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. | ||
The ''aggregate generator'' is the logarithmic sum of all intervals in the GS. | |||
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]. | 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]. | ||
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. | 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. | ||
Revision as of 23:49, 22 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 logarithmic sum of all intervals in the GS.
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].
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.
