Generator sequence: Difference between revisions

Line 1:

:''Note: This page is chiefly maintained by Inthar. Terms indicated as idiosyncratic are his coinages, not necessarily Scott Dakota's.''

'''{{PAGENAME}}''' ('''AGS''') is a scale-building procedure first described by [[Scott Dakota]]. The notation AGS(''x''1, ..., ''x''r) denotes a scale-building procedure where a ([[Periodic scale|periodic]]) scale is built by stacking ''x''1 first, ''x''2 second, ..., reducing by the scale's [[equave]] when necessary. An enumerated chord can be used instead for the argument: the chord's steps are the generators, and the chord's stacked end-to-end, e.g. AGS(4:5:6)[7] for [[Zarlino]]. When ''x''r is stacked, we go back to ''x''1 and start stacking ''x''1 again, then ''x''2, ... 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. 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.

'''{{PAGENAME}}''' ('''AGS''') is a scale-building procedure first described by [[Scott Dakota]]. The notation AGS(''x''1, ..., ''x''r) denotes a scale-building procedure where a ([[Periodic scale|periodic]]) scale is built by stacking ''x''1 first, ''x''2 second, ..., reducing by the scale's [[equave]] when necessary. An enumerated chord can be used instead for the argument: the chord's steps are the generators, and the chord's stacked end-to-end, e.g. AGS(4:5:6)[7] for [[Zarlino]], which is syntactic sugar for AGS(5/4, 6/5)[7]. When ''x''r is stacked, we go back to ''x''1 and start stacking ''x''1 again, then ''x''2, ... 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. 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.

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]].

@@ Line 1: / Line 1: @@
 :''Note: This page is chiefly maintained by Inthar. Terms indicated as idiosyncratic are his coinages, not necessarily Scott Dakota's.''
-'''{{PAGENAME}}''' ('''AGS''') is a scale-building procedure first described by [[Scott Dakota]]. The notation 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. An enumerated chord can be used instead for the argument: the chord's steps are the generators, and the chord's stacked end-to-end, e.g. AGS(4:5:6)[7] for [[Zarlino]]. 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. 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.
+'''{{PAGENAME}}''' ('''AGS''') is a scale-building procedure first described by [[Scott Dakota]]. The notation 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. An enumerated chord can be used instead for the argument: the chord's steps are the generators, and the chord's stacked end-to-end, e.g. AGS(4:5:6)[7] for [[Zarlino]], which is syntactic sugar for AGS(5/4, 6/5)[7]. 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. 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.
 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]].