Generated collection

(Johnson, 2003, p. 83) The C major diatonic collection can be generated by adding a cycle of perfect fifths (C7) starting at F: F-C-G-D-A-E-B = C-D-E-F-G-A-B.

Using integer notation and 12-tone equal temperament, the standard tuning of Western music: 5 + 7 = 0, 0 + 7 = 7, 7 + 7 = 2, 2 + 7 = 9, 9 + 7 = 4, 4 + 7 = 11.

For example, the diatonic collection is well formed, for the perfect fifth (the generic interval 4) corresponds to the generator 7.

In earlier (1975) work, theoretician Erv Wilson defined the properties of the idea, and called such a scale a MOS, an acronym for "Moment of Symmetry".

[1] While unpublished until it appeared online in 1999, this paper was widely distributed and well known throughout the microtonal music community, which adopted the term.