Fourier Oracles for Computer-Aided Improvisation
Emmanuel Amiot, Thomas E. Noll, Moreno Andreatta, Carlos Agón · 2006
The mathematical study of the diatonic and chromatic universes 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 transform 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 evenness (5) and well-formedness (4), allow alternative characterizations in terms of their Fourier transforms. The paper explores two particularly interesting cases: vanishing Fourier coefficients as an expression of chord symmetry and maximal Fourier coefficients as a reinterpretation of maximally even scales. In order to experimentally explore the Fourier