Augmented family: Difference between revisions
CompactStar (talk | contribs) No edit summary |
Restore POTE tuning by request |
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: mapping generators: ~5/4, ~3 | : mapping generators: ~5/4, ~3 | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[CTE]]: ~5/4 = 1\3, ~3/2 = 701.9550 | |||
* [[POTE]]: ~5/4 = 1\3, ~3/2 = 706.638 | |||
{{Optimal ET sequence|legend=1| 3, 12, 27, 39, 51c, 90cc }} | {{Optimal ET sequence|legend=1| 3, 12, 27, 39, 51c, 90cc }} | ||
Line 32: | Line 34: | ||
{{Multival|legend=1| 3 0 6 -7 1 14 }} | {{Multival|legend=1| 3 0 6 -7 1 14 }} | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[CTE]]: ~5/4 = 1\3, ~3/2 = 692.1237 | |||
* [[POTE]]: ~5/4 = 1\3, ~3/2 = 696.011 | |||
{{Optimal ET sequence|legend=1| 9, 12, 45cd, 57cd, 69cdd }} | {{Optimal ET sequence|legend=1| 9, 12, 45cd, 57cd, 69cdd }} | ||
Line 45: | Line 49: | ||
Mapping: {{mapping| 3 0 7 -1 1 | 0 1 0 2 2 }} | Mapping: {{mapping| 3 0 7 -1 1 | 0 1 0 2 2 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~5/4 = 1\3, ~3/2 = 687.6853 | |||
* POTE: ~5/4 = 1\3, ~3/2 = 692.514 | |||
{{Optimal ET sequence|legend=1| 9, 12, 21, 33e, 45cde }} | {{Optimal ET sequence|legend=1| 9, 12, 21, 33e, 45cde }} | ||
Line 58: | Line 64: | ||
Mapping: {{mapping| 3 0 7 -1 1 -3 | 0 1 0 2 2 3 }} | Mapping: {{mapping| 3 0 7 -1 1 -3 | 0 1 0 2 2 3 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~5/4 = 1\3, ~3/2 = 685.0836 | |||
* POTE: ~5/4 = 1\3, ~3/2 = 688.783 | |||
{{Optimal ET sequence|legend=1| 9, 12f, 21, 33ef, 54bceeff }} | {{Optimal ET sequence|legend=1| 9, 12f, 21, 33ef, 54bceeff }} | ||
Line 71: | Line 79: | ||
Mapping: {{mapping| 3 0 7 -1 1 11 | 0 1 0 2 2 0 }} | Mapping: {{mapping| 3 0 7 -1 1 11 | 0 1 0 2 2 0 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~5/4 = 1\3, ~3/2 = 687.6853 | |||
* POTE: ~5/4 = 1\3, ~3/2 = 685.356 | |||
{{Optimal ET sequence|legend=1| 9, 12, 21f }} | {{Optimal ET sequence|legend=1| 9, 12, 21f }} | ||
Line 86: | Line 96: | ||
{{Multival|legend=1| 3 0 -6 -7 -18 -14 }} | {{Multival|legend=1| 3 0 -6 -7 -18 -14 }} | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[CTE]]: ~5/4 = 1\3, ~3/2 = 709.5948 | |||
* [[POTE]]: ~5/4 = 1\3, ~3/2 = 709.257 | |||
{{Optimal ET sequence|legend=1| 12, 27, 39d, 66cd }} | {{Optimal ET sequence|legend=1| 12, 27, 39d, 66cd }} | ||
Line 99: | Line 111: | ||
Mapping: {{mapping| 3 0 7 18 20 | 0 1 0 -2 -2 }} | Mapping: {{mapping| 3 0 7 18 20 | 0 1 0 -2 -2 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~5/4 = 1\3, ~3/2 = 713.5701 | |||
* POTE: ~5/4 = 1\3, ~3/2 = 711.177 | |||
{{Optimal ET sequence|legend=1| 12, 15, 27e }} | {{Optimal ET sequence|legend=1| 12, 15, 27e }} | ||
Line 112: | Line 126: | ||
Mapping: {{mapping| 3 0 7 18 20 16 | 0 1 0 -2 -2 -1 }} | Mapping: {{mapping| 3 0 7 18 20 16 | 0 1 0 -2 -2 -1 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~5/4 = 1\3, ~3/2 = 716.1234 | |||
