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 , a visualization method of hierarchical pitch-class relations in pieces of music.
Building on this work, we are currently developing midiVERTO , 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.
- Amiot (2016). Music Through Fourier Space: Discrete Fourier Transform in Music Theory. Springer.
- Noll (2019). Insiders’ Choice: Studying Pitch Class Sets Through Their Discrete Fourier Transformations. In Mathematics and Computation in Music (pp. 371–378). Springer. https://doi.org/10.1007/978-3-030-21392-3_32
- Tymoczko & Yust (2019). Fourier Phase and Pitch-Class Sum. In Mathematics and Computation in Music (pp. 46–58). Springer. https://doi.org/10.1007/978-3-030-21392-3_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. https://doi.org/10.1177/10298649211034906
- Harasim, D., Affatato, G., & Moss, F. C. (2022). midiVERTO: A Web Application to Visualize Tonality in Real Time. arXiv:2203.13158 [cs]. http://arxiv.org/abs/2203.13158
Apr 4, 2022 2:30 PM — 4:00 PM
Faculdade de Engenharia da Universidade do Porto (FEUP)