Mathematics and Music

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.

Solution 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 this page of author's homepage.

Solution 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.

Solution 3:

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.

Solution 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.

Solution 5:

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