Composite Number Polyrhythms: Animating and Sonifying the Divisor Plot
Jeffrey Ventrella

Proceedings of Bridges 2022: Mathematics, Art, Music, Architecture, Culture
Pages 237–244
Regular Papers

Abstract

The divisors of composite numbers generate an endless complex pattern when plotted perpendicular to the number line as a function of size. This pattern—the divisor plot—is an infinite set of 2D points with integer values that can be described as a visualization of the Sieve of Eratosthenes. It has a lot of curious patterns, but if we include the element of time (with animation or sonification), even more patterns are revealed, as well as polyrhythms. When interpreted as a musical score, the divisors present a large palette of parameters for generating minimalist math music. This paper describes the discoveries, experiments, and design methods I have used to transform this mathematical canvas into visual and sonic expressions.

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