Music Through Fourier Space : Discrete Fourier Transform in Music Theory
Amiot, Emmanuel
Music Through Fourier Space : Discrete Fourier Transform in Music Theory by Emmanuel Amiot - Cham Springer International Publishing 2016 - 1 recurso en línea (XV, 206 páginas) 129 ilustraciones, 45 ilustraciones en color - Computational Music Science 1868-0305 .
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.
9783319455815
Música
Matemáticas
NX260 / .A456 2016
004
Music Through Fourier Space : Discrete Fourier Transform in Music Theory by Emmanuel Amiot - Cham Springer International Publishing 2016 - 1 recurso en línea (XV, 206 páginas) 129 ilustraciones, 45 ilustraciones en color - Computational Music Science 1868-0305 .
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.
9783319455815
Música
Matemáticas
NX260 / .A456 2016
004