Computational Music Science

Music Through Fourier Space

Discrete Fourier Transform in Music Theory

Authors: Amiot, Emmanuel

  • First textbook dedicated to this subject
  • Supported throughout with examples and exercises, and online supplementary material
  • Suitable also for practitioners
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Buy this book

eBook 47,59 €
price for Spain (gross)
  • ISBN 978-3-319-45581-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 59,27 €
price for Spain (gross)
  • ISBN 978-3-319-45580-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this Textbook

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.

About the authors

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.

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)


Table of contents (8 chapters)

  • Discrete Fourier Transform of Distributions

    Amiot, Emmanuel

    Pages 1-26

    Preview Buy Chapter 30,19 €
  • Homometry and the Phase Retrieval Problem

    Amiot, Emmanuel

    Pages 27-49

    Preview Buy Chapter 30,19 €
  • Nil Fourier Coefficients and Tilings

    Amiot, Emmanuel

    Pages 51-89

    Preview Buy Chapter 30,19 €
  • Saliency

    Amiot, Emmanuel

    Pages 91-133

    Preview Buy Chapter 30,19 €
  • Continuous Spaces, Continuous FT

    Amiot, Emmanuel

    Pages 135-155

    Preview Buy Chapter 30,19 €

Buy this book

eBook 47,59 €
price for Spain (gross)
  • ISBN 978-3-319-45581-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 59,27 €
price for Spain (gross)
  • ISBN 978-3-319-45580-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Music Through Fourier Space
Book Subtitle
Discrete Fourier Transform in Music Theory
Authors
Series Title
Computational Music Science
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-45581-5
DOI
10.1007/978-3-319-45581-5
Hardcover ISBN
978-3-319-45580-8
Series ISSN
1868-0305
Edition Number
1
Number of Pages
XV, 206
Number of Illustrations and Tables
84 b/w illustrations, 45 illustrations in colour
Topics