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.

The aggregate generator is the (possibly equave-reduced) logarithmic sum of all intervals in the GS.

For example: 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.