In diatonic set theory Myhill's property is the quality of 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 be a well formed generated collection. 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) Diatonic set theory is a subdivision or application of musical set theory which applies the techniques and insights of set theory to properties of the diatonic collection such as maximal evenness, Myhills property, well formedness, the deep scale property, cardinality equals variety, and structure implies multiplicity. ... In diatonic set theory a specific interval is the shortest possible clockwise distance between pitch classes on the chromatic circle (interval class), in other words the number of half steps between notes. ... In diatonic set theory a generic interval is the number of scale steps between notes of a collection or scale. ... In Music theory, the diatonic major scale (also known as the Guido scale), from the Greek diatonikos or to stretch out, is a fundamental building block of the European-influenced musical tradition. ...

Further reading

• Clough, Engebretsen, and Kochavi. "Scales, Sets, and Interval Cycles": 78-84.

Source

• Johnson, Timothy (2003). Foundations of Diatonic Theory: A Mathematically Based Approach to Music Fundamentals. Key College Publishing. ISBN 1930190808.