Musical variations from a chaotic mapping.
A chaotic mapping provides a technique for generating musical variations of an original work. This technique, based on the sensitivity of chaotic trajectories to initial conditions, produces changes in the pitch sequence of a piece. A sequence of musical pitches {p(i)}, i.e., any piece ranging from Bach (or earlier) to contemporary music, is paired with the x-components {x(i)} of a Lorenz chaotic trajectory. Each p(i) is marked on the x axis at the point designated by its x(i). In this way, the x axis becomes a pitch axis configured according to the notes of the original composition. Then, a second chaotic trajectory, whose initial condition differs from the first, is launched. Its x-components trigger pitches on the pitch axis (via the mapping) that vary in sequence from the original work, thus creating a variation. There are virtually an unlimited number of variations possible, many appealing to expert and nonexpert alike. (c) 1996 American Institute of Physics.
Dabby
Diana S.
DS
Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139.