Generator sequence: Difference between revisions
| Line 28: | Line 28: | ||
A generator sequence can be analyzed in terms of its length and variety. | A generator sequence can be analyzed in terms of its length and variety. | ||
=== Length === | === Length === | ||
The ''length'' of a generator sequence ''s'' is the length at which the GS repeats; it is the smallest ''n'' > 0 such that ''s''[''k'' + ''n''] = ''s''[''k'']. It is known that a length-2 WFGS gives rise to regular SV3 scales; see [[Ternary scale theorems]]. | The ''length'' of a generator sequence ''s'' is the length at which the GS repeats; it is the smallest ''n'' > 0 such that ''s''[''k'' + ''n''] = ''s''[''k'']. It is known that a length-2 WFGS gives rise to regular SV3 scales; see [[Ternary scale theorems]]. | ||
=== Generator variety === | === Generator variety === | ||
If a scale has a [[generator sequence]] or is a union of multiple offset copies of the same generator sequence, then the ''generator variety'' is the number of generators in that sequence, not including the closing interval. | If a scale has a [[generator sequence]] or is a union of multiple offset copies of the same generator sequence, then the ''generator variety'' is the number of generators in that sequence, not including the closing interval. | ||