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003 OCoLC;

005 20141212054527.0;

008 050629m20062007maua b 001 0 eng ;

010 a| 2005051090;

019 a| 70893995;

020 a| 9780262122825 (v. 1 : alk. paper);

020 a| 0262122820 (v. 1 : alk. paper);

020 a| 9780262122856 (v. 2 : alk. paper);

020 a| 0262122855 (v. 2 : alk. paper);

035 a| (Sirsi) o60856240;

035 a| (OCoLC)60856240;

042 a| pcc;

049 a| EREM;

050 00 a| ML3805b| .L78 2006;

050 4 a| QA19 M87L69 2006;

082 00 a| 781.22| 22;

100 1 a| Loy, D. Gareth.=| ^A294929;

245 10 a| Musimathics :b| the mathematical foundations of music /c| Gareth Loy.;

300 a| 2 volumes :b| illustrations ;c| 24 cm;

336 a| text2| rdacontent;

337 a| unmediated2| rdamedia;

338 a| volume2| rdacarrier;

504 a| Includes bibliographical references and indexes.;

505 0 a| v. 1. Music and sound -- Representing music -- Musical scales, tuning, and intonation -- Physical basis of sound -- Geometrical basis of sound -- Psychophysical basis of sound -- Introduction to acoustics -- Vibrating systems -- Composition and methodology -- v. 2. Digital signals and sampling -- Musical signals -- Spectral analysis and synthesis -- Convolution -- Filtering -- Resonance -- The wave equation -- Acoustical systems -- Sound synthesis -- Dynamic spectra.;

505 0 a| v. 1. Music and sound. Basic properties of sound ; Waves ; Summary -- Representing music. Notation ; Tones, notes, and scores ; Pitch ; Scales ; Interval sonorities ; Onset and duration ; Musical loudness ; Timbre ; Summary -- Musical scales, tuning, and intonation. Equal-tempered intervals ; Equal-tempered scale ; Just intervals and scales ; The Cent scale ; A taxonomy of scales ; Do scales come from timbre or proportion? ; Harmonic proportion ; Pythagorean diatonic scale ; The problem of transposing just scales ; Consonance of intervals ; The powers of the fifth and the octave do not form a closed system ; Designing useful scales requires compromise ; Tempered tuning systems ; Microtonality ; Rule of 18 ; Deconstructing tonal harmony ; Deconstructing the octave ; The prospects for alternative tunings ; Summary -- Physical basis of sound. Distance ; Dimension ; Time ; Mass ; Density ; Displacement ; Speed ; Velocity ; Instantaneous velocity ; Acceleration ; Relating displacement, velocity, acceleration, and time ; Newton's laws of motion ; Types of force ; Work and energy ; Internal and external forces ; The work-energy theorem ; Conservative and nonconservative forces ; Power ; Power of vibrating systems ; Wave propagation ; Amplitude and pressure ; Intensity ; Inverse square law ; Measuring sound intensity ; Summary -- Geometrical basis of sound. Circular motion and simple harmonic motion ; Rotational motion ; Projection of circular motion ; Constructing a sinusoid ; Energy of waveforms ; Summary -- Psychophysical basis of sound. Signaling systems ; The ear ; Psychoacoustics and psychophysics ; Pitch ; Loudness ; Frequency domain masking ; Beats ; Combination tones ; Critical bands ; Duration ; Consonance and dissonance ; Localization ; Externalization ; Timbre ; Summary -- Introduction to acoustics. Sound and signal ; A simple transmission model ; How vibrations travel in air ; Speed of sound ; Pressure waves ; Sound radiation models ; Superposition and interference ; Reflection ; Refraction ; Absorption ; Diffraction ; Doppler effect ; Room acoustics ; Summary -- Vibrating systems. Simple harmonic motion revisited ; Frequency of vibrating systems ; Some simple vibrating systems ; The harmonic oscillator ; Modes of vibration ; A taxonomy of vibrating systems ; One-dimensional vibrating systems ; Two-dimensional vibrating elements ; Resonance (continued) ; Transiently driven vibrating systems ; Summary -- Composition and methodology. Guido's method ; Methodology and composition ; MUSIMAT: a simple programming language for music ; Program for Guido's method ; Other music representation systems ; Delegating choice ; Randomness ; Chaos and determinism ; Combinatorics ; Atonality ; Composing functions ; Traversing and manipulating musical materials ; Stochastic techniques ; Probability ; Information theory and the mathematics of expectation ; Music, information, and expectation ; Form in unpredictability ; Monte Carlo methods ; Markov chains ; Causality and composition ; Learning ; Music and connectionism ; Representing musical knowledge ; Next-generation Musikalische Wurfelspiel ; Calculating beauty -- Appendix A. Exponents ; Logarithms ; Series and summations ; About trigonometry ; Xeno's paradox ; Modulo arithmetic and congruence ; Whence 0.161 in Sabine's equation? ; Excerpts from Pope John XXII's Bull regarding church music ; Greek alphabet -- Appendix B. MUSIMAT ; Music datatypes in MUSIMAT ; Unicode (ASCII) character codes ; Operator associativity and precedence in MUSIMAT.;

