Music Through Fourier Space: Discrete Fourier Transform In Music Theory by Emmanuel AmiotMusic Through Fourier Space: Discrete Fourier Transform In Music Theory by Emmanuel Amiot

Music Through Fourier Space: Discrete Fourier Transform In Music Theory

byEmmanuel Amiot

Hardcover | November 4, 2016

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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.

This is the first textbook dedicated to this subject, and with supporting examples and exercises this is suitable for researchers and advanced undergraduate and graduate students of music, computer science and engineering. The author has made online supplementary material available, and the book is also suitable for practitioners who want to learn about techniques for understanding musical notions and who want to gain musical insights into mathematical problems.
Emmanuel Amiot teaches mathematics at the Lycée François Arago in Perpignan, he is a researcher in the Laboratoire de Mathématiques et Physique (LAMPS) of Université de Perpignan Via Domitia, and he is a regular collaborator with researchers at the Institut de Recherche et Coordination Acoustique/Musique (IRCAM), Paris. He is a pioneer...
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Title:Music Through Fourier Space: Discrete Fourier Transform In Music TheoryFormat:HardcoverDimensions:206 pages, 23.5 × 15.5 × 0.03 inPublished:November 4, 2016Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:331945580X

ISBN - 13:9783319455808

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Reviews

Table of Contents

Discrete Fourier Transform of Distributions.- Homometry and the Phase Retrieval Problem.- Nil Fourier Coefficients and Tilings.- Saliency.- Continuous Spaces, Continuous Fourier Transform.- Phases of Fourier Coefficients.

Editorial Reviews

"Amiot's nice book gives the state of the art in the usage of DFT of abstract musical structures such as rhythms, scales, chords, pitch class distributions, and so on. . This is possibly the first textbook on the topic. . The target readership includes graduates and advanced undergraduates of computational music science and engineering. Researchers in music should also find it of interest." (Soubhik Chakraborty, Computing Reviews, May, 2017)