Cardinality equals variety

The musical operation of scalar transposition shifts every note in a melody by the same number of scale steps.

The musical operation of chromatic transposition shifts every note in a melody by the same distance in pitch class space.

In diatonic set theory cardinality equals variety when, for any melodic line L in a particular scale S, the number of these classes is equal to the number of distinct pitch classes in the line L. For example, the melodic line C-D-E has three distinct pitch classes.

The property was first described by John Clough and Gerald Myerson in "Variety and Multiplicity in Diatonic Systems" (1985) (Johnson 2003, p. 68, 151).

"Nondegenerate well-formed scales" are those that possess Myhill's property.