Burnside, William (1852–1927) change ringing, 329 lemma, 345, 356 Chinese, 139 Buxtehude, Dietrich (ca. 1637–1707), 382 tubular, 122 Byrd, William (1543–1623), 188, 321, 382 Bendeler, P. (1654–1709) temperaments, 192 C1 function, 47 bending moment, 124 C++ Benedetti, Giovanni Battista (1530–1590), 171 Bessel calculator, 363 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-61999-8 - Music: A Mathematical Offering Dave Benson Index More information Index 395 C programming language, 291 Chowning, John, 278 calculus Chowning, Maureen, 236 vector, 118 chromatic calm temperaments, 199 genus, 203 Calvin and Hobbes, scale, 207 campanology, 329 church modes, medieval, 379 canal circle of fifths, 164, 337 auditory, 7 circular motion, 26 semicircular, 8 circulating temperament, 189 Cancrizans, 314 clarinet, 15, 41, 91, 110, 234, 289, 304 canon classes, pitch, 300, 334 retrograde/crab, 314 classical harmony, 181 capacitor, 277 clef, 367, 374 cards, shuffling, 359 clipping, 292 Carlos, Wendy (1939–), 207, 212, 231, 369, 382 clock arithmetic, 333 Carpenter, Charles, 237, 383 closed carrier frequency, 277 bounded region, 118 carry feature (CSound), 299 interval, 47, 50 Carter, Elliott, 348 tube, 108 Cartesian cochlea, 8, 13, 19 product, 339 collision frequency, 5 cascade modulation, 285 coloratura soprano, 236 Cataldi, P. A. (1548–1623), 215 colour, 4, 146 cathode ray tube, 53 columnella, 9 Cauchy, Augustin Louis (1789–1857) combination tone, 155 integral formula, 67 comma, 163, 164, 166, 168, 171, 172, 181 principal value, 74 BP 7/3, 235, 369 Caus, Salomon de (ca. 1576–1626) ditonic, 163 monochord, 175 notation (superscript), 172 causality, 87 of Didymus, 168 cello, 186 ordinary, 168 centroid, 125 Ptolemaic, 168 cents, 16, 166, 369 Pythagorean, 163, 166, 190, 201, 223, 225, 369 cepstrum, 88 scale of, 226 Ces`aro, Ernesto (1859–1906) septimal, 171, 369 sum, 47, 51, 55 syntonic, 168, 369, 377 chain commutative ossicular, 8 law, 87, 325 rule, multivariable, 96 ring, 355 Chalmers, John (1940–), 212 compact disc, 245 Chambonni`eres, Jacques Champion de Alves, 214, 381 (ca. 1601–1672), 383, 385 Bach/Christophe Rousset, 198, 381 change ringing, 329 Bach/Hans Fagius, 198, 381 Chao Jung-Tze, 217 Between the Keys, 228, 381 chaos, 47, 288, 291 Biber, 188, 381 character theory, 261, 337 Blackwood, 228, 381 Chaw, Ousainou, 103 Buxtehude, 382 Chebyshev, Pafnuti L. (1821–1894) Byrd, 321, 382 polynomials, 309 Carlos, 207, 214, 382 chimaeric sounds, 90 Carpenter, 237, 383 Chinese Chambonni`eres, 188, 383 bells, 139 Chapman, 189, 383 L¨u scale, 211 Chemillier, 324, 383 Chladni, Ernst F. F. (1756–1827) Computer Music Journal, 381 drawings, 137 Cook, 237, 383 patterns, 115 d’Anglebert, 189, 383 Chopin, Fr´ed´eric Fran¸cois (1810–1849), 205, 384 Froberger, 189 Etude´ , Op. 25 No. 10, 338 Harrison, 198, 214, 383 Waltz, Op. 34 No. 2, 314 Harvey, 384 chordophones, 91 Haverstick, 228, 384 chorus, 251, 268 Haydn, 321, 384 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-61999-8 - Music: A Mathematical Offering Dave Benson Index More information 396 Index compact disc (cont.) cos, cosh, cosinv (CSound), 307 Houtsma, Rossing & Wagenaars, 160, 384 coset, 239, 342 Johnson, 384 representatives, 237, 343 Katahn/Foote, 189, 198, 384 counting problems, 353 Lagac´e, Wellesley organ, 189, 384 Couperin, Fran¸cois (1668–1733), 198, 385 Machaut/Hilliard Ensemble, 165, 322, 384 Couperin, Louis (1626–1661), 385 Mathews & Pierce, 237, 384 coupled oscillators, 222 Microtonal Works, 384 crab canon, 314 Parmentier, 189, 385 critical bandwidth, 150, 151 Partch, 214, 385 critically damped system, 30 Rich, 214, 385 crystallography, 318 Sethares, 155, 385 Cscore, 307 Tomita/Mussorgsky, 266, 385 CSound, 291, 381 Winkelman, 189, 198, 385 AV, 308 Xentonality (Sethares), 228, 385 The CSound book, 308 complementary function, 32 curvature, radius of, 125 completeness, 119 cycle complex per second, 13 analysis, 67 index, 354 exponential, 54 notation, 327 numbers, 33, 54, 223 of fifths, 164 Composers Recordings Inc., 385 cyclic group, 312, 335 compression, data, 249 Cygwin, 364 concert hall acoustics, 142 cylinder of thirds and fifths, 186 concert pitch, 21 cymbal, 13, 91, 137 concertina, 204 conch shell, 91 d’Alembert, Jean-le-Rond (1717–1783), 37, 94, 143 concha, 7 d’Anglebert, Jean-Henri (1635–1691), 383, 385 configuration, 353 damped harmonic motion, 17, 28 counting series, 355 DAT, 245 congruence, 334 data conical tube, 110 compression, 249 conjunction of tetrachords, 202 transmission, MIDI, 251 consonance, 144, 146, 148 DATA chunk, 249 continued fractions, 214, 219, 230 dB, 14 for e, 218 dB SPL, 14 / for log2(3 2), 223 dBA, 14 / / / for log2(3 2) log2(5 4), 232 dead beat, 29 / for log3(7 3), 234 Debussy, Claude (1862–1918) for √π, 216 Reverieˆ , 320 for 2, 222 decay, 266 periodic, 222 of Fourier coefficients, 50 continued subtraction, 163 stretching, 275 continuous decibels, 14 dependence on initial conditions, 102 deciem (bell), 138 function, 46 delay, 257, 268, 271, 273 nowhere differentiable, 47 t, time between samples, 251 piecewise, 50 δ(t), Dirac delta function, 82, 251 control rate (CSound), 292 δs(t), sampling function, 252 convergence density, 93, 112, 124, 133 mean square, 48 derivative, 46 pointwise, 51, 53 partial, 92 uniform, 40, 42, 51, 53 descending node, 222 convergents, 217, 234 determinant, 239 convex drums, 120 Deutsch, Diana, 159 convolution, 86, 259 diaschisma, 171, 174, 369 convolve, 86 diatonic Cooley and Tukey, 263, 264 genus, 203 coordinates, polar, 75, 80, 113 syntonic scale, 202 Cordier, Serge, 201 Didymus ho mousicos (1st c.
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