Generic and specific intervals

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.

Myhill's property is the quality of musical scales or collections with exactly two specific intervals for every generic interval, and thus also have the properties of cardinality equals variety, structure implies multiplicity, and being a well formed generated collection.

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).