# Review: The Math behind the Music

Leon Harkleroad (2006).

*The Math Behind the Music*. Cambridge University Press. ISBN 0-521-81095-7. A book on math and music, with such an ugly cover... how not to look like a nerd with all that... whatever... the book was really good and not that nerdy anyway ! In the fact, the first interesting feature is that the author wrote the book for non-mathematician and non-musician. Well, I guess you have to be interested a little bit in one or the other to read it, but it's true: you don't need to know any mathematical stuff and the only required musical concept is about the most basic structure of musical scores. Second interesting feature: within 130 pages, the reader is taken on an impressive tour of musical and mathematical concepts. Within the world of music:- pitch, tone, timber and attack
- tunes (with the various historical tuning systems)
- composing (and most especially varying a theme)
- bell playing (where I first learned about the sophisticated art of
*change ringing*) - composing with computers (with the famous Xenakis )
- melodic patterns (asking the question: what makes a tune interesting for its listeners)

- frequency analysis to define a pitch (with the famous Fourier)
- transient phases to define the attack
- group theory (( ex: groups of (theme) variations or groups of permutations ))
- probabilities
- fractals
- L-systems

*tour de force*but there's more: explanatory figures abound and a CD with musical samples comes with the whole ! The most impressive feat however is that the author manages to guide his readers through the discovery of various mathematical properties, avoiding anything that could come close to mathematical jargon (which is sometimes mentioned in specific frames). At the end of the day, the only piece of criticism I have would be about*what's not in the book*. I can easily imagine that the analysis of each musical concept could dig a little deeper, and that the deductions coming from their mathematical interpretation could lead us to some more "discoveries". Last but not least, the book concludes itself on two "recreative" chapters: the penultimate is about graphical representation of music and the very last is a "worst of" musical experiments conducted with only maths in mind.