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The Discrete FourierFourier Transform is commonly used in music theory as a model for basic musical structures such as scales, chords, rhythms, etc. In this first chapter, we will focus on the one-dimensional DFT, starting with a definition of the mathematical model. We will then explain how we move to the two-dimensional case, and especially how we aim to model a musical bar using the DFT. The chapter ends with the main definition of this book, the DFT-distance, that provides a new metric on the set of musical bars.

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The DFT for Modeling Basic Musical Structures

  • 章节

  • 发表日期：

    2025年

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  • Victoria Callet-Feltz

摘要

The Discrete FourierFourier Transform is commonly used in music theory as a model for basic musical structures such as scales, chords, rhythms, etc. In this first chapter, we will focus on the one-dimensional DFT, starting with a definition of the mathematical model. We will then explain how we move to the two-dimensional case, and especially how we aim to model a musical bar using the DFT. The chapter ends with the main definition of this book, the DFT-distance, that provides a new metric on the set of musical bars.