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Music Through Fourier Space : Discrete Fourier Transform in Music Theory / by Emmanuel Amiot.
- Format:
- Book
- Author/Creator:
- Amiot, Emmanuel, 1961- author.
- Series:
- Computer Science (Springer-11645)
- Computational music science 1868-0305
- Computational Music Science, 1868-0305
- Language:
- English
- Subjects (All):
- Application software.
- Music.
- Mathematics.
- Computer science--Mathematics.
- Computer science.
- User interfaces (Computer systems).
- Signal processing.
- Image processing.
- Speech processing systems.
- Computer Appl. in Arts and Humanities.
- Mathematics in Music.
- Mathematics of Computing.
- User Interfaces and Human Computer Interaction.
- Signal, Image and Speech Processing.
- Local Subjects:
- Computer Appl. in Arts and Humanities.
- Music.
- Mathematics in Music.
- Mathematics of Computing.
- User Interfaces and Human Computer Interaction.
- Signal, Image and Speech Processing.
- Physical Description:
- 1 online resource (XV, 206 pages) : 129 illustrations, 45 illustrations in color.
- Edition:
- First edition 2016.
- Contained In:
- Springer eBooks
- Place of Publication:
- Cham : Springer International Publishing : Imprint: Springer, 2016.
- System Details:
- text file PDF
- 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.
- 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.
- Other Format:
- Printed edition:
- ISBN:
- 978-3-319-45581-5
- 9783319455815
- Access Restriction:
- Restricted for use by site license.
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