TITLE: Books on music theory intended for mathematicians
QUESTION [85 upvotes]: Some time ago I attended a colloquium given by Princeton music theorist Dmitri Tymoczko, where he gave a fascinating talk on the connection between music composition and certain geometric objects (as I recall, the work of Chopin can naturally be viewed as walks among lattice points lying in some hyperbolic surface, which gives some sense of canonicity to his compositions). I am asking whether there exist books on music theory that is intended for an audience with a reasonably sophisticated mathematical background. This question is in the same spirit as this one regarding physics.
Any suggestions would be great!

REPLY [2 votes]: 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.