* POTE: ~5/4 = 1\3, ~3/2 = 712.013 | |||
{{Optimal ET sequence|legend=1| 12f, 15, 27eff }} | {{Optimal ET sequence|legend=1| 12f, 15, 27eff }} | ||
Line 125: | Line 141: | ||
Mapping: {{mapping| 3 0 7 18 20 -8 | 0 1 0 -2 -2 4 }} | Mapping: {{mapping| 3 0 7 18 20 -8 | 0 1 0 -2 -2 4 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~5/4 = 1\3, ~3/2 = 711.9020 | |||
* POTE: ~5/4 = 1\3, ~3/2 = 712.609 | |||
{{Optimal ET sequence|legend=1| 12, 15, 27e, 69bceef }} | {{Optimal ET sequence|legend=1| 12, 15, 27e, 69bceef }} | ||
Line 138: | Line 156: | ||
Mapping: {{mapping| 3 0 7 18 20 35 | 0 1 0 -2 -2 -5 }} | Mapping: {{mapping| 3 0 7 18 20 35 | 0 1 0 -2 -2 -5 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~5/4 = 1\3, ~3/2 = 712.5722 | |||
* POTE: ~5/4 = 1\3, ~3/2 = 709.677 | |||
{{Optimal ET sequence|legend=1| 12f, 27e }} | {{Optimal ET sequence|legend=1| 12f, 27e }} | ||
Line 151: | Line 171: | ||
Mapping: {{mapping| 3 0 7 18 -4 | 0 1 0 -2 3 }} | Mapping: {{mapping| 3 0 7 18 -4 | 0 1 0 -2 3 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~5/4 = 1\3, ~3/2 = 713.0025 | |||
* POTE: ~5/4 = 1\3, ~3/2 = 714.150 | |||
{{Optimal ET sequence|legend=1| 12e, 15, 27, 42 }} | {{Optimal ET sequence|legend=1| 12e, 15, 27, 42 }} | ||
Line 170: | Line 192: | ||
{{Multival|legend=1| 3 0 9 -7 6 21 }} | {{Multival|legend=1| 3 0 9 -7 6 21 }} | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[CTE]]: ~5/4 = 1\3, ~3/2 = 717.5172 | |||
* [[POTE]]: ~5/4 = 1\3, ~3/2 = 722.719 | |||
{{Optimal ET sequence|legend=1| 3d, 12d, 15 }} | {{Optimal ET sequence|legend=1| 3d, 12d, 15 }} | ||
Line 183: | Line 207: | ||
Mapping: {{mapping| 3 0 7 -6 -4 | 0 1 0 3 3 }} | Mapping: {{mapping| 3 0 7 -6 -4 | 0 1 0 3 3 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~5/4 = 1\3, ~3/2 = 717.5172 | |||
* POTE: ~5/4 = 1\3, ~3/2 = 722.663 | |||
{{Optimal ET sequence|legend=1| 3de, 12de, 15 }} | {{Optimal ET sequence|legend=1| 3de, 12de, 15 }} | ||
Line 198: | Line 224: | ||
{{Multival|legend=1| 3 0 -3 -7 -13 -7 }} | {{Multival|legend=1| 3 0 -3 -7 -13 -7 }} | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[CTE]]: ~5/4 = 1\3, ~3/2 = 684.8473 | |||
* [[POTE]]: ~5/4 = 1\3, ~3/2 = 681.629 | |||
{{Optimal ET sequence|legend=1| 3, 9 }} | {{Optimal ET sequence|legend=1| 3, 9 }} | ||
Line 211: | Line 239: | ||
Mapping: {{mapping| 3 0 7 13 15 | 0 1 0 -1 -1 }} | Mapping: {{mapping| 3 0 7 13 15 | 0 1 0 -1 -1 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~5/4 = 1\3, ~3/2 = 679.881 | |||
* POTE: ~5/4 = 1\3, ~3/2 = 680.042 | |||
{{Optimal ET sequence|legend=1| 3, 9 }} | {{Optimal ET sequence|legend=1| 3, 9 }} | ||
Line 228: | Line 258: | ||
{{Multival|legend=1| 6 0 0 -14 -17 0 }} | {{Multival|legend=1| 6 0 0 -14 -17 0 }} | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[CTE]]: ~28/25 = 1\6, ~3/2 = 701.9550 | |||
* [[POTE]]: ~28/25 = 1\6, ~3/2 = 710.963 | |||
