Generator sequence: Difference between revisions

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== 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 ~~and~~ 65~~-forms.~~

* The Zarlino series, AGS(5/4, 6/5): 5, 7, 10, 17, 24, 41, 65

** Other scales with the same AGS structure of two thirds adding up to 3/2 share the same CS sizes, including undecimal Zarlino (AGS(11/9, 27/22)), and Neogothic Zarlino (AGS(14/11, 13/11) with [[364/363]] tempered), although the latter may break at higher sizes depending on how the intervals are tuned.

* The Tas/[[diasem]] series, AGS(7/6, 8/7): 5, 9, 14, 19, 24, ~~and~~ 29~~-forms~~

* The Tas/[[diasem]] series, AGS(7/6, 8/7): 5, 9, 14, 19, 24, 29

* The Tri-Stone series, AGS(3/2, 14/9): 5, 8, 13, ~~and~~ 18~~-forms.~~

* The Tri-Stone series, AGS(3/2, 14/9): 5, 8, 13, 18

* 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.~~

* 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, 24

* The Porcusmine series, AGS(9/5, 50/27): 5, 6, 7, 8, 15, 23, 38, 61, ~~and~~ 99~~-forms.~~

* The Porcusmine series, AGS(9/5, 50/27): 5, 6, 7, 8, 15, 23, 38, 61, 99

* An unnamed 5-limit Mavila detemper, AGS(3/2, 3/2, 64/45): 5, 7, 9, 16, ~~and~~ 25~~-forms.~~

* An unnamed 5-limit Mavila detemper, AGS(3/2, 3/2, 64/45): 5, 7, 9, 16, 25

* The Rhombi series, AGS(14/9, 11/7, 52/33, 81/52): 5, 8, 11, 14, 17, 31, 48, ~~and~~ 65~~-forms.~~

* The Rhombi series, AGS(14/9, 11/7, 52/33, 81/52): 5, 8, 11, 14, 17, 31, 48, 65

* The Dwyn series: AGS(25/24 21/20 22/21 23/22 24/23 21/20 22/21 23/22 24/23): 15, 16, 31, ~~and~~ 46~~-forms.~~

* The Dwyn series: AGS(25/24 21/20 22/21 23/22 24/23 21/20 22/21 23/22 24/23): 15, 16, 31, 46

* AGS(7/5, 19/14, 80/57)

* AGS(19/14, 51/38, 23/17, 63/46, 19/14, 51/38, 23/17, 896/621)

* AGS(13/11, 16/13, 77/64, 13/11, 16/13, 33/28): 7, 11, 15, 19

== Conjectures about AGS scales ==

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 == 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 and 65-forms.
+* The Zarlino series, AGS(5/4, 6/5): 5, 7, 10, 17, 24, 41, 65
 ** Other scales with the same AGS structure of two thirds adding up to 3/2 share the same CS sizes, including undecimal Zarlino (AGS(11/9, 27/22)), and Neogothic Zarlino (AGS(14/11, 13/11) with [[364/363]] tempered), although the latter may break at higher sizes depending on how the intervals are tuned.
-* The Tas/[[diasem]] series, AGS(7/6, 8/7): 5, 9, 14, 19, 24, and 29-forms
+* The Tas/[[diasem]] series, AGS(7/6, 8/7): 5, 9, 14, 19, 24, 29
-* The Tri-Stone series, AGS(3/2, 14/9): 5, 8, 13, and 18-forms.
+* The Tri-Stone series, AGS(3/2, 14/9): 5, 8, 13, 18
-* 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.
+* 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, 24
-* The Porcusmine series, AGS(9/5, 50/27): 5, 6, 7, 8, 15, 23, 38, 61, and 99-forms.
+* The Porcusmine series, AGS(9/5, 50/27): 5, 6, 7, 8, 15, 23, 38, 61, 99
-* An unnamed 5-limit Mavila detemper, AGS(3/2, 3/2, 64/45): 5, 7, 9, 16, and 25-forms.
+* An unnamed 5-limit Mavila detemper, AGS(3/2, 3/2, 64/45): 5, 7, 9, 16, 25
-* The Rhombi series, AGS(14/9, 11/7, 52/33, 81/52): 5, 8, 11, 14, 17, 31, 48, and 65-forms.
+* The Rhombi series, AGS(14/9, 11/7, 52/33, 81/52): 5, 8, 11, 14, 17, 31, 48, 65
-* The Dwyn series: AGS(25/24 21/20 22/21 23/22 24/23 21/20 22/21 23/22 24/23): 15, 16, 31, and 46-forms.
+* The Dwyn series: AGS(25/24 21/20 22/21 23/22 24/23 21/20 22/21 23/22 24/23): 15, 16, 31, 46
 * AGS(7/5, 19/14, 80/57)
 * AGS(19/14, 51/38, 23/17, 63/46, 19/14, 51/38, 23/17, 896/621)
+* AGS(13/11, 16/13, 77/64, 13/11, 16/13, 33/28): 7, 11, 15, 19
 == Conjectures about AGS scales ==