Music through Fourier space discrete Fourier transform in music theory /
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, salienc...
| Main Author: | Amiot, Emmanuel, 1961- |
|---|---|
| Other Authors: | SpringerLink (Online service) |
| Format: | eBook |
| Language: | English |
| Published: |
Cham, Switzerland :
Springer,
©2016.
|
| Physical Description: |
1 online resource (xv, 206 pages) : illustrations (some color). |
| Series: |
Computational music science.
|
| Subjects: |
| Summary: |
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. |
|---|---|
| Item Description: |
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. 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. Includes bibliographical references and index. |
| Physical Description: |
1 online resource (xv, 206 pages) : illustrations (some color). |
| Bibliography: |
Includes bibliographical references and index. |
| ISBN: |
9783319455815 3319455818 331945580X 9783319455808 |
| ISSN: |
1868-0305. |