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Kleismic family: Difference between revisions

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Line 89: Line 89:
Comma list: 225/224, 385/384, 4375/4374
Comma list: 225/224, 385/384, 4375/4374


Mapping: {{mapping| 1 0 1 -3 9 | 0 6 5 22 -21 }}
{{Mapping|legend=0| 1 0 1 -3 9 | 0 6 5 22 -21 }}


Optimal tunings:  
Optimal tunings:  
Line 108: Line 108:
Comma list: 169/168, 225/224, 325/324, 385/384
Comma list: 169/168, 225/224, 325/324, 385/384


Mapping: {{mapping| 1 0 1 -3 9 0 | 0 6 5 22 -21 14 }}
{{Mapping|legend=0| 1 0 1 -3 9 0 | 0 6 5 22 -21 14 }}


Optimal tunings:  
Optimal tunings:  
Line 127: Line 127:
Comma list: 99/98, 176/175, 2200/2187
Comma list: 99/98, 176/175, 2200/2187


Mapping: {{mapping| 1 0 1 -3 -5 | 0 6 5 22 32 }}
{{Mapping|legend=0| 1 0 1 -3 -5 | 0 6 5 22 32 }}


Optimal tunings:  
Optimal tunings:  
Line 142: Line 142:
Comma list: 99/98, 169/168, 176/175, 275/273
Comma list: 99/98, 169/168, 176/175, 275/273


Mapping: {{mapping| 1 0 1 -3 -5 0 | 0 6 5 22 32 14 }}
{{Mapping|legend=0| 1 0 1 -3 -5 0 | 0 6 5 22 32 14 }}


Optimal tunings:  
Optimal tunings:  
Line 157: Line 157:
Comma list: 225/224, 441/440, 4375/4374
Comma list: 225/224, 441/440, 4375/4374


Mapping: {{mapping| 1 0 1 -3 -10 | 0 6 5 22 51 }}
{{Mapping|legend=0| 1 0 1 -3 -10 | 0 6 5 22 51 }}


Optimal tunings:  
Optimal tunings:  
Line 172: Line 172:
Comma list: 169/168, 225/224, 325/324, 1716/1715
Comma list: 169/168, 225/224, 325/324, 1716/1715


Mapping: {{mapping| 1 0 1 -3 -10 0 | 0 6 5 22 51 14 }}
{{Mapping|legend=0| 1 0 1 -3 -10 0 | 0 6 5 22 51 14 }}


Optimal tunings:  
Optimal tunings:  
Line 187: Line 187:
Comma list: 100/99, 225/224, 864/847
Comma list: 100/99, 225/224, 864/847


Mapping: {{mapping| 1 0 1 -3 4 | 0 6 5 22 -2 }}
{{Mapping|legend=0| 1 0 1 -3 4 | 0 6 5 22 -2 }}


Optimal tunings:  
Optimal tunings:  
Line 202: Line 202:
Comma list: 78/77, 100/99, 144/143, 676/675
Comma list: 78/77, 100/99, 144/143, 676/675


Mapping: {{mapping| 1 0 1 -3 4 0 | 0 6 5 22 -2 14 }}
{{Mapping|legend=0| 1 0 1 -3 4 0 | 0 6 5 22 -2 14 }}


Optimal tunings:  
Optimal tunings:  
Line 217: Line 217:
Comma list: 225/224, 243/242, 4375/4356
Comma list: 225/224, 243/242, 4375/4356


Mapping: {{mapping| 2 0 2 -6 -1 | 0 6 5 22 15 }}
{{Mapping|legend=0| 2 0 2 -6 -1 | 0 6 5 22 15 }}
: mapping generators: ~99/70, ~6/5
: mapping generators: ~99/70, ~6/5


Line 233: Line 233:
Comma list: 169/168, 225/224, 243/242, 325/324
Comma list: 169/168, 225/224, 243/242, 325/324


Mapping: {{mapping| 2 0 2 -6 -1 0 | 0 6 5 22 15 14 }}
{{Mapping|legend=0| 2 0 2 -6 -1 0 | 0 6 5 22 15 14 }}


Optimal tunings:  
Optimal tunings:  
Line 248: Line 248:
Comma list: 169/168, 221/220, 225/224, 243/242, 325/324
Comma list: 169/168, 221/220, 225/224, 243/242, 325/324


Mapping: {{mapping| 2 0 2 -6 -1 0 5 | 0 6 5 22 15 14 6 }}
{{Mapping|legend=0| 2 0 2 -6 -1 0 5 | 0 6 5 22 15 14 6 }}


Optimal tunings:  
Optimal tunings:  
Line 263: Line 263:
Comma list: 153/152, 169/168, 221/220, 225/224, 243/242, 325/324
Comma list: 153/152, 169/168, 221/220, 225/224, 243/242, 325/324


