MIT Department of Electrical Engineering & Computer Science

Art Science: A Chaotic Mapping for Musical Variation

Diana Dabby
Middlebury College; MIT, EECS & LIDS

Monday, March 30, 1998
4:00 PM (refreshments 3:45)
Edgerton Hall, Room 34-101
EECS Colloquium

Abstract

This talk presents recent work* on a chaotic mapping technique for generating musical variations of an original piece. Based on the sensitivity of chaotic trajectories to initial conditions, the technique employs two chaotic trajectories that map the pitch sequence of a musical score into a variation based on the pitch events of a given piece. The variations can be close to the original, diverge from it substantially, or achieve degrees of variability between those extremes.

The chaotic mapping is designed to provide two mechanisms --- linking and tracking --- to help the variation retain its connection to the original. Using the technique as an idea generator, the artist can accept, reject or alter any variation. Each accepted change in the variation is a thought-out process, as is the addition of notes (or rhythms) not the original. A composer writing a variation suggested by this technique will listen for the more far-reaching implications of the variation, and decide whether --- at least intuitively --- the resulting language is self-consistent. Musically, the chaotic mapping can be extended to include variations in rhythm and dynamics, in addition to pitch. More generally, the technique can produce variations on any sequence of context-dependent symbols, e.g., parsed pixel sequences from scanned art work.

Examples will be presented, including variations of Bach, Gershwin, Dabby, and imagery. Once variations of an entire piece are available, the composition can change with successive listenings, from performance to performance, or even within the same concert. In a broad sense, the music has become dynamic --- it changes with time much the same way as a river changes from day to day, season to season, yet is still recognized in its essence.

*Dabby, "Musical variations from a chaotic mapping," CHAOS, American Institute of Physics, June 1996, 95-107.