000 06432nam a22003858i 4500
001 CR9780511811722
003 UkCbUP
005 20200124160259.0
006 m|||||o||d||||||||
007 cr||||||||||||
008 101021s2007||||enk o ||1 0|eng|d
020 _a9780511811722 (ebook)
020 _z9780521853873 (hardback)
020 _z9780521619998 (paperback)
040 _aUkCbUP
_beng
_erda
_cUkCbUP
050 0 0 _aML3805
_b.B35 2007
082 0 0 _a781.2
_222
100 1 _aBenson, D. J.
_q(David J.),
_d1955-
_eauthor.
245 1 0 _aMusic :
_ba mathematical offering /
_cDave Benson.
264 1 _aCambridge :
_bCambridge University Press,
_c2007.
300 _a1 online resource (xiii, 411 pages) :
_bdigital, PDF file(s).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
500 _aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 0 _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 0 0 _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 0 0 _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 0 0 _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.
520 _aSince the time of the Ancient Greeks, much has been written about the relation between mathematics and music: from harmony and number theory, to musical patterns and group theory. Benson provides a wealth of information here to enable the teacher, the student, or the interested amateur to understand, at varying levels of technicality, the real interplay between these two ancient disciplines. The story is long as well as broad and involves physics, biology, psycho acoustics, the history of science, and digital technology as well as, of course, mathematics and music. Starting with the structure of the human ear and its relationship with Fourier analysis, the story proceeds via the mathematics of musical instruments to the ideas of consonance and dissonance, and then to scales and temperaments. This is a must-have book if you want to know about the music of the spheres or digital music and many things in between.
650 0 _aMusic
_xAcoustics and physics.
650 0 _aMusic theory
_xMathematics.
776 0 8 _iPrint version:
_z9780521853873
856 4 0 _uhttps://doi.org/10.1017/CBO9780511811722
999 _c520254
_d520252