Music Through Fourier Space Discrete Fourier Transform in Music Theory

• Main Author: Amiot, Emmanuel
• Format: eBook
• Language: English
• Published: Cham Springer Nature 2016; Springer International Publishing AG; Springer International Publishing
• Edition: 1
• Series: Computational Music Science
• Subjects: Computer Appl. in Arts and Humanities; Computer Science; Data processing Computer science; Fourier transformations; Mathematics in Music; Mathematics of Computing; Music; Music-Mathematics; Signal, Image and Speech Processing; User Interfaces and Human Computer Interaction
• ISBN: 9783319455815; 3319455818; 9783319455808; 331945580X
• ISSN: 1868-0305; 1868-0313
• DOI: 10.1007/978-3-319-45581-5

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.