LEADER 00000nam a22003738i 4500 
001    CR9780511811722 
003    UkCbUP 
005    20151005020621.0 
006    m|||||o||d|||||||| 
007    cr|||||||||||| 
008    101021s2007||||enk     o     ||1 0|eng|d 
020    9780511811722|q(ebook) 
020    |z9780521853873|q(hardback) 
020    |z9780521619998|q(paperback) 
040    UkCbUP|beng|erda|cUkCbUP 
050 00 ML3805|b.B35 2007 
082 00 781.2|222 
100 1  Benson, D. J.|q(David J.),|d1955- 
245 10 Music :|ba mathematical offering /|cDave Benson. 
264  1 Cambridge :|bCambridge University Press,|c2007. 
300    1 online resource (xiii, 411 pages) :|bdigital, PDF 
336    text|btxt|2rdacontent 
337    computer|bc|2rdamedia 
338    online resource|bcr|2rdacarrier 
500    Title from publisher's bibliographic system (viewed on 05 
       Oct 2015). 
505 00 |gPreface --|gAcknowledgements --|gIntroduction --|g1.
       |tWaves and harmonics --|g1.1.|tWhat is sound? --|g1.2.
       |tThe human ear --|g1.3.|tLimitations of the ear --|g1.4.
       |tWhy sine waves? --|g1.5.|tHarmonic motion --|g1.6.
       |tVibrating strings --|g1.7.|tSine waves and frequency 
       spectrum --|g1.8.|tTrigonometric identities and beats --
       |g1.9.|tSuperposition --|g1.10.|tDamped harmonic motion --
       |g1.11.|tResonance --|g2.|tFourier theory --|g2.1.
       |tIntroduction --|g2.2.|tFourier coefficients --|g2.3.
       |tEven and odd unctions --|g2.4.|tConditions for 
       convergence --|g2.5.|tThe Gibbs phenomenon --|g2.6.
       |tComplex coefficients --|g2.7.|tProof of Fejér's theorem 
       --|g2.8.|tBessel functions --|g2.9.|tProperties of Bessel 
       functions --|g2.10.|tBessel's equation and power series --
       |g1.11.|tFourier series for FM feedback and planetary 
       motion --|g2.12.|tPulse streams --|g2.13.|tThe Fourier 
       transform --|g2.14.|tProof of the inversion formula --
       |g2.15.|tSpectrum --|g2.16.|tThe Poisson summation formula
       --|g2.17.|tThe Dirac delta function --|g2.18.|tConvolution
       --|g2.19.|tCepstrum --|g2.20.|tThe Hilbert transform and 
       instantaneous frequency --|g3.|tA mathematician's guide to
       the orchestra --|g3.1.|tIntroduction --|g3.2.|tThe wave 
       equation for strings --|g3.3.|tInitial conditions --|g3.4.
       |tThe bowed string --|g3.5.|tWind instruments --|g3.6.
       |tThe drum --|g3.7.|tEigenvalues of the Laplace operator -
       -|g3.8.|tThe horn --|g3.9.|tXylophones and tubular bells -
       -|g3.10.|tThe mbira --|g3.11.|tThe gong --|g3.12.|tThe 
       bell --|g3.13.|tAcoustics. 
505 00 |g9.|tSymmetry in music --|g9.1.|tSymmetries --|g9.2.|tThe
       harp of the Nzakara --|g9.3.|tSets and groups --|g9.4.
       |tChange ringing --|g9.5.|tCayley's theorem --|g9.6.
       |tClock arithmetic and octave equivalence --|g9.7.
       |tGenerators --|g9.8.|tTone rows --|g9.9.|tCartesian 
       products --|g9.10.|tDihedral groups --|g9.11.|tOrbits and 
       cosets --|g9.12.|tNormal subgroups and quotients --|g9.13.
       |tBurnside's lemma --|g9.14.|tPitch class sets --|g9.15.
       |tPólya's enumeration theorem --|g9.16.|tThe Mathieu group
       M₁₂ --|tAppendix A : Bessel functions --|tAppendix B : 
       Equal tempered scales --|tAppendix C : Frequency and MIDI 
       chart --|tAppendix D : Intervals --|tAppendix E : Just, 
       equal and meantone scales compared --|tAppendix F : Music 
       theory --|tAppendix G : Recordings --|gReferences --
       |gBibliography --|gIndex. 
505 00 |g7.|tDigital music --|g7.1.|tDigital signals --|g7.2.
       |tDithering --|g7.3.|tWAV and MP3 files --|g7.4.|tMIDI --
       |g7.5.|tDelta functions and sampling --|g7.6.|tNyquist's 
       theorem --|g7.7.|tThe z-transform --|g7.8.|tDigital 
       filters --|g7.9.|tThe discrete Fourier transform --|g7.10.
       |tThe fast Fourier transform --|g8.|tSynthesis --|g8.1.
       |tIntroduction --|g8.2.|tEnvelopes and LFOs --|g8.3.
       |tAdditive synthesis --|g8.4.|tPhysical modelling --|g8.5.
       |tThe Karplus-Strong algorithm --|g8.6.|tFilter analysis 
       for the Karplus-Strong algorithm --|g8.7.|tAmplitude and 
       frequency modulation --|g8.8.|tThe Yamaha DX7 and FM 
       synthesis --|g8.9.|tFeedback, or self-modulation --|g8.10.
       |tCSound --|g8.11.|tFM synthesis using CSound --|g8.12.
       |tSimple FM instruments --|g8.13.|tFurther techniques in 
       CSound --|g8.14.|tOther methods of synthesis --|g8.15.
       |tThe phase vocoder --|g8.16.|tChebyshev polynomials. 
505 00 |g4.|tConsonance and dissonance --|g4.1.|tHarmonics --
       |g4.2.|tSimple integer rations --|g4.3.|tHistory of 
       consonance and dissonance --|g4.4.|tCritical bandwidth --
       |g4.5.|tComplex tones --|g4.6.|tArtificial spectra --
       |g4.7.|tCombination tones --|g4.8.|tMusical paradoxes --
       |g5.|tScales and temperaments : the fivefold way --|g5.1.
       |tIntroduction --|g5.2.|tPythagorean scale --|g5.3.|tThe 
       cycle of fifths --|g5.4.|tCents --|g5.5.|tJust intonation-
       -|g5.6.|tMajor and minor --|g5.7.|tThe dominant seventh --
       |g5.8.|tCommas and schismas --|g5.9.|tEitz's notation --
       |g5.10.|tExamples of just scales --|g5.11.|tClassical 
       harmony --|g5.12.|tMeantone scale --|g5.13.|tIrregular 
       temperaments --|g5.14.|tEqual temperament --|g5.15.
       |tHistorical remarks --|g6.|tMore scales and temperaments 
       --|g6.1.|tHarry Partch's 43 tone and other just scales --
       |g6.2.|tContinued fractions --|g6.3.|tFifty-three tempered
       scales --|g6.5.|tThirty-one tone scale --|g6.6.|tThe 
       scales of Wendy Carlos --|g6.7.|tThe Bohlen-Pierce scale -
       -|g6.8.|tUnion vectors and periodicity blocks --|g6.9.
       |tSeptimal harmony. 
506 1  Unlimited number of concurrent users.|5UkHlHU 
650  0 Music|xAcoustics and physics. 
650  0 Music theory|xMathematics. 
856 40 |uhttps://doi.org/10.1017/CBO9780511811722|zGo to eBook 
936    Camb-E-2018/19