{{Optimal ET sequence|legend=1| 6, 12, 30d, 42dd, 54cdd }} | {{Optimal ET sequence|legend=1| 6, 12, 30d, 42dd, 54cdd }} | ||
Line 241: | Line 273: | ||
Mapping: {{mapping| 6 0 14 17 21 | 0 1 0 0 0 }} | Mapping: {{mapping| 6 0 14 17 21 | 0 1 0 0 0 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~28/25 = 1\6, ~3/2 = 701.9550 | |||
* POTE: ~28/25 = 1\6, ~3/2 = 714.304 | |||
{{Optimal ET sequence|legend=1| 6, 12, 30dee, 42ddeee }} | {{Optimal ET sequence|legend=1| 6, 12, 30dee, 42ddeee }} | ||
Line 254: | Line 288: | ||
Mapping: {{mapping| 6 0 14 17 21 13 | 0 1 0 0 0 1 }} | Mapping: {{mapping| 6 0 14 17 21 13 | 0 1 0 0 0 1 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~28/25 = 1\6, ~3/2 = 692.4327 | |||
* POTE: ~28/25 = 1\6, ~3/2 = 710.005 | |||
{{Optimal ET sequence|legend=1| 6f, 12f }} | {{Optimal ET sequence|legend=1| 6f, 12f }} | ||
Line 273: | Line 309: | ||
{{Multival|legend=1| 6 0 3 -14 -12 7 }} | {{Multival|legend=1| 6 0 3 -14 -12 7 }} | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[CTE]]: ~5/4 = 1\3, ~7/4 = 952.2948 | |||
* [[POTE]]: ~5/4 = 1\3, ~7/4 = 952.951 | |||
{{Optimal ET sequence|legend=1| 6, 9, 15, 24, 39, 63cd, 102ccdd }} | {{Optimal ET sequence|legend=1| 6, 9, 15, 24, 39, 63cd, 102ccdd }} | ||
Line 286: | Line 324: | ||
Mapping: {{mapping| 3 0 7 6 8 | 0 2 0 1 1 }} | Mapping: {{mapping| 3 0 7 6 8 | 0 2 0 1 1 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~5/4 = 1\3, ~7/4 = 952.2495 | |||
* POTE: ~5/4 = 1\3, ~7/4 = 952.932 | |||
{{Optimal ET sequence|legend=1| 6, 9, 15, 24, 39 }} | {{Optimal ET sequence|legend=1| 6, 9, 15, 24, 39 }} | ||
Line 303: | Line 343: | ||
Mapping: {{mapping| 3 0 7 6 8 4 | 0 2 0 1 1 3 }} | Mapping: {{mapping| 3 0 7 6 8 4 | 0 2 0 1 1 3 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~5/4 = 1\3, ~7/4 = 950.8049 | |||
* POTE: ~5/4 = 1\3, ~7/4 = 951.687 | |||
{{Optimal ET sequence|legend=1| 6, 9, 15, 24 }} | {{Optimal ET sequence|legend=1| 6, 9, 15, 24 }} | ||
Line 321: | Line 363: | ||
: mapping generators: ~44/39, ~7/4 | : mapping generators: ~44/39, ~7/4 | ||
Optimal | Optimal tunings: | ||
* CTE: ~44/39 = 1\6, ~7/4 = 952.5307 | |||
* POTE: ~44/39 = 1\6, ~7/4 = 953.358 | |||
{{Optimal ET sequence|legend=1| 6, 18bd, 24 }} | {{Optimal ET sequence|legend=1| 6, 18bd, 24 }} | ||
Line 338: | Line 382: | ||
{{Multival|legend=1| 6 0 15 -14 7 35 }} | {{Multival|legend=1| 6 0 15 -14 7 35 }} | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[CTE]]: ~5/4 = 1\3, ~14/9 = 752.8335 (~36/35 = 47.1665) | |||
* [[POTE]]: ~5/4 = 1\3, ~14/9 = 754.882 (~36/35 = 45.118) | |||
{{Optimal ET sequence|legend=1| 24, 27 }} | {{Optimal ET sequence|legend=1| 24, 27 }} | ||
Line 351: | Line 397: | ||
Mapping: {{mapping| 3 1 7 -1 1 | 0 2 0 5 5 }} | Mapping: {{mapping| 3 1 7 -1 1 | 0 2 0 5 5 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~5/4 = 1\3, ~14/9 = 752.0512 (~36/35 = 47.9488) | |||
