Fourier Oracles for Computer-Aided Improvisation

The mathematical study of the diatonic and chromatic uni- verses in the tradition of David Lewin (9) and John Clough (6) is a point of departure for several recent investigations. Surprisingly, Lewin’s original idea to apply finite Fourier trans- form to musical structures has not been further investigated for four decades. It turns out that several music-theoretically interesting properties of certain types of musical structures, as the partial symmetry of Fourier balances, maximal even- ness (5) and well-formedness (4), allow alternative charac- terizations in terms of their Fourier transforms. The paper ex- plores two particularly interesting cases: vanishing Fourier coefficients as an expression of chord symmetry and maxi- mal Fourier coefficients as a reinterpretation of maximally even scales. In order to experimentally explore the Fourier approach we design an interactive playground for rhythmic loops. We propose a Fourier-based approach to be integrated as an ”Scratching”-interface in the OMAX environment (built on OpenMusic and MaxMSP) which allows to interactively change a rhythm through a gestural control of its Fourier im- age. A collection of theoretical tools in OpenMusic visual programming language helps the improviser to explore some new musical situations by inspecting mathematical and visual characteristics of the Fourier image.