Generator sequence

A generator sequence (GS) is a cyclically repeating sequence of stacked intervals called generators. A GS can be denoted:

GS(interval1, interval2, interval3, ..., intervaln),

which means: stack interval2 on top of interval1, interval3 on top of interval2, etc. up to intervaln, then stack interval1 again and repeat.

This article adopts a convention where an enumerated chord can be used instead for part or whole of the argument, where the chord's steps are generators, for example writing Ptolemy's intense diatonic as GS(4:5:6)[7], which is abbreviation for GS(5/4, 6/5)[7].

The aggregate generator is the logarithmic sum of all intervals in the GS.

For example: GS(6:7:8) = GS(7/6, 8/7) means an alternating stack of 7/6 and 8/7 (where the first interval is 7/6). Like for temperaments, [n] can be used to mean "octave reduce at each step and stop stacking at n notes", so GS(7/6, 8/7)[9] denotes the 2.3.7 (right-hand) diasem scale. The aggregate generator is 4/3.

Certain generator sequences generalize MOS scales, and GSes are often used to create higher-rank scales.