* POTE: ~5/4 = 1\3, ~14/9 = 754.212 (~36/35 = 45.788) | |||
{{Optimal ET sequence|legend=1| 24, 27e, 51ce }} | {{Optimal ET sequence|legend=1| 24, 27e, 51ce }} | ||
Line 364: | Line 412: | ||
Mapping: {{mapping| 3 1 7 -1 1 13 | 0 2 0 5 5 -1 }} | Mapping: {{mapping| 3 1 7 -1 1 13 | 0 2 0 5 5 -1 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~5/4 = 1\3, ~14/9 = 752.1284 (~36/35 = 47.8716) | |||
* POTE: ~5/4 = 1\3, ~14/9 = 753.750 (~36/35 = 46.250) | |||
{{Optimal ET sequence|legend=1| 24, 27e, 51ce }} | {{Optimal ET sequence|legend=1| 24, 27e, 51ce }} | ||
Line 381: | Line 431: | ||
{{Multival|legend=1| 6 0 -9 -14 -31 -21 }} | {{Multival|legend=1| 6 0 -9 -14 -31 -21 }} | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[CTE]]: ~5/4 = 1\3, ~32/21 = 747.9484 (~21/20 = 52.0516) | |||
* [[POTE]]: ~5/4 = 1\3, ~32/21 = 747.907 (~21/20 = 52.093) | |||
{{Optimal ET sequence|legend=1| 21, 24, 45c }} | {{Optimal ET sequence|legend=1| 21, 24, 45c }} | ||
Line 394: | Line 446: | ||
Mapping: {{mapping| 3 1 7 14 16 | 0 2 0 -3 -3 }} | Mapping: {{mapping| 3 1 7 14 16 | 0 2 0 -3 -3 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~5/4 = 1\3, ~32/21 = 748.2962 (~33/32 = 51.7038) | |||
* POTE: ~5/4 = 1\3, ~32/21 = 748.345 (~33/32 = 51.655) | |||
{{Optimal ET sequence|legend=1| 21, 24 }} | {{Optimal ET sequence|legend=1| 21, 24 }} | ||
Line 407: | Line 461: | ||
Mapping: {{mapping| 3 1 7 14 16 13 | 0 2 0 -3 -3 -1 }} | Mapping: {{mapping| 3 1 7 14 16 13 | 0 2 0 -3 -3 -1 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~5/4 = 1\3, ~32/21 = 748.5255 (~33/32 = 51.4745) | |||
* POTE: ~5/4 = 1\3, ~32/21 = 748.452 (~33/32 = 51.548) | |||
{{Optimal ET sequence|legend=1| 21, 24 }} | {{Optimal ET sequence|legend=1| 21, 24 }} | ||
Line 424: | Line 480: | ||
{{Multival|legend=1| 12 0 3 -28 -29 7 }} | {{Multival|legend=1| 12 0 3 -28 -29 7 }} | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[CTE]]: ~5/4 = 1\3, ~28/25 = 175.3586 | |||
* [[POTE]]: ~5/4 = 1\3, ~28/25 = 176.646 | |||
{{Optimal ET sequence|legend=1| 6, 21, 27, 75c, 102ccd, 129bccd }} | {{Optimal ET sequence|legend=1| 6, 21, 27, 75c, 102ccd, 129bccd }} | ||
Line 437: | Line 495: | ||
Mapping: {{mapping| 3 3 7 8 10 | 0 4 0 1 1 }} | Mapping: {{mapping| 3 3 7 8 10 | 0 4 0 1 1 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~5/4 = 1\3, ~11/10 = 175.0533 | |||
* POTE: ~5/4 = 1\3, ~11/10 = 176.981 | |||
{{Optimal ET sequence|legend=1| 6, 21, 27e }} | {{Optimal ET sequence|legend=1| 6, 21, 27e }} | ||
Line 450: | Line 510: | ||
Mapping: {{mapping| 3 3 7 8 10 12 | 0 4 0 1 1 -2 }} | Mapping: {{mapping| 3 3 7 8 10 12 | 0 4 0 1 1 -2 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~5/4 = 1\3, ~11/10 = 175.2524 | |||
* POTE: ~5/4 = 1\3, ~11/10 = 176.551 | |||
{{Optimal ET sequence|legend=1| 6, 21, 27e }} | {{Optimal ET sequence|legend=1| 6, 21, 27e }} | ||
Line 467: | Line 529: | ||
