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Musimathics: The Mathematical Foundations of Music (Volume 1) 1st Ed Edition

4.5 out of 5 stars 17 customer reviews
ISBN-13: 978-0262122825
ISBN-10: 0262122820
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Due Date: May 29, 2016 Rental Details
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Editorial Reviews


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)

Musimathics is destined to be required reading and a valued reference for every composer, music researcher, multimedia engineer, and anyone else interested in the interplay between acoustics and music theory. This is truly a landmark work of scholarship and pedagogy, and Gareth Loy presents it with quite remarkable rigor and humor.

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

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.

Product Details

  • Hardcover: 504 pages
  • Publisher: The MIT Press; 1st Ed edition (June 16, 2006)
  • Language: English
  • ISBN-10: 0262122820
  • ISBN-13: 978-0262122825
  • Product Dimensions: 7 x 0.8 x 9 inches
  • Shipping Weight: 2.1 pounds
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (17 customer reviews)
  • Amazon Best Sellers Rank: #1,405,409 in Books (See Top 100 in Books)

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Customer Reviews

Top Customer Reviews

Format: Hardcover Verified Purchase
After about a ten year hiatus on books of this type being published, this is one of several new books combining mathematics, music, and programming aimed at musicians who want to know more about the math behind their musical compositions and are not content to just know what drop-down windows to click on using the latest musical software. The book starts with the basics of music and sound and works up to basic music theory, physics and sound, and acoustics and psychoacoustics. The final chapter of the book is the most interesting, since it concerns mathematics and composition techniques using the author's C++ based library "Musimat". Both this book and Musimat have companion websites, although the Musimat site is the most interesting with plenty of downloads in case you are interested in how to use this compositional library. There is a volume two scheduled for release in Spring 2007 that gets into signal processing, the role of digital signals, and the wave equation, so together they are a very complete treatise on math, music, and programming aimed at the musical composer. I highly recommend it. Of course, if you want to dig deep into individual subjects such as acoustics and psychoacoustics, you are going to need additional references. But this text is clear enough to get you started. The following is the table of contents:

1 Music and Sound 1

1.1 Basic Properties of Sound 1

1.2 Waves 3

1.3 Summary 9

2 Representing Music 11

2.1 Notation 11

2.2 Tones, Notes, and Scores 12

2.3 Pitch 13

2.4 Scales 16

2.5 Interval Sonorities 18

2.6 Onset and Duration 26

2.7 Musical Loudness 27

2.8 Timbre 28

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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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Music and mathematics are not quite synonymous, in spite of what the ancient Greeks asserted. This book however convinces the reader that music is a close approximation of mathematics, and vice versa, and that a purely mathematical formulation of music is possible, this formalism encompassing all conceivable compositional techniques and able to capture completely the aural sensibility of any composer. Whatever their background, the author has done an excellent job of presenting to readers the role that mathematics can play in musical theory. Best of all, one need not even have a background in music to understand the book, since the author presents this background as the text proceeds.

Indeed in chapters 1-3 the author gives a detailed overview of basic music theory, including scales, equal-tempered intervals, and tempering. For non-musicians, such as this reviewer, there is much to absorb, but the author's presentation is lucid enough as to make the material easy to digest and remember. The most amazing thing that is brought out from the study of these chapters is the relative paucity of scales compared to what could be obtained from the entire range of human hearing. The most interesting discussion from a mathematical standpoint is that of the use of recursion and continued fractions in fret calculations.

The most interesting chapter of the book is the one on composition and methodology, for it is here that the author touches on the subject of automated musical composition. Markov chains, Petri nets, neural networks, fractal geometry, genetic programming, and predicate transition nets are all discussed in terms of their efficacy in generating musical compositions that emulate a particular composer's musical style and their creative musical ability.
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