Generator sequence: Difference between revisions
No edit summary Tags: Mobile edit Mobile web edit |
|||
| Line 35: | Line 35: | ||
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 that the ''p'' generators are linearly independent and that ''k'' stacked generators equave-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. | 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 that the ''p'' generators are linearly independent and that ''k'' stacked generators equave-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. | One-period MOS scales have step variety 2 and generator variety 1, and certain [[MOS substitution]] scales (including all regular SV3 scales) have step variety 3 and generator variety 2. | ||
== JI scales obtained from guided generator sequences == | == JI scales obtained from guided generator sequences == | ||