{{Multival|legend=1| 12 0 18 -28 -5 42 }} | {{Multival|legend=1| 12 0 18 -28 -5 42 }} | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[CTE]]: ~54/49 = 1\6, ~45/28 = 853.1901 (~36/35 = 53.1901) | |||
* [[POTE]]: ~54/49 = 1\6, ~45/28 = 855.485 (~36/35 = 55.485) | |||
{{Optimal ET sequence|legend=1| 18, 24, 42 }} | {{Optimal ET sequence|legend=1| 18, 24, 42 }} | ||
Line 480: | Line 544: | ||
Mapping: {{mapping| 6 1 14 4 8 | 0 2 0 3 3 }} | Mapping: {{mapping| 6 1 14 4 8 | 0 2 0 3 3 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~54/49 = 1\6, ~18/11 = 852.5968 (~36/35 = 52.5968) | |||
* POTE: ~54/49 = 1\6, ~18/11 = 855.220 (~36/35 = 55.220) | |||
{{Optimal ET sequence|legend=1| 24, 42e, 66ce, 108bccee }} | {{Optimal ET sequence|legend=1| 24, 42e, 66ce, 108bccee }} | ||
Line 499: | Line 565: | ||
{{Multival|legend=1| 9 0 9 -21 -11 21 }} | {{Multival|legend=1| 9 0 9 -21 -11 21 }} | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[CTE]]: ~49/45 = 1\9, ~3/2 = 702.0044 | |||
* [[POTE]]: ~49/45 = 1\9, ~3/2 = 707.167 | |||
{{Optimal ET sequence|legend=1| 9, 18, 27, 63c, 90cc }} | {{Optimal ET sequence|legend=1| 9, 18, 27, 63c, 90cc }} | ||
Line 512: | Line 580: | ||
Mapping: {{mapping| 9 0 21 11 17 | 0 1 0 1 1 }} | Mapping: {{mapping| 9 0 21 11 17 | 0 1 0 1 1 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~12/11 = 1\9, ~3/2 = 699.6216 | |||
* POTE: ~12/11 = 1\9, ~3/2 = 706.726 | |||
{{Optimal ET sequence|legend=1| 9, 18e, 27e, 63cee }} | {{Optimal ET sequence|legend=1| 9, 18e, 27e, 63cee }} | ||
Line 525: | Line 595: | ||
Mapping: {{mapping| 9 0 21 11 17 19 | 0 1 0 1 1 1 }} | Mapping: {{mapping| 9 0 21 11 17 19 | 0 1 0 1 1 1 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~14/13 = 1\9, ~3/2 = 700.4330 | |||
* POTE: ~14/13 = 1\9, ~3/2 = 706.889 | |||
{{Optimal ET sequence|legend=1| 9, 18e, 27e }} | {{Optimal ET sequence|legend=1| 9, 18e, 27e }} | ||
Line 540: | Line 612: | ||
: mapping generators: ~5/4, ~48/35 | : mapping generators: ~5/4, ~48/35 | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[CTE]]: ~5/4 = 1\3, ~48/35 = 498.6367 | |||
* [[POTE]]: ~5/4 = 1\3, ~48/35 = 501.980 | |||
{{Optimal ET sequence|legend=1| 9bd, 12 }} | {{Optimal ET sequence|legend=1| 9bd, 12 }} | ||
[[Badness]]: 0.138279 | [[Badness]]: 0.138279 | ||
== Ternary == | == Ternary == | ||
Line 558: | Line 631: | ||
{{Multival|legend=1| 0 0 3 0 5 7 }} | {{Multival|legend=1| 0 0 3 0 5 7 }} | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[POTE]]: ~5/4 = 1\3, ~7/4 = 1034.013 | |||
{{Optimal ET sequence|legend=1| 3d, 6, 9bd, 15bbd }} | {{Optimal ET sequence|legend=1| 3d, 6, 9bd, 15bbd }} | ||
Line 571: | Line 645: | ||
Mapping: {{mapping| 3 5 7 0 2 | 0 0 0 1 1 }} | Mapping: {{mapping| 3 5 7 0 2 | 0 0 0 1 1 }} | ||
Optimal | Optimal tunings: | ||
* POTE: ~5/4 = 1\3, ~7/4 = 1033.153 | |||
{{Optimal ET sequence|legend=1| 3de, 6, 15bbdee }} | {{Optimal ET sequence|legend=1| 3de, 6, 15bbdee }} |