In diatonic set theory a generic interval is the number of scale steps between notes of a collection or scale. The largest generic interval is one less than the number of scale members. (Johnson 2003, p.26)
In the diatonic collection the generic interval is one less than the corresponding diatonic interval:
- Adjacent intervals, seconds, are 1
- Thirds = 2
- Fourths = 3
- Fifths = 4
- Sixths = 5
- Sevenths = 6
The largest generic interval in the diatonic scale being 7-1 = 6.
Myhill's property is the quality of musical scales or collections with exactly two specific intervals for every generic interval. In other words, each generic interval can be made from one of two possible different specific intervals.
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