Music Through Fourier Space

Discrete Fourier Transform in Music Theory

  • Emmanuel Amiot

Part of the Computational Music Science book series (CMS)

Table of contents

  1. Front Matter
    Pages I-XV
  2. Emmanuel Amiot
    Pages 27-49
  3. Emmanuel Amiot
    Pages 51-89
  4. Emmanuel Amiot
    Pages 91-133
  5. Emmanuel Amiot
    Pages 135-155
  6. Emmanuel Amiot
    Pages 157-178
  7. Emmanuel Amiot
    Pages 179-181
  8. Emmanuel Amiot
    Pages 183-197
  9. Back Matter
    Pages 199-206

About this book


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.


Discrete Fourier Transform (DFT) Music Theory Cyclic Groups Tiling Homometry Saliency

Authors and affiliations

  • Emmanuel Amiot
    • 1
  1. 1.Laboratoire de Mathématiques et PhysiqueUniversité de Perpignan Via DomitiaPerpignanFrance

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Computer Science
  • Print ISBN 978-3-319-45580-8
  • Online ISBN 978-3-319-45581-5
  • Series Print ISSN 1868-0305
  • Series Online ISSN 1868-0313
  • Buy this book on publisher's site