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Musimathics. The Mathematical Foundations of Music, Vol. 1

by Gareth Loy
The MIT Press, Cambridge, MA, 2006
608 pp., illus. 263 b/w. Trade, $50
ISBN: 0-262-12282-0.

Reviewed by Stefaan Van Ryssen
Hogeschool Gent
Jan Delvinlaan 115, 9000 Gent, Belgium


There are numerous books on the mathematical foundations of music, and most of them follow more or less the same line: from the early musing of the Greek mathematicians who tried to explain the scale in terms of ratio's between integers, through the physical aspects of music (frequency, duration, loudness, timbre) and the basics of organology or the way artifacts are made to sound to the perception of music. Musimathics is no exception to this — except maybe that from time to time the author lets something of his personal life shimmer through the otherwise dry and almost monotonous text. (I liked his story of a test he did with the pitch of a wine bottle.)

What makes this book exceptional, however, is the attempt Loy makes to gradually build a mathematical, or rather algorithmical foundation of composition. Using a programming language of his own conception, and giving numerous examples of pieces of code, he turns the activity of composing upside down and inside out. He shows how underlying rules and structures are implicit in any composer’s work (here of course using Western models and assumptions, but the exercise could be done for any musical tradition) and how choice, aesthetics and the desire to please, distract, shock or infuriate overlay these basic foundations. Divine inspiration lies on top of a lot of concrete layers.

There are, however, some questions to be answered. I am sure Loy has good reasons to think that a lengthy treatment of the historical evolution of the theory of harmony and scales from the Greeks through medieval times till the 'well tempered' keyboard has some relevance for composers today, but I for my part am not convinced it does. It might be interesting for encyclopaedic purposes, but is it really necessary to use more then 50 pages to go through all this? Wouldn't it have been enough to outline the problem, describe the most important historical solutions, and treat some of the most interesting ones (like Harry Partch's system) a bit more in depth?

A second problem I have is with his treatment of the physical aspects of music. A lot of pages are spent on basic physical concepts and laws. Sure enough, it is necessary to know what they are if one wants to understand how instruments work and what acoustics is all about. But as soon as things get really interesting and maths and physics are getting really important, Loy skips the issue and refers to the second volume "where we will further develop this in detail". It is very frustrating for the reader to take on a cartload of theoretical baggage and, then, having to wait to use it just when the fun begins… in the next volume.

In the same vein, Loy's treatment of the algorithmic underpinnings of composition is very promising. But where does it all lead? Lengthy digressions on neural networks or referencing systems in computer programs may be unavoidable, but at least one would like to know what the ultimate goal would be.

To sum it up: There is something for everyone in this book. It is clear and well written at times, with humour and insight, but it is only one of a pair of legs. As a devoted biped I certainly hope the second volume will be published soon; otherwise, the foundations of music are prone to topple over.



Updated 1st May 2007

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