Mathematics and Music

Question

I have heard that, in recent years, many mathematicians as well as music theorists have applied different branches of mathematics to music.

I would like to know about some books/resources relating to this topic.

Answer 1

You may want to take a look at the book Music: a Mathematical Offering by David J. Benson. It can be downloaded for free in PDF format from the author's homepage.

Answer 2

I would suggest A Geometry of Music by Professor Dmitri Tymoczko at Princeton University. It would also be interesting to read his Science papers (this and this) and their references if you have full-text access.

Answer 3

Rob Schneiderman has an article in the AMS Notices titled "Can One Hear the Sound of a Theorem?"

Answer 4

There is a book entitled "The Topos of Music: Geometric Logic of Concepts, Theory, and Performance" by G. Mazzola. It should be noted that the mathematics used in this book is quite advanced: parts of the musical theory is described by means of differential geometry, algebraic moduli theory and Topos theory. Here's a link.

Answer 5

A couple of books not yet mentioned: Leon Harkleroad, The Math Behind the Music, Cambridge University Press, and David Wright, Mathematics and Music, Volume 28 in the Mathematical World series of the American Mathematical Society. Also, Gareth Loy has a 2-volume set called Musimathics published by the MIT Press. Last and least, I paper I wrote with John Clough, Musical Scales and the Generalized Circle of Fifths, American Mathematical Monthly, Vol. 93, No. 9, Nov., 1986, 695-701.

Answer 6

hopefully will be interesting 12Tones. And Math and Music: Harmonious Connections with high review grade. This book can be downloaded for free Music and Mathematics

Answer 7

The Euclidean Algorithm Generates Traditional Musical Rhythms by Godfried Toussaint

Answer 8

Neo-riemannian theory is a branch of musical analysis which relies heavily on group theory to explain chord progressions, especially among triads. It started with David Lewin's seminal book, "Generalized Musical Intervals and Transformations", and was later enriched by the contributions of Cohn, Douthett, Hook, Hyers, etc.

This presentation is a very nice introduction to this theory.

Julian Hook has developped a nice generalization using an order 288 group of "Uniform Triadic Transformations", UTTs. A sum-up of this work can be found here.

Finally a handbook of Neo-Riemannian theory should be published shortly. I don't know the contents yet but it will probably sum-up everything that has been made in this field for the past thirty years.

Answer 9

Maybe this will lead you somewhere. Mathematics in Music and Mathematics in Music