Title
Musical Variations from a Chaotic Mapping
Description
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.
Date Published
2018-03-26 15:07:08