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
file(s).
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
