The Linear Diophantine Equation in Music Theory - Abstract

Jack Douthett and Richard Krantz
Bridges: Mathematical Connections in Art, Music, and Science (2001)
Pages 339–339

Abstract

In this presentation, we will demonstrate how the linear Diophantine equation may be used to construct microtonal musical scales (i.e. Balzano's 20-fold systems and the Bohlen-Pierce 13-note scale) having the modulation properties associated with the familiar circle of fifths.

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