Music Through Fourier Space: Discrete Fourier Transform in Music Theory by Emman

Description: Music Through Fourier Space by Emmanuel Amiot 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. FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description 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. Back Cover 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. Author Biography 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 of the techniques described in this textbook, with considerable research and teaching experience in the related areas, geometry, topology, and applied mathematics. 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. Review "This book is a short exposition of important material in the field of mathematics and music. It describes a number of topics to which Amiot has contributed significant research. ... This book should prove to be a real delight for aficionados of mathematics and music. It contains a wealth of important material and is certain to drive further investigations in this fascinating interdisciplinary field." (James Stephan Walker, Mathematical Reviews, June, 2018)"Amiots 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) Review Quote "This book is a short exposition of important material in the field of mathematics and music. It describes a number of topics to which Amiot has contributed significant research. ... This book should prove to be a real delight for aficionados of mathematics and music. It contains a wealth of important material and is certain to drive further investigations in this fascinating interdisciplinary field." (James Stephan Walker, Mathematical Reviews, June, 2018) "Amiots 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) Feature First textbook dedicated to this subject Supported throughout with examples and exercises, and online supplementary material Suitable also for practitioners Details ISBN3319833235 Author Emmanuel Amiot ISBN-10 3319833235 ISBN-13 9783319833231 Format Paperback Series Computational Music Science Year 2018 Subtitle Discrete Fourier Transform in Music Theory DEWEY 004 Pages 206 Imprint Springer International Publishing AG Place of Publication Cham Country of Publication Switzerland Publication Date 2018-06-16 Short Title Music Through Fourier Space Language English UK Release Date 2018-06-16 Narrator Patrick Osborne Edited by Kumbirai Musiyiwa Birth 1974 Affiliation Massachusetts Institute of Technology Position journalist Qualifications Ph.D. Publisher Springer International Publishing AG Edition Description Softcover reprint of the original 1st ed. 2016 Alternative 9783319455808 Audience Professional & Vocational Illustrations 45 Illustrations, color; 84 Illustrations, black and white; XV, 206 p. 129 illus., 45 illus. in color. 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