505 0 a| v. 2. Foreword / by John Chowning -- Digital signals and sampling. Measuring the ephemeral ; Analog-to-digital conversion ; Aliasing ; Digital-to-analog conversion ; Binary numbers ; Synchronization ; Discretization ; Precision and accuracy ; Quantization ; Noise and distortion ; Information density of digital audio ; Codecs ; Further refinements ; Cultural impact of digital audio ; Summary -- Musical signals. Why imaginary numbers? ; Operating with imaginary numbers ; Complex numbers ; De Moivre's theorem ; Euler's formula ; Phasors ; Graphing complex signals ; Spectra of complex sampled signals ; Multiplying phasors ; Graphing complex spectra ; Analytic signals ; Summary -- Spectral analysis and synthesis. Introduction to the Fourier transform ; Discrete Fourier transform ; Discrete Fourier transform in action ; Inverse discrete Fourier transform ; Analyzing real-world signals ; Windowing ; Fast Fourier transform ; Properties of the discrete Fourier transform ; A practical Hilbert transform ; Summary -- Convolution. Rolling shutter camera ; Defining convolution ; Numerical examples of convolution ; Convolving spectra ; Convolving signals ; Convolution and the Fourier transform ; Domain symmetry between signals and spectra ; Convolution and sampling theory ; Convolution and windowing ; Correlation functions ; Summary -- Filtering. Tape recorder as a model of filtering ; Introduction to filtering ; A sample filter ; Finding the frequency response ; Linearity and time invariance of filters ; FIR filters ; IIR filters ; Canonical filters ; Time domain behavior of filters ; Filtering as convolution ; Z transform ; Z transform of the general difference equation ; Filter families -- Resonance. The derivative ; Differential equations ; Mathematics of resonance ; Summary -- The wave equation. One-dimensional wave equation and string motion ; An example ; Modeling vibration with finite difference equations ; Striking points, plucking points, and spectra ; Summary -- Acoustical systems. Dissipation and radiation ; Acoustical current ; Linearity of frictional force ; Inertance, inductive reactance ; Compliance, capacitive reactance ; Reactance and alternating current ; Capacitive reactance and frequency ; Inductive reactance and frequency ; Combining resistance, reactance, and alternating current ; Resistance and alternating current ; Capacitance and alternating current ; Acoustical impedance ; Sound propagation and sound transmission ; Input impedance: fingerprinting a resonance system ; Scattering junctions ; Summary -- Sound synthesis. Forms of synthesis ; A graphical patch language for synthesis ; Amplitude modulation ; Frequency modulation ; Vocal synthesis ; Synthesizing concert hall acoustics ; Physical modeling ; Source models and receiver models ; Summary -- Dynamic spectra. Gabor's elementary signal ; Short-time Fourier transform ; Phase vocoder ; Improving on the Fourier transform ; Psychoacoustic audio encoding ; Summary -- Appendix. About algebra ; About trigonometry ; Series and summations ; Trigonometric identities ; Modulo arithmetic and congruence ; Finite difference approximations ; Walsh-Hadamard transform ; Sampling, reconstruction, and the sinc function ; Fourier shift theorem ; Spectral effects of ring modulation ; Derivation of the reflection coefficient.;

650 0 a| Musicx| Acoustics and physics.=| ^A16688;

650 0 a| Musicx| Mathematics.=| ^A876782;

650 0 a| Computer sound processing.=| ^A15942;

949 a| ML3805.L78 2006v| v. 2h| JMUSIC53i| 30372014409585o| jnln;

994 a| C0b| ERE;

596 a| 3;

998 a| 2386145;

