Musimathics, Volume 2, 2e

The Mathematical Foundations of Music

ISBN: 9780262278607 | Copyright 2007

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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.

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From his long and successful experience as a composer and computer-music researcher, Gareth Loy knows what is challenging and what is important. That comprehensiveness makes Musimathics both exciting and enlightening. The book is crystal clear, so that even advanced issues appear simple. Musimathics will be essential for those who want to understand the scientific foundations of music, and for anyone wishing to create or process musical sounds with computers.

Jean-Claude Risset, Laboratoire de Mécanique et d'Acoustique CNRS, France

Volume 1 of Musimathics is the ideal introduction to the science of musical acoustics and composition theory, and volume 2 succeeds as no other tutorial does in making the theory of computer music and digital signal processing accessible to a broad audience. Loy's typically careful treatment leads to a book that combines readability and fun with exhaustive and meticulous coverage of each of the topics he addresses. It can serve equally well as an introduction and as a desk reference for experts.

Stephen Travis Pope CREATE Lab, Department of Music, University of California, Santa Barbara

Music and mathematics enjoy many points of intersection. Just think of musical scales and number theory, or the impact of computers - both analog and digital - on the composition and creation of musical sounds. The second volume of Musimathics ably covers these and many other instances of this happy union: Fourier and wavelet transforms, natural and artificial reverberation, and much more.

Manfred Schroeder Professor of Physics, University of Goettingen
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Contents (pg. vii)
Foreword (pg. xi)
Preface (pg. xiii)
Acknowledgments (pg. xiv)
1 Digital Signals and Sampling (pg. 1)
2 Musical Signals (pg. 49)
3 Spectral Analysis and Synthesis (pg. 103)
4 Convolution (pg. 159)
5 Filtering (pg. 195)
6 Resonance (pg. 263)
7 The Wave Equation (pg. 299)
8 Acoustical Systems (pg. 325)
9 Sound Synthesis (pg. 363)
10 Dynamic Spectra (pg. 453)
Epilogue (pg. 511)
Appendix (pg. 513)
Notes (pg. 533)
Glossary (pg. 539)
References (pg. 543)
Index of Equations and Mathematical Formulas (pg. 547)
Subject Index (pg. 551)
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