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Musical Variations from a Chaotic Mapping

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Title

Musical Variations from a Chaotic Mapping

Description

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.

Date Published

2018-03-26 15:10:39

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  • Download Dabby_MusicalVariations.pdf

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Olin College of Engineering

An undergraduate engineering institution exploring innovative approaches to engineering education since its founding in 1997.

1000 Olin Way
Needham, MA 02492
781.292.2390