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Music Through Fourier Space [electronic resource] : Discrete Fourier Transform in Music Theory / by Emmanuel Amiot.

By: Amiot, Emmanuel [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Computational Music Science: Publisher: Cham : Springer International Publishing : Imprint: Springer, 2016Description: XV, 206 p. 129 illus., 45 illus. in color. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783319455815.Subject(s): Computer science | Music | Computer science -- Mathematics | User interfaces (Computer systems) | Application software | Mathematics | Computer Science | Computer Appl. in Arts and Humanities | Music | Mathematics in Music | Mathematics of Computing | User Interfaces and Human Computer Interaction | Signal, Image and Speech ProcessingAdditional physical formats: Printed edition:: No titleDDC classification: 004 Online resources: Click here to access online
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.
In: Springer eBooksSummary: 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.
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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.

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