Insiders’ Choice: Studying Pitch Class Sets Through Their Discrete Fourier Transformations

Abstract

This contribution responds to a growing interest in the application of Discrete Fourier Transform (DFT) to the study of pitch class sets and pitch class profiles. Theoretical fundaments, references to previous work and explorations of various directions of study have been eloquently assembled by Emmanuel Amiot. Recent pioneering work in the application to music analysis and the reinterpretation of theoretical knowledge has been accomplished by Jason Yust. The intention of this paper is to show ways to make Yust’s strategies and methods more easily accessible and reproducible for a broader readership, especially students. This includes the introduction of concepts as well as interactive experiments with the help of computation and visualization tools. The theoretical starting point is the interpretation of pitch class sets in terms of their characteristic functions, i.e. as pitch class profiles with values 0 and 1. Apart from the magnitudes of the respective partials, the study of their phases is particularly illuminating. The paper shows how the contents of this approach can be made accessible in a four steps proceedure.