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In diatonic set theory 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 maximal evenness, cardinality equals variety, structure implies multiplicity, and being a well formed generated collection. In other words, each generic interval can be made from one of two possible different specific intervals. For example, there are major or minor and perfect or augmented/diminished variants of all the diatonic intervals:
The diatonic and pentatonic collections possess Myhill's property. The concept appears to have been first described by John Clough and Gerald Myerson and named after their associate the mathematician John Myhill. (Johnson 2003, p. 106, 158)