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A chaotic mapping provides a technique for generating musical variations of an original work. Thistechnique, based on the sensitivity of chaotic trajectories to initial conditions, produces changes inthe 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 chaotictrajectory. Each pi is marked on the x axis at the point designated by its xi . In this way, the x axisbecomes a pitch axis configured according to the notes of the original composition. Then, a secondchaotic trajectory, whose initial condition differs from the first, is launched. Its x-componentstrigger pitches on the pitch axis ~via the mapping! that vary in sequence from the original work, thuscreating a variation. There are virtually an unlimited number of variations possible, many appealingto expert and nonexpert alike.


© (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 at

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