Generator sequence: Difference between revisions
| Line 33: | Line 33: | ||
The ''generator variety''{{idiosyncratic}} is the number of generators in the generator sequence, not including the closing interval. | The ''generator variety''{{idiosyncratic}} is the number of generators in the generator sequence, not including the closing interval. | ||
There is in general no simple relationship between a scale's [[step variety]] and its generator variety. For any generator variety ''p'' > 1 and for any ''k'' > 1 it is possible to construct a long WFGS so that all combinatorially possible sums of ''k'' generators (there are <math>{k + p - 1 \choose k}</math> of them) are obtained for scale steps. | There is in general no simple relationship between a scale's [[step variety]] and its generator variety. For any generator variety ''p'' > 1 and for any ''k'' > 1 if we assume ''k'' generators reduce to a step, it is possible to construct a long WFGS so that all combinatorially possible sums of ''k'' generators (there are <math>{k + p - 1 \choose k}</math> of them) are obtained for scale steps. | ||
MOS scales have step variety 2 and generator variety 1, and [[MOS substitution]] scales (including all regular SV3 scales) have step variety 3 and generator variety 2. | MOS scales have step variety 2 and generator variety 1, and [[MOS substitution]] scales (including all regular SV3 scales) have step variety 3 and generator variety 2. | ||