Tell me more ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
up vote 16 down vote favorite
14

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.

share|improve this question
1  
I am not 100% sure but group theory is used to find the symmetries in the songs of The Beatles. Also, you may find the book Gödel-Escher-Bach interesting. I did not read much, there was a chapter about the symmetries of the fugues of Bach. – Erno Nemecsek Nov 7 '11 at 15:25
2  
There was a paper of Euler's which was "too musical for mathematicians and too mathematical for musicians". You can search for the quote to find out more... – user1729 Nov 7 '11 at 16:41
Traditionally there was the quadrivium of arithmetic, geometry, astronomy and music, leading to ideas like the music of the spheres and Kepler's Harmonices Mundi – Henry Nov 7 '11 at 20:43
This is not a book, but a topic which you might want to research is the role of fractals in music. The researcher Hsu has shown some interesting results. Don't just look for the creation of fractal music (though this is interesting) but look for the fractal structure of already existing music. – analysisj Nov 8 '11 at 23:34

9 Answers

up vote 16 down vote

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.

share|improve this answer
Thanks for the link. – The Chaz 2.0 Nov 7 '11 at 16:26
up vote 8 down vote

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.

share|improve this answer
up vote 7 down vote

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

share|improve this answer
up vote 7 down vote

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.

share|improve this answer
up vote 5 down vote

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.

share|improve this answer
up vote 4 down vote

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

share|improve this answer
up vote 4 down vote

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.

share|improve this answer
And by the way, neo-riemannian theory has nothing to do with riemannian geometry... it was named after Hugo Riemann, a musical theorician of the XIXth century – AlexPof Nov 14 '11 at 22:44

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.