Generator sequence: Difference between revisions
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'''{{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 | '''{{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 x1 first, x2 second, ..., reducing by the equave when necessary. When xr 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 scales 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(x1) is stacking a single generator x1 to make a rank-2 scale, such as a [[MOS scale]]. | ||
Revision as of 03:00, 14 July 2023
Generator sequence (AGS) is a scale-building procedure first described by Scott Dakota. AGS(x1, ..., xr) denotes a scale-building procedure where a (periodic) scale is built by stacking x1 first, x2 second, ..., reducing by the 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 scales obtained by stopping the stacking procedure at scale sizes that yield constant-structure scales.
Certain 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.
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 mosses), 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
Only CS sizes at least 5 are listed.
- The Zarlino series, AGS(5/4, 6/5): 5, 7, 10, 17, 24, 41, 65-forms
- The Tas/diasem series, AGS(7/6, 8/7): 5, 9, 14, 19, 24, and 29-forms
- AGS(3/2, 14/9): 5, 8, 13, and 18-forms.
- The Zil series, AGS(8/7, 7/6, 8/7, 7/6, 8/7, 7/6, 8/7, 189/160, 8/7, 7/6): 5, 9, 14, 19, and 24-forms.