Geometry and Harmony

Year: 2005 Authors: David Rappaport

Core claim

Complementary maximal area sets provide a mathematical characterization that includes Levine’s four fundamental jazz scales.

Topics

musical scales, clock diagrams, integer partitions, combinatorial geometry, jazz harmony

Domains

combinatorics, discrete geometry, polygon area, integer partitions, music theory, jazz improvisation, visualization, music education

Methods

clock-diagram representation, integer partition construction, geometric maximization, scale classification

Media

12-tone chromatic circle, convex polygons, figure-based diagrams

Source status

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