999 a| ML3805 .L78 2006 V. 2w| LCc| 1i| 30372014479585d| 7/17/2014f| 4/25/2024g| 3l| MSTm| JMUSICr| Ys| Yt| MGESBKu| 12/17/2010x| BOOKz| MCIRCo| .STAFF. jnln; enhanced 12/14/23 -jjab;

999 a| ML3805 .L78 2006 V. 1w| LCc| 1i| 30372014481383d| 7/17/2014e| 6/6/2011f| 4/25/2024g| 4l| MSTm| JMUSICq| 1r| Ys| Yt| MGESBKu| 6/6/2011x| BOOKz| MCIRCo| .STAFF. jnln; enhanced 12/14/23 -jjab;

Musimathics : the mathematical foundations of music / Gareth Loy.

Author/creator	Loy, D. Gareth
Format	Book
Publication Info	Cambridge, MA ; London : MIT Press, ©2006-2007.
Description	2 volumes : illustrations ; 24 cm
Subjects	Music--Acoustics and physics. Music--Mathematics. Computer sound processing.

Contents	v. 1. Music and sound -- Representing music -- Musical scales, tuning, and intonation -- Physical basis of sound -- Geometrical basis of sound -- Psychophysical basis of sound -- Introduction to acoustics -- Vibrating systems -- Composition and methodology -- v. 2. Digital signals and sampling -- Musical signals -- Spectral analysis and synthesis -- Convolution -- Filtering -- Resonance -- The wave equation -- Acoustical systems -- Sound synthesis -- Dynamic spectra.
Contents	v. 1. Music and sound. Basic properties of sound ; Waves ; Summary -- Representing music. Notation ; Tones, notes, and scores ; Pitch ; Scales ; Interval sonorities ; Onset and duration ; Musical loudness ; Timbre ; Summary -- Musical scales, tuning, and intonation. Equal-tempered intervals ; Equal-tempered scale ; Just intervals and scales ; The Cent scale ; A taxonomy of scales ; Do scales come from timbre or proportion? ; Harmonic proportion ; Pythagorean diatonic scale ; The problem of transposing just scales ; Consonance of intervals ; The powers of the fifth and the octave do not form a closed system ; Designing useful scales requires compromise ; Tempered tuning systems ; Microtonality ; Rule of 18 ; Deconstructing tonal harmony ; Deconstructing the octave ; The prospects for alternative tunings ; Summary -- Physical basis of sound. Distance ; Dimension ; Time ; Mass ; Density ; Displacement ; Speed ; Velocity ; Instantaneous velocity ; Acceleration ; Relating displacement, velocity, acceleration, and time ; Newton's laws of motion ; Types of force ; Work and energy ; Internal and external forces ; The work-energy theorem ; Conservative and nonconservative forces ; Power ; Power of vibrating systems ; Wave propagation ; Amplitude and pressure ; Intensity ; Inverse square law ; Measuring sound intensity ; Summary -- Geometrical basis of sound. Circular motion and simple harmonic motion ; Rotational motion ; Projection of circular motion ; Constructing a sinusoid ; Energy of waveforms ; Summary -- Psychophysical basis of sound. Signaling systems ; The ear ; Psychoacoustics and psychophysics ; Pitch ; Loudness ; Frequency domain masking ; Beats ; Combination tones ; Critical bands ; Duration ; Consonance and dissonance ; Localization ; Externalization ; Timbre ; Summary -- Introduction to acoustics. Sound and signal ; A simple transmission model ; How vibrations travel in air ; Speed of sound ; Pressure waves ; Sound radiation models ; Superposition and interference ; Reflection ; Refraction ; Absorption ; Diffraction ; Doppler effect ; Room acoustics ; Summary -- Vibrating systems. Simple harmonic motion revisited ; Frequency of vibrating systems ; Some simple vibrating systems ; The harmonic oscillator ; Modes of vibration ; A taxonomy of vibrating systems ; One-dimensional vibrating systems ; Two-dimensional vibrating elements ; Resonance (continued) ; Transiently driven vibrating systems ; Summary -- Composition and methodology. Guido's method ; Methodology and composition ; MUSIMAT: a simple programming language for music ; Program for Guido's method ; Other music representation systems ; Delegating choice ; Randomness ; Chaos and determinism ; Combinatorics ; Atonality ; Composing functions ; Traversing and manipulating musical materials ; Stochastic techniques ; Probability ; Information theory and the mathematics of expectation ; Music, information, and expectation ; Form in unpredictability ; Monte Carlo methods ; Markov chains ; Causality and composition ; Learning ; Music and connectionism ; Representing musical knowledge ; Next-generation Musikalische Wurfelspiel ; Calculating beauty -- Appendix A. Exponents ; Logarithms ; Series and summations ; About trigonometry ; Xeno's paradox ; Modulo arithmetic and congruence ; Whence 0.161 in Sabine's equation? ; Excerpts from Pope John XXII's Bull regarding church music ; Greek alphabet -- Appendix B. MUSIMAT ; Music datatypes in MUSIMAT ; Unicode (ASCII) character codes ; Operator associativity and precedence in MUSIMAT.
