Generic and specific intervals

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 generic interval is the number of scale steps between notes of a collection or scale. The largest generic interval is one less than the number of scale members. (Johnson 2003, p. 26)

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)

In the diatonic collection the generic interval is one less than the corresponding diatonic interval:

• Adjacent intervals, seconds, are 1
• Thirds = 2
• Fourths = 3
• Fifths = 4
• Sixths = 5
• Sevenths = 6

The largest generic interval in the diatonic scale being 7-1 = 6.

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.