Construction and interpretation of equal-tempered scales using frequency ratios, maximally even sets, and P-cycles.

Using recent developments in music theory, which are generalizations of the well-known properties of the familiar 12-tone, equal-tempered musical scale, an approach is described for constructing equal-tempered musical scales (with "diatonic" scales and the associated chord structure) based on good-fitting intervals and a generalization of the modulation properties of the circle of fifths. An analysis of the usual 12-tone equal-tempered system is provided as a vehicle to introduce the mathematical details of these recent music-theoretic developments and to articulate the approach for constructing musical scales. The formalism is extended to describe equal-tempered musical scales with nonoctave closure.