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Are there any good books on musical theory from a mathematical standpoint? Is "Music theory and mathematics : chords, collections, and transformations", edited by Jack Douthett, Martha M. Hyde, and Charles J. Smith, one on them?

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    $\begingroup$ I am not a big fan of "is X a good book in subject Y" questions. Whether a book is suitable for a reader depends on a lot more than just the book itself. $\endgroup$ May 3, 2011 at 14:55
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    $\begingroup$ Seen this? $\endgroup$ May 3, 2011 at 14:59
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    $\begingroup$ Can you give more objective criteria that "good"? $\endgroup$
    – Rasmus
    May 3, 2011 at 15:45
  • $\begingroup$ There is also this related post on MO: Books on music theory intended for mathematicians $\endgroup$ Feb 27, 2017 at 4:00

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There's Music: a mathematical offering by Dave Benson. It can be downloaded from his website.

There's Philip Ball's the Music Instinct, although this would be more from the science point of view than the mathematical one.

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    $\begingroup$ The author website you can download Music: a mathematical offering from is here. It's a really great book! $\endgroup$ Jun 5, 2011 at 17:50
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    $\begingroup$ New link here. $\endgroup$ Aug 16, 2014 at 22:08
  • $\begingroup$ @CristianGarcia: Not working... Now here. $\endgroup$
    – user21820
    Feb 16, 2018 at 11:07
  • $\begingroup$ Not working either. Now here $\endgroup$ Aug 3, 2023 at 13:54
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If you like category theory and topos theory you might want to look at Mazzolas, Topos of Music: Geometric Logic of Concepts, Theory, and Performance

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    $\begingroup$ This is by far the most mathematically intense book on music theory ever written. $\endgroup$
    – Matt
    Feb 16, 2012 at 6:41
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I don't know which level you mean, but Mathematics and Music seems nice. There is also Musimathics, which seems more advanced. [Disclaimer: I don't have first-hand experience with either book.]

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    $\begingroup$ I've actually flipped through Musimathics a long time ago; for mathematicians/scientists/engineers who have been interested in music for a long time, there's not a lot of new stuff in there, but it's a terrific book for people with some experience/interest in math or the natural sciences who want to learn it all properly. $\endgroup$
    – Gerben
    May 3, 2011 at 20:38
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Besides the ones already mentioned, there is A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice by Dmitri Tymoczko, which takes an orbifold approach.

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If you want to understand scales from a mathematical/dsp perspective, and why a certain scale is the most "natural" for the music of a given instrument or culture, you should check out Tuning, Timbre, Spectrum, Scale by Sethares.

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I don't think it's explicitly mathematical, but Peter Westergaard's An Introduction to Tonal Theory might be appealing (I haven't read it myself).

There is also a blog which seems to have much about it:

http://mathemusicality.wordpress.com/category/westergaardian-theory/

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Don't know the book you cite, but 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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Along our colleagues contributions (Mazzola and Tymoczko), check out David Lewin’s “Generalized Musical Intervals and Transformations”. Also search a few papers by Richard Cohn.

In the rhythm domain, Godfried Toussaint’s “The Geometry of Musical Rhythm” and Miles Okazaki’s “Visual Reference for Musicians”.

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Math and Music Kids of new generation should have different methods of training. They are capable to perceive information faster, with cross-modal processing, activating all senses at once : visual perception, audio analyzers, neuromotor functions.
It is well known that the difficulties in the perception of any information, including musical one, cause strain of the main functional systems in the child’s organism. One can see the interdependence between the perception of information ( Readout Algorithm ) and the synapse transmission (Action Potential ).It proves the possibility of development of muscular fatigue in hands depending on the quantity of eyeballs’ fluctuations. The innovative technology " Reflection " gives us some explanation in this direction and raises the topic on the necessity of applying of Digital Key in Elementary Music Education. http://reflectionmusic.ucoz.com/
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Amiot, Emmanuel. 2016. Music Through Fourier Space. Springer.

From the Springer website:

This book explains the state of the art in the use of the discrete Fourier transform (DFT) of musical structures such as rhythms or scales. In particular the author explains the DFT of pitch-class distributions, homometry and the phase retrieval problem, nil Fourier coefficients and tilings, saliency, extrapolation to the continuous Fourier transform and continuous spaces, and the meaning of the phases of Fourier coefficients.

Perspectives of New Music 49/2 (Summer 2011) is devoted almost entirely to "Tiling Rhythmic Canons", including articles by many of the authors mentioned in other posts.1


1 The origin of the mathematics in this book can be found in Dan Vuza's four-part article "Supplementary Sets and Regular Complementary Unending Canons" in Perspectives of New Music (vols. 29/2–31/1). It is the founding article of an area of research ("Tiling Rhythmic Canons") for many of the authors mentioned here, including Tom Johnson, Guerino Mazzola, Emmanuel Amiot, Carlos Agon, and Moreno Andreatta.

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I have not the reference but the Great Leonahrd Euler wrote a book on the subject.Considered at the 18th century as too mathematical for the musicians and too musical for the mathematicians.

Ps:Make a comment if you have found something.

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Maybe the The Structure of Atonal Music by Allen Forte

found here https://www.youtube.com/watch?v=KFKMvFzobbw

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