Musical Variations from a Chaotic Mapping

Diana Dabby, Franklin W. Olin College of Engineering

Article comments

© (1996) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The article appeared in Chaos, Vol 6, (1996), and may be found here.

Abstract

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 {pi}, i.e., any piece ranging from Bach (or earlier) to contemporary music, is paired with the x‐components {xi} of a Lorenz chaotic trajectory. Each pi is marked on the x axis at the point designated by its xi. 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.