Generator sequence: Difference between revisions

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== Terminology ==

* The term '''generator sequence'''{{idiosyncratic}} (GS) may be preferable, as ''alternating'' is usually used for sequences and series that repeat every two terms in mathematical terminology.

* Consider a scale whose steps are all positive. Suppose that there exists a positive integer ''k'' such that for every generator ''x''''i'' in the GS recipe GS(''x''1, ..., ''x''''r''), every occurrence of ''x''''i'' in the scale [[subtend]]s ''k'' steps.

* This automatically implies that the gap between the next higher equave and the result of stacking len(scale) − 1 of the generators in the recipe, called the ''imperfect generator'' since it is analogous to the imperfect generator in [[MOS]] scales, also subtends this number of steps. Suppose also that the imperfect generator is distinct from all of the generators used in the generator sequence and occurs only once in the scale.

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 == Terminology ==
-* The term '''generator sequence'''{{idiosyncratic}} (GS) may be preferable, as ''alternating'' is usually used for sequences and series that repeat every two terms in mathematical terminology.
 * Consider a scale whose steps are all positive. Suppose that there exists a positive integer ''k'' such that for every generator ''x''<sub>''i''</sub> in the GS recipe GS(''x''<sub>1</sub>, ..., ''x''<sub>''r''</sub>), every occurrence of ''x''<sub>''i''</sub> in the scale [[subtend]]s ''k'' steps.
 * This automatically implies that the gap between the next higher equave and the result of stacking len(scale) &minus; 1 of the generators in the recipe, called the ''imperfect generator'' since it is analogous to the imperfect generator in [[MOS]] scales, also subtends this number of steps. Suppose also that the imperfect generator is distinct from all of the generators used in the generator sequence and occurs only once in the scale.