Animated Harmonic Analysis Using DFT Phase Spaces and Coefficient Products

Abstract

MidiVerto is an interactive music analysis tool that uses the discrete Fourier transform on pitch-class vectors. It performs a windowed analysis of a midi file and displays the results of a DFT in wavescapes and coefficient spaces, showing how DFT coefficients change over the course of passage and with changes in the size of the window. A playback feature creates analytical animations by timing output to audio. In this digital poster we illustrate two new modules added to midiVerto, a coefficient product space and phase space. Products of the 2nd, 3rd, and 7th (f2f3f7) and 3rd, 4th, and 5th (f3f4f5) coefficients illustrate typical features of functional harmony, especially a tendency towards coherence (phase values staying close to zero) in the f2f3f7 space, but in the f3f4f5 space, and an association of the imaginary dimension with mode. Modulations are visible in the phase space on the 3rd and 5th coefficients. The ability to produce animated analyses timed to audio output provides a new medium for analytical interaction with music.

Fabian C. Moss

Assistant Professor for Digital 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.