Contents	v. 2. Foreword / by John Chowning -- Digital signals and sampling. Measuring the ephemeral ; Analog-to-digital conversion ; Aliasing ; Digital-to-analog conversion ; Binary numbers ; Synchronization ; Discretization ; Precision and accuracy ; Quantization ; Noise and distortion ; Information density of digital audio ; Codecs ; Further refinements ; Cultural impact of digital audio ; Summary -- Musical signals. Why imaginary numbers? ; Operating with imaginary numbers ; Complex numbers ; De Moivre's theorem ; Euler's formula ; Phasors ; Graphing complex signals ; Spectra of complex sampled signals ; Multiplying phasors ; Graphing complex spectra ; Analytic signals ; Summary -- Spectral analysis and synthesis. Introduction to the Fourier transform ; Discrete Fourier transform ; Discrete Fourier transform in action ; Inverse discrete Fourier transform ; Analyzing real-world signals ; Windowing ; Fast Fourier transform ; Properties of the discrete Fourier transform ; A practical Hilbert transform ; Summary -- Convolution. Rolling shutter camera ; Defining convolution ; Numerical examples of convolution ; Convolving spectra ; Convolving signals ; Convolution and the Fourier transform ; Domain symmetry between signals and spectra ; Convolution and sampling theory ; Convolution and windowing ; Correlation functions ; Summary -- Filtering. Tape recorder as a model of filtering ; Introduction to filtering ; A sample filter ; Finding the frequency response ; Linearity and time invariance of filters ; FIR filters ; IIR filters ; Canonical filters ; Time domain behavior of filters ; Filtering as convolution ; Z transform ; Z transform of the general difference equation ; Filter families -- Resonance. The derivative ; Differential equations ; Mathematics of resonance ; Summary -- The wave equation. One-dimensional wave equation and string motion ; An example ; Modeling vibration with finite difference equations ; Striking points, plucking points, and spectra ; Summary -- Acoustical systems. Dissipation and radiation ; Acoustical current ; Linearity of frictional force ; Inertance, inductive reactance ; Compliance, capacitive reactance ; Reactance and alternating current ; Capacitive reactance and frequency ; Inductive reactance and frequency ; Combining resistance, reactance, and alternating current ; Resistance and alternating current ; Capacitance and alternating current ; Acoustical impedance ; Sound propagation and sound transmission ; Input impedance: fingerprinting a resonance system ; Scattering junctions ; Summary -- Sound synthesis. Forms of synthesis ; A graphical patch language for synthesis ; Amplitude modulation ; Frequency modulation ; Vocal synthesis ; Synthesizing concert hall acoustics ; Physical modeling ; Source models and receiver models ; Summary -- Dynamic spectra. Gabor's elementary signal ; Short-time Fourier transform ; Phase vocoder ; Improving on the Fourier transform ; Psychoacoustic audio encoding ; Summary -- Appendix. About algebra ; About trigonometry ; Series and summations ; Trigonometric identities ; Modulo arithmetic and congruence ; Finite difference approximations ; Walsh-Hadamard transform ; Sampling, reconstruction, and the sinc function ; Fourier shift theorem ; Spectral effects of ring modulation ; Derivation of the reflection coefficient.
Bibliography note	Includes bibliographical references and indexes.
LCCN	2005051090
ISBN	9780262122825 (v. 1 : alk. paper)
ISBN	0262122820 (v. 1 : alk. paper)
ISBN	9780262122856 (v. 2 : alk. paper)
ISBN	0262122855 (v. 2 : alk. paper)

Musimathics : the mathematical foundations of music / Gareth Loy.

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