Music Through Fourier Space

Discrete Fourier Transform in Music Theory
Softcover Nachdruck of the original 1. Auflage 2016
ISBN: 978-3-319-83323-1
Verlag: Springer International Publishing

Buch, Englisch, 206 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 347 g

Reihe: Computational Music Science

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Amiot, Emmanuel

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
• Geisteswissenschaften Musikwissenschaft Musikwissenschaft Allgemein Musiktheorie, Musikästhetik, Kompositionslehre
• Mathematik | Informatik EDV | Informatik Angewandte Informatik Computeranwendungen in Geistes- und Sozialwissenschaften

Inhaltsverzeichnis

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.

Über Autor(innen)

Emmanuel Amiot teaches mathematics at the Lycée François Arago in Perpignan, he is a researcher in the Laboratoire de Mathématiques et Physique (LAMPS) of Université de Perpignan Via Domitia, and he is a regular collaborator with researchers at the Institut de Recherche et Coordination Acoustique/Musique (IRCAM), Paris. He is a pioneer of the techniques described in this textbook, with considerable research and teaching experience in the related areas, geometry, topology, and applied mathematics.