Ternary scale theorems: Difference between revisions

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** 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 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 ''closing generator'', or the ''imperfect generator'' since it is analogous to the imperfect generator in [[MOS]] scales, also subtends this number of steps.

** The closing generator must be distinct from all of the generators used in the generator sequence and occur only once in the scale.

* The property of having a WFGS of period 2, denoted AGS (''alternating generator sequence'') in this article, is important as it is equivalent to being an odd-regular MV3 scale; see below~~. It used to be called the "SGA property" in past versions of this article~~.

* The property of having a WFGS of period 2, denoted AGS (''alternating generator sequence'') in this article, is important as it is equivalent to being an odd-regular MV3 scale; see below.

* An ''odd-step'' is a ''k''-step where ''k'' is odd; an ''even-step'' is defined similarly.

* Given a linear or circular word ''s'' with a step size '''X''', define ''E'''''X'''(''s'') as the scale word resulting from deleting all instances of '''X''' from ''s''.

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 ** 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 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 ''closing generator'', or the ''imperfect generator'' since it is analogous to the imperfect generator in [[MOS]] scales, also subtends this number of steps.
 ** The closing generator must be distinct from all of the generators used in the generator sequence and occur only once in the scale.
-* The property of having a WFGS of period 2, denoted AGS (''alternating generator sequence'') in this article, is important as it is equivalent to being an odd-regular MV3 scale; see below. It used to be called the "SGA property" in past versions of this article.
+* The property of having a WFGS of period 2, denoted AGS (''alternating generator sequence'') in this article, is important as it is equivalent to being an odd-regular MV3 scale; see below.
 * An ''odd-step'' is a ''k''-step where ''k'' is odd; an ''even-step'' is defined similarly.
 * Given a linear or circular word ''s'' with a step size '''X''', define ''E''<sub>'''X'''</sub>(''s'') as the scale word resulting from deleting all instances of '''X''' from ''s''.