Specific interval

The major scale is maximally even. For example, for every generic interval of a second there are only two possible specific intervals: 1 semitone (a minor second) or 2 semitones (a major second).

In diatonic set theory a specific interval is the clockwise distance between pitch classes on the chromatic circle (interval class), in other words the number of half steps between notes. The largest specific interval is one less than the number of "chromatic" pitches. In twelve tone equal temperament the largest specific interval is 11. (Johnson 2003, p. 26)

Myhill's property is the quality of musical scales or collections with exactly two specific intervals for every generic interval. In other words, each generic interval can be made from one of two possible different specific intervals.

Sources

Johnson, Timothy (2003). Foundations of Diatonic Theory: A Mathematically Based Approach to Music Fundamentals. Key College Publishing. ISBN 1-930190-80-8.

Musical set theory

All-interval tetrachord Complement Forte number Identity Interval class Interval vector Multiplication Permutation Pitch class Pitch interval Pitch-interval class Set List Similarity relation Transformation Z-relation

Diatonic set theory	Bisector Cardinality equals variety Common tone Diatonic scale Deep scale property Generated collection Generic interval Maximal evenness Myhill's property Rothenberg propriety Specific interval Structure implies multiplicity

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