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This book explains the state of the art in the use of the discrete Fourier transform (DFT) in music theory. In particular the author explains the DFT of distributions, homometry and the phase retrieval problem, nil Fourier coefficients and tilings, saliency, continuous spaces, the continuous Fourier transform, and phases of Fourier coefficients.

This is the first textbook dedicated to this subject, and with supporting examples and exercises this is suitable for advanced undergraduate and graduate students of music, computer science and engineering. The author has made online...