Structure implies multiplicity

In diatonic set theory structure implies multiplicity is a quality of a collection or scale.

For collections or scales which have this property, the interval series formed by the shortest distance around a diatonic circle of fifths between members of a series indicates the number of unique interval patterns (adjacently, rather than around the circle of fifths) formed by diatonic transpositions of that series.

The property was first described by John Clough and Gerald Myerson in "Variety and Multiplicity in Diatonic Systems" (1985).

68, 151) Structure implies multiplicity is true of the diatonic collection and the pentatonic scale, and any subset.

Cardinality equals variety and structure implies multiplicity are true of all collections with Myhill's property.