Interactive Music Analysis using the DFT and Pitch-Class Distributions extracted from MIDI files


The discrete Fourier transform (DFT) is a cornerstone of digital signal processing and commonly used to extract periodicities in time-continuous signals. In recent years, however, mathematical music theorists have begun to explore DFT’s potential when applied not to the time but to the pitch-class domain, where the periodicities are given by equal divisions of the octave [1-3]. Earlier this year, we introduced wavescapes [4], a visualization method of hierarchical pitch-class relations in pieces of music. Building on this work, we are currently developing midiVERTO [5], an interactive web app to analyze MIDI files using the DFT, that allows users to create wavescapes and inspect the dynamics of pitch-class distributions at several hierarchical levels. In my presentation, I will briefly introduce the underlying theoretical work followed by a tutorial on how to use the app for music analysis.

  1. Amiot (2016). Music Through Fourier Space: Discrete Fourier Transform in Music Theory. Springer.
  2. Noll (2019). Insiders’ Choice: Studying Pitch Class Sets Through Their Discrete Fourier Transformations. In Mathematics and Computation in Music (pp. 371–378). Springer.
  3. Tymoczko & Yust (2019). Fourier Phase and Pitch-Class Sum. In Mathematics and Computation in Music (pp. 46–58). Springer.
  4. Viaccoz, C., Harasim, D., Moss, F. C., & Rohrmeier, M. (2022). Wavescapes: A visual hierarchical analysis of tonality using the discrete Fourier transform. Musicae Scientiae.
  5. Harasim, D., Affatato, G., & Moss, F. C. (2022). midiVERTO: A Web Application to Visualize Tonality in Real Time. arXiv:2203.13158 [cs].

Apr 4, 2022 2:30 PM — 4:00 PM
Faculdade de Engenharia da Universidade do Porto (FEUP)
Fabian C. Moss
Fabian C. Moss
Assistant Professor for Music Philology and Music Theory

Fabian C. Moss is an assistant professor for Digital Music Philology and Music Theory at Julius-Maximilians University Würzburg (JMU), Germany.