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
Research Fellow in Cultural Analytics

Fabian C. Moss is a Research Fellow in Cultural Analytics at University of Amsterdam (UvA). He was born in Cologne, Germany, and studied Mathematics and Educational Studies at University of Cologne, and Music Education (Major Piano) and Musicology at Hochschule für Musik und Tanz, Köln. He obtained is PhD in Digital Humanities from École Polytechnique Fédérale de Lausanne (EPFL). Working with large symbolic datasets of musical scores and harmonic annotations, he is primarily interested in Computational Music Analysis, Music Theory, Music Cognition, and their mutual relationship.