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.