Generator sequence: Difference between revisions

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Certain [[generator-offset property|generator-offset]] scales are examples. For example, [[diasem]] is AGS(8/7, 7/6) or AGS(7/6, 8/7) depending on [[chirality]]. The trivial case AGS(''x'') is stacking a single generator ''x'' to make a rank-2 scale, such as a [[MOS scale]].

== Terminology ==

~~When~~ all generators ''x''''i'' in the AGS recipe AGS(''x''1, ..., ''x''''r'') [[subtend]] the same number of steps (not depending on ''i'')~~, this article calls the resulting scale ''well-formed GS'' (WFGS){{idiosyncratic}}~~. This automatically implies that the leftover interval after stacking len(scale) − 1 of the generators in the recipe (analogous to the imperfect generator in [[MOS]] scales) also subtends this number of steps. In such a situation, we call the (logarithmic) average of the generators the ''guide generator''. The choice of "well-formed" is informed by the well-formed property of single-period MOS scales: the property that each occurrence of the generator subtends the same number of steps.

* Suppose that all generators ''x''''i'' in the AGS recipe AGS(''x''1, ..., ''x''''r'') [[subtend]] the same number of steps (not depending on ''i'').

* This automatically implies that the leftover interval after stacking len(scale) − 1 of the generators in the recipe callwd ''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 in the generator sequence.

When all of the above hold, this article calls the resulting scale ''well-formed GS'' (WFGS){{idiosyncratic}}. In such a situation, we call the (logarithmic) average of the generators the ''guide generator''. The choice of "well-formed" is informed by the well-formed property of single-period MOS scales: the property that each occurrence of the generator subtends the same number of steps.

To exclude the case when the generator is a 1-step or a (len(scale) − 1)-step, the modifier ''non-step''{{idiosyncratic}} can be used.

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 Certain [[generator-offset property|generator-offset]] scales are examples. For example, [[diasem]] is AGS(8/7, 7/6) or AGS(7/6, 8/7) depending on [[chirality]]. The trivial case AGS(''x'') is stacking a single generator ''x'' to make a rank-2 scale, such as a [[MOS scale]].
 == Terminology ==
-When all generators ''x''<sub>''i''</sub> in the AGS recipe AGS(''x''<sub>1</sub>, ..., ''x''<sub>''r''</sub>) [[subtend]] the same number of steps (not depending on ''i''), this article calls the resulting scale ''well-formed GS'' (WFGS){{idiosyncratic}}. This automatically implies that the leftover interval after stacking len(scale) &minus; 1 of the generators in the recipe (analogous to the imperfect generator in [[MOS]] scales) also subtends this number of steps. In such a situation, we call the (logarithmic) average of the generators the ''guide generator''. The choice of "well-formed" is informed by the well-formed property of single-period MOS scales: the property that each occurrence of the generator subtends the same number of steps.
+* Suppose that all generators ''x''<sub>''i''</sub> in the AGS recipe AGS(''x''<sub>1</sub>, ..., ''x''<sub>''r''</sub>) [[subtend]] the same number of steps (not depending on ''i'').
+* This automatically implies that the leftover interval after stacking len(scale) &minus; 1 of the generators in the recipe callwd ''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 in the generator sequence.
+When all of the above hold, this article calls the resulting scale ''well-formed GS'' (WFGS){{idiosyncratic}}. In such a situation, we call the (logarithmic) average of the generators the ''guide generator''. The choice of "well-formed" is informed by the well-formed property of single-period MOS scales: the property that each occurrence of the generator subtends the same number of steps.
 To exclude the case when the generator is a 1-step or a (len(scale) &minus; 1)-step, the modifier ''non-step''{{idiosyncratic}} can be used.