Generator sequence: Difference between revisions

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The notation GS(''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. When ''x''''r'' is stacked, we go back to ''x''1 and start stacking ''x''1 again, then ''x''2, ... This article adopts a convention where an enumerated chord can be used instead for part or whole of the argument, where the chord's steps are generators, for example writing [[Zarlino]] as GS(4:5:6)[7], which is syntactic sugar for GS(5/4, 6/5)[7].

Currently, the study of GSs is dominated by certain [[constant structure]] GS scales, called ''guided generator sequence'' scales, which are obtained by taking a GS of detempered MOS generators and stopping the stacking procedure at the ~~correspondibg~~ MOS scale sizes, which yields constant scales. In such a situation, we call the (logarithmic) average of the generators the ''guide generator''.

Currently, the study of GSs is dominated by certain [[constant structure]] GS scales, called ''guided generator sequence'' scales, which are obtained by taking a GS of detempered MOS generators and stopping the stacking procedure at the corresponding MOS scale sizes, which yields constant scales. In such a situation, we call the (logarithmic) average of the generators the ''guide generator''.

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

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 The notation GS(''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>, ... This article adopts a convention where an enumerated chord can be used instead for part or whole of the argument, where the chord's steps are generators, for example writing [[Zarlino]] as GS(4:5:6)[7], which is syntactic sugar for GS(5/4, 6/5)[7].
-Currently, the study of GSs is dominated by certain [[constant structure]] GS scales, called ''guided generator sequence'' scales, which are obtained by taking a GS of detempered MOS generators and stopping the stacking procedure at the correspondibg MOS scale sizes, which yields constant scales. In such a situation, we call the (logarithmic) average of the generators the ''guide generator''.
+Currently, the study of GSs is dominated by certain [[constant structure]] GS scales, called ''guided generator sequence'' scales, which are obtained by taking a GS of detempered MOS generators and stopping the stacking procedure at the corresponding MOS scale sizes, which yields constant scales. In such a situation, we call the (logarithmic) average of the generators the ''guide generator''.
 Certain [[generator-offset property|generator-offset]] scales are examples. For example, [[diasem]] is GS(8/7, 7/6) or GS(7/6, 8/7) depending on [[chirality]]. The trivial case GS(''x'') is stacking a single generator ''x'' to make a rank-2 scale, such as a [[MOS scale]].