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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.

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    $\begingroup$ 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. $\endgroup$ – Karatuğ Ozan Bircan Nov 7 '11 at 15:25
  • $\begingroup$ Music and Mathematics: From Pythagoras to Fractals $\endgroup$ – Peđa Terzić Nov 7 '11 at 15:53
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    $\begingroup$ 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... $\endgroup$ – user1729 Nov 7 '11 at 16:41
  • $\begingroup$ 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 $\endgroup$ – Henry Nov 7 '11 at 20:43
  • $\begingroup$ 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. $\endgroup$ – analysisj Nov 8 '11 at 23:34

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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.

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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.

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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.

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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.

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

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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

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The Euclidean Algorithm Generates Traditional Musical Rhythms by Godfried Toussaint

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

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Gödel, Escher, Bach: An Eternal Golden Braid, by Douglas Hofstadter

Not exactly direct, but the he looks at ideas supporting math and logical systems, and relates these ideas to Bach and his music, which I think is interesting.

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some good references are:

Mathematical Theory of Music, by Franck Jedrzejewski Also by him, and Tom Johnson, Looking at Numbers, might interest you as well. Of course the one mentioned above Topos of Music, though in my opinion tends to take things a little too far from music. Music and Mathematics: from Pythagoras to fractals, from Oxford University Press Fractals in Music, by Charles Madden. These last two seem to me a lot more adequate as music theory books.

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I found this paper very enticing as a way to get to the definition of harmony as a path in a phase space. The structure of musical harmony as an ordered phase of sound: A statistical mechanics approach to music theory

https://advances.sciencemag.org/content/5/5/eaav8490

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