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]].

== Other definitions ==

* When all generators xi in the AGS recipe AGS(x1, ..., xr), and the leftover interval after stacking ''n'' − 1 of the generators in the recipe (analogous to the imperfect generator in [[~~mos~~]]~~ses~~), [[subtend]] the same number of steps, we call the resulting scale ''well-formed AGS''. In such a situation, we call the (logarithmic) average of the generators the ''guide generator''.

* When all generators xi in the AGS recipe AGS(x1, ..., xr), and the leftover interval after stacking ''n'' − 1 of the generators in the recipe (analogous to the imperfect generator in [[MOS]] scales), [[subtend]] the same number of steps, we call the resulting scale ''well-formed AGS''. In such a situation, we call the (logarithmic) average of the generators the ''guide generator''.

== AGS scale series ==

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== Conjectures about AGS scales ==

* Let ''n'' be the cardinality of a well-formed AGS scale ''S'' with equave E. Then ''n'' is the cardinality of an E-equivalent [[primitive]] ~~mos~~ generated by the guide generator of ''S''.

* Let ''n'' be the cardinality of a well-formed AGS scale ''S'' with equave E. Then ''n'' is the cardinality of an E-equivalent [[primitive]] MOS generated by the guide generator of ''S''.

[[Category:Terms]]

[[Category:Scale]]

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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]].
 == Other definitions ==
-* When all generators x<sub>i</sub> in the AGS recipe AGS(x<sub>1</sub>, ..., x<sub>r</sub>), and the leftover interval after stacking ''n'' &minus; 1 of the generators in the recipe (analogous to the imperfect generator in [[mos]]ses), [[subtend]] the same number of steps, we call the resulting scale ''well-formed AGS''. In such a situation, we call the (logarithmic) average of the generators the ''guide generator''.
+* When all generators x<sub>i</sub> in the AGS recipe AGS(x<sub>1</sub>, ..., x<sub>r</sub>), and the leftover interval after stacking ''n'' &minus; 1 of the generators in the recipe (analogous to the imperfect generator in [[MOS]] scales), [[subtend]] the same number of steps, we call the resulting scale ''well-formed AGS''. In such a situation, we call the (logarithmic) average of the generators the ''guide generator''.
 == AGS scale series ==
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 == Conjectures about AGS scales ==
-* Let ''n'' be the cardinality of a well-formed AGS scale ''S'' with equave E. Then ''n'' is the cardinality of an E-equivalent [[primitive]] mos generated by the guide generator of ''S''.
+* Let ''n'' be the cardinality of a well-formed AGS scale ''S'' with equave E. Then ''n'' is the cardinality of an E-equivalent [[primitive]] MOS generated by the guide generator of ''S''.
 [[Category:Terms]]
 [[Category:Scale]]