Generator sequence: Difference between revisions
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which means: stack interval2 on top of interval1, interval3 on top of interval2, etc. up to intervaln, then stack interval1 again and repeat. | which means: stack interval2 on top of interval1, interval3 on top of interval2, etc. up to intervaln, then stack interval1 again and repeat. | ||
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 the (possibly equave-reduced) 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. | Certain generator sequences generalize [[MOS]] scales, and GSes are often used to create higher-rank scales. | ||
[[Category:Scale construction]] | [[Category:Scale construction]] | ||
Revision as of 16:41, 21 December 2025
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) 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.
