Generator sequence: Difference between revisions

Line 1:

'''{{PAGENAME}}''' ('''AGS''') is a scale-building procedure first described by [[Scott Dakota]]. AGS(x1, ..., xr) denotes a scale-building procedure where a ([[Periodic scale|periodic]]) scale is built by stacking x1 first, x2 second, ..., reducing by the scale's [[equave]] when necessary. When xr is stacked, we go back to x1 and start stacking x1 again, then x2, ... Currently, the study of AGSs is dominated by [[constant structure]] AGS scales, which are obtained by stopping the stacking procedure at scale sizes that yield constant-structure scales.

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(x1) is stacking a single generator x1 to make a rank-2 scale, such as a [[MOS scale]].

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''.

@@ Line 1: / Line 1: @@
 '''{{PAGENAME}}''' ('''AGS''') is a scale-building procedure first described by [[Scott Dakota]]. AGS(x<sub>1</sub>, ..., x<sub>r</sub>) denotes a scale-building procedure where a ([[Periodic scale|periodic]]) scale is built by stacking x<sub>1</sub> first, x<sub>2</sub> second, ..., reducing by the scale's [[equave]] when necessary. When x<sub>r</sub> is stacked, we go back to x<sub>1</sub> and start stacking x<sub>1</sub> again, then x<sub>2</sub>, ... Currently, the study of AGSs is dominated by [[constant structure]] AGS scales, which are obtained by stopping the stacking procedure at scale sizes that yield constant-structure scales.
-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(x1) is stacking a single generator x1 to make a rank-2 scale, such as a [[MOS scale]].
+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''.