The Linear Diophantine Equation in Music Theory

Year: 2001 Authors: Jack Douthett; Richard Krantz

Core claim

Unidirectional P-cycles and related maximally even sets can be constructed using the equation cl_g - dg = ±1.

Topics

music theory, microtonal scales, circle of fifths, P-cycles

Domains

linear Diophantine equations, coprime integers, set classes, music composition, microtonal design, auditory structure

Methods

theoretical construction, music-theoretic analysis, scale generation

Media

microtonal musical scales, Balzano’s 20-fold system, Bohlen-Pierce 13-note scale

Source status

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