Generator sequence: Difference between revisions
Fix Zarlino sizes: 135/128 subtends 2 and 1 in 24; 3 and 4 in 41; 5 and 6 in 65. See https://gist.github.com/frostburn/38e49973d7d6230934055f3764a0b847 for the verification script. Add more sizes to others. |
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== JI scales obtained from guided generator sequences == | == JI scales obtained from guided generator sequences == | ||
Only CS sizes at least 5 are listed. Todo: check for larger CS sizes. | Only CS sizes at least 5 are listed. Todo: check for larger CS sizes. | ||
* The Zarlino series, GS(5/4, 6/5) = GS(4:5:6): 7, 10, 17, | * The Zarlino series, GS(5/4, 6/5) = GS(4:5:6): 7, 10, 17, 34, 58, 82 | ||
** Other scales with the same GS structure of two thirds adding up to 3/2 share the same CS sizes, including undecimal Zarlino (GS(11/9, 27/22)), and Neogothic Zarlino (GS(14/11, 13/11) with [[364/363]] tempered), although the latter may break at higher sizes depending on how the intervals are tuned. | ** Other scales with the same GS structure of two thirds adding up to 3/2 share the same CS sizes, including undecimal Zarlino (GS(11/9, 27/22)), and Neogothic Zarlino (GS(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, GS(6:7:8): 5, 9, 14, 19, 24, 29 | * The Tas/[[diasem]] series, GS(6:7:8): 5, 9, 14, 19, 24, 29, 53 | ||
* GS(3/2, 14/9): 5, 8, 13, 18 | * GS(3/2, 14/9): 5, 8, 13, 18, 31, 49, 67, 85 | ||
* The Zil series, GS(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 Zil series, GS(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, 43 | ||
* The Porcusmine series, GS(9/5, 50/27): 5, 6, 7, 8, 15, 23, 38, 61, 99 | * The Porcusmine series, GS(9/5, 50/27): 5, 6, 7, 8, 15, 23, 38, 61, 99 | ||
* An unnamed 5-limit Mavila detemper, GS(3/2, 3/2, 64/45): 5, 7, 9, 16, 25 | * An unnamed 5-limit Mavila detemper, GS(3/2, 3/2, 64/45): 5, 7, 9, 16, 25, 84 | ||
* The Rhombi series, GS(14/9, 11/7, 52/33, 81/52): 5, 8, 11, 14, 17, 31, 48, 65 | * The Rhombi series, GS(14/9, 11/7, 52/33, 81/52): 5, 8, 11, 14, 17, 31, 48, 65 | ||
* The Dwyn series: GS(25/24 21/20 22/21 23/22 24/23 21/20 22/21 23/22 24/23): 15, 16, 31, 46 | * The Dwyn series: GS(25/24 21/20 22/21 23/22 24/23 21/20 22/21 23/22 24/23): 15, 16, 31, 46, 77 | ||
* GS(13/11, 16/13, 77/64, 13/11, 16/13, 33/28): 7, 11, 15, 19 | * GS(13/11, 16/13, 77/64, 13/11, 16/13, 33/28): 7, 11, 15, 19 | ||
* A "Magic" detemper, GS(13:16:20:25:31:39): 7, 10, 13, 16, 19, 22, 41 | * A "Magic" detemper, GS(13:16:20:25:31:39): 7, 10, 13, 16, 19, 22, 41 | ||
* GS(30:42:57:80) | * GS(30:42:57:80): 5, 7, 9, 11, 13, 15, 17, 19, 36, 53 | ||
* GS(19/14, 51/38, 23/17, 63/46, 19/14, 51/38, 23/17, 896/621) | * GS(19/14, 51/38, 23/17, 63/46, 19/14, 51/38, 23/17, 896/621): 5, 6, 7, 8, 9, 10, 11, 20 | ||
* A Porcupine detemper, GS(9:10:11:12) | * A Porcupine detemper, GS(9:10:11:12): 5, 6, 7, 8, 15, 22, 29 | ||
* GS(9:10:11:12, 9:10:11:12, 9:10:11, 189/176) | * GS(9:10:11:12, 9:10:11:12, 9:10:11, 189/176): 5, 6, 7, 8, 15, 22 | ||
* A "Bleu" detemper, GS(22:24:26:28:31:33) | * A "Bleu" detemper, GS(22:24:26:28:31:33): 5, 6, 7, 8, 9, 17 | ||
* A Machine detemper, GS(8/7, 9/8, 112/99, 9/8) | * A Machine detemper, GS(8/7, 9/8, 112/99, 9/8): 5, 6, 11, 17, 28, 45 | ||
* A Slendric detemper, GS(8/7, 147/128, 8/7) | * A Slendric detemper, GS(8/7, 147/128, 8/7): 5, 6, 11, 16, 21, 26, 31, 36, 41, 77 | ||
== Ternary scales and WFGS == | == Ternary scales and WFGS == | ||