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Musimathics: The Mathematical Foundations of Music (Volume 2) Paperback – August 19, 2011


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Musimathics: The Mathematical Foundations of Music (Volume 2) + Musimathics: The Mathematical Foundations of Music (Volume 1) + Music and Probability
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Product Details

  • Paperback: 584 pages
  • Publisher: The MIT Press (August 19, 2011)
  • Language: English
  • ISBN-10: 026251656X
  • ISBN-13: 978-0262516563
  • Product Dimensions: 7 x 0.9 x 9 inches
  • Shipping Weight: 11.2 ounces (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (10 customer reviews)
  • Amazon Best Sellers Rank: #399,391 in Books (See Top 100 in Books)

Editorial Reviews

Review

"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

About the Author

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.

Customer Reviews

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If you know someone even vaguely into music and computers, let 'em know that this book exists.
FlockAndField
The first volume of Musicmathics is primarily an intro to the mathematical aspects of music theory, harmonics, scale construction, music perceptions, etc..
tangent
Novices have the possibility to learn the math-based laws of music by means of a non-academic language.
Piermario Calderan

Most Helpful Customer Reviews

28 of 32 people found the following review helpful By calvinnme HALL OF FAMETOP 1000 REVIEWERVINE VOICE on June 13, 2007
Format: Hardcover
If you are to really understand what is going on in this book you need volume one where the foundations are discussed. Likewise, volume one of Musimathics will often stop short of a truly complete explanation and say that further study will be picked up in volume two. Thus, these two volumes are actually just the halves of one book. However, if you are interested in musical signal processing, you probably need to read volume two. It covers much ground in depth, and gives numerous examples that are very practical and accessible for people who are working with musical and audio signals. The appendix has some useful tutorials and tables involving mathematics if you happen to be rusty. The following is the table of contents:

1 Digital Signals and Sampling 1
1.1 Measuring the Ephemeral 1
1.2 Analog-to-Digital Conversion 9
1.3 Aliasing 11
1.4 Digital-to-Analog Conversion 20
1.5 Binary Numbers 22
1.6 Synchronization 28
1.7 Discretization 28
1.8 Precision and Accuracy 29
1.9 Quantization 29
1.10 Noise and Distortion 33
1.11 Information Density of Digital Audio 38
1.12 Codecs 40
1.13 Further Refinements 42
1.14 Cultural Impact of Digital Audio 46

2 Musical Signals 49
2.1 Why Imaginary Numbers? 49
2.2 Operating with Imaginary Numbers 51
2.3 Complex Numbers 52
2.4 de Moivre's Theorem 62
2.5 Euler's Formula 64
2.6 Phasors 68

2.7 Graphing Comlpex Signals 86
2.8 Spectra of Complex Sampled Signals 87
2.9 Multiplying Phasors 89
2.10 Graphing Complex Spectra 92
2.11 Analytic Signals 95

3 Spectral Analysis and Synthesis 103
3.1 Introduction to the Fourier Transform 103
3.2 Discrete Fourier Transform 103
3.
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10 of 10 people found the following review helpful By Let's Compare Options Preptorial TOP 500 REVIEWER on June 17, 2010
Format: Hardcover Verified Purchase
The sad thing about this series is that the keywords that invite readers to stop by, hide the fact that these texts go far beyond music, to USE music as a gentle introduction to extremely complex, relevant and timely math concepts. The best teachers use four paths to explain a math concept: verbal, formulaic, algorithmic and pictographic. These help the brain comprehend the topic regardless of our learning modality. The authors here are simply MASTERFUL math teachers, and clarify everything from Eulers Law (relation of e, the base of the natural logarithms to pi, the base of the trig functions) to Fourier Transforms, in a way that a bright High School student will get. If you've been out of math (any math) for a long time, and want a masterful review of math concepts and techniques, this series is THE place to start. You can then extend that foundation to many other applied areas, from signal processing to physics, voice recognition, etc. Fourier transforms (and their more recent spin off in Cepstrums) are being used in too many fields to list today, from radar and electronic engineering, to whale songs.

In every section, the author's excitement is contagious. Rather than give a bunch of dry proofs that reek of hubris and disregard for the reader, Gareth uses a "curious mind" tone, as if he were just learning and discovering this too, like a kind of puzzle or murder mystery. Loy is Monk, Holmes and Columbo combined. For example, he gives a few expansion series for e, then says: "Wow, there seems to be a striking and beautiful pattern here, doesn't there? Wonder what it can be?" Leave it to a guy into both math and music to see the wonder in a time series!

One more example. Any texts on waveforms have to involve deep calculus, especially PDE's.
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7 of 7 people found the following review helpful By tangent VINE VOICE on December 26, 2009
Format: Hardcover
The first volume of Musicmathics is primarily an intro to the mathematical aspects of music theory, harmonics, scale construction, music perceptions, etc.. The second volume is basically an introduction to Digital Signal Processing (DSP) with discussion of how it applies to music.

My background is in Electrical Engineering so I am well versed in the basic DSP concepts outlined in this book. Gareth Loy has done a fantastic job of 'gently' presenting this material so that even musicians without extensive advanced mathematical training should be able to grasp it. I have seen these concepts presented in a number of different textbooks and this book is far more straightforward than many of the EE signal processing books. Loy goes out of his way to highlight which concepts are the most important and often gives multiple illustrations to highlight the implications of these key concepts. I wish I had this book when I was first learning DSP!

The one complaint I have is that too much attention is given to Fourier techniques and not enough attention paid to Wavelet based methods which are increasingly replacing windowed fourier variants like STFT in many real world applications. However, with the background material presented here the interested reader should be able to quickly grasp the fundamentals of wavelets.

Highly recommended for anyone interested in DSP, music synthesis/analysis, sound modeling, etc..
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2 of 2 people found the following review helpful By FlockAndField on April 17, 2012
Format: Paperback Verified Purchase
The first volume is mind-blowing enough, but this one is more math-heavy and super-cool -- a gripping thriller! Before this book reached my hands, I had no idea such a clear view of mathematics + music was available, and now that this book has turned my world upside-down I find myself studying complex numbers and calculus with renewed fervor. If you know someone even vaguely into music and computers, let 'em know that this book exists.
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