Musimathics: The Mathematical Foundations of Music

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MIT Press, Aug 19, 2011 - Music - 584 pages
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The second volume of a commonsense, self-contained introduction to the mathematics and physics of music, focusing on the digital and computational domain; essential reading for musicians, music engineers, and anyone interested in the intersection of art and science.

Volume 2 of Musimathics continues the story of music engineering begun in Volume 1, focusing on the digital and computational domain. Loy goes deeper into the mathematics of music and sound, beginning with digital audio, sampling, and binary numbers, as well as complex numbers and how they simplify representation of musical signals. Chapters cover the Fourier transform, convolution, filtering, resonance, the wave equation, acoustical systems, sound synthesis, the short-time Fourier transform, and the wavelet transform. These subjects provide the theoretical underpinnings of today's music technology. The examples given are all practical problems in music and audio.

Additional material can be found at http://www.musimathics.com.

 

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Contents

1 Digital Signals and Sampling
1
2 Musical Signals
49
3 Spectral Analysis and Synthesis
103
4 Convolution
159
5 Filtering
195
6 Resonance
263
7 The Wave Equation
299
8 Acoustical Systems
325
10 Dynamic Spectra
453
Epilogue
511
Appendix
513
Notes
533
Glossary
539
References
543
Index of Equations and Mathematical Formulas
547
Subject Index
551

9 Sound Synthesis
363

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About the author (2011)

Gareth Loy is a musician and award-winning composer. He has published widely and, during a long and successful career at the cutting edge of multimedia computing, has worked as a researcher, lecturer, programmer, software architect, and digital systems engineer. He is President of Gareth, Inc., a provider of software engineering and consulting services internationally.

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