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In this paper we demonstrate how to create and analyze musical compositions using Mathematica. In §1, we begin by demonstrating how to create a musical composition for an orchestra based on the butterfly curve using traditional means. In §2, we then show how a computer generated piece based on any curve can be composed using Mathematica. Finally, in §3, we show how Mathematica can be used to analyze musical compositions using the methods from nonlinear time series analysis.
Machado, Marianella P.; Kulp, Christopher W.; and Schlingman, Dirk, "Composition and Analysis of Music Using Mathematica" (2007). Languages, Cultures, and Humanities Faculty and Staff Research. Paper 1.