Mapping: {{mapping| 2 0 2 -6 -1 0 5 -1 | 0 6 5 22 15 14 6 18 }}
{{Mapping|legend=0| 2 0 2 -6 -1 0 5 -1 | 0 6 5 22 15 14 6 18 }}


Optimal tunings:  
Optimal tunings:  
Line 302: Line 302:
Comma list: 49/48, 56/55, 100/99
Comma list: 49/48, 56/55, 100/99


Mapping: {{mapping| 1 0 1 2 4 | 0 6 5 3 -2 }}
{{Mapping|legend=0| 1 0 1 2 4 | 0 6 5 3 -2 }}


Optimal tunings:  
Optimal tunings:  
Line 321: Line 321:
Comma list: 49/48, 56/55, 65/64, 100/99
Comma list: 49/48, 56/55, 65/64, 100/99


Mapping: {{mapping| 1 0 1 2 4 5 | 0 6 5 3 -2 -5 }}
{{Mapping|legend=0| 1 0 1 2 4 5 | 0 6 5 3 -2 -5 }}


Optimal tunings:  
Optimal tunings:  
Line 340: Line 340:
Comma list: 49/48, 56/55, 91/90, 100/99
Comma list: 49/48, 56/55, 91/90, 100/99


Mapping: {{mapping| 1 0 1 2 4 0 | 0 6 5 3 -2 14 }}
{{Mapping|legend=0| 1 0 1 2 4 0 | 0 6 5 3 -2 14 }}


Optimal tunings:  
Optimal tunings:  
Line 360: Line 360:
Comma list: 40/39, 49/48, 56/55, 66/65
Comma list: 40/39, 49/48, 56/55, 66/65


Mapping: {{mapping| 1 0 1 2 4 4 | 0 6 5 3 -2 -1 }}
{{Mapping|legend=0| 1 0 1 2 4 4 | 0 6 5 3 -2 -1 }}


Optimal tunings:  
Optimal tunings:  
Line 375: Line 375:
Comma list: 45/44, 49/48, 126/125
Comma list: 45/44, 49/48, 126/125


Mapping: {{mapping| 1 0 1 2 -1 | 0 6 5 3 17 }}
{{Mapping|legend=0| 1 0 1 2 -1 | 0 6 5 3 17 }}


Optimal tunings:  
Optimal tunings:  
Line 390: Line 390:
Comma list: 45/44, 49/48, 78/77, 126/125
Comma list: 45/44, 49/48, 78/77, 126/125


Mapping: {{mapping| 1 0 1 2 -1 0 | 0 6 5 3 17 14 }}
{{Mapping|legend=0| 1 0 1 2 -1 0 | 0 6 5 3 17 14 }}


Optimal tunings:  
Optimal tunings:  
Line 405: Line 405:
Comma list: 49/48, 55/54, 77/75
Comma list: 49/48, 55/54, 77/75


Mapping: {{mapping| 1 0 1 2 0 | 0 6 5 3 13 }}
{{Mapping|legend=0| 1 0 1 2 0 | 0 6 5 3 13 }}


Optimal tunings:  
Optimal tunings:  
Line 420: Line 420:
Comma list: 49/48, 55/54, 66/65, 77/75
Comma list: 49/48, 55/54, 66/65, 77/75


Mapping: {{mapping| 1 0 1 2 0 0 | 0 6 5 3 13 14 }}
{{Mapping|legend=0| 1 0 1 2 0 0 | 0 6 5 3 13 14 }}


Optimal tunings:  
Optimal tunings:  
Line 456: Line 456:
Comma list: 64/63, 100/99, 1331/1323
Comma list: 64/63, 100/99, 1331/1323


Mapping: {{mapping| 1 0 1 6 4 | 0 6 5 -12 -2 }}
{{Mapping|legend=0| 1 0 1 6 4 | 0 6 5 -12 -2 }}


Optimal tunings:  
Optimal tunings:  
Line 475: Line 475:
Comma list: 64/63, 100/99, 144/143, 275/273
Comma list: 64/63, 100/99, 144/143, 275/273


Mapping: {{mapping| 1 0 1 6 4 0 | 0 6 5 -12 -2 14 }}
{{Mapping|legend=0| 1 0 1 6 4 0 | 0 6 5 -12 -2 14 }}


Optimal tunings:  
Optimal tunings:  
Line 511: Line 511:
Comma list: 385/384, 2200/2187, 3388/3375
Comma list: 385/384, 2200/2187, 3388/3375


Mapping: {{mapping| 1 0 1 11 -5 | 0 6 5 -31 32 }}
{{Mapping|legend=0| 1 0 1 11 -5 | 0 6 5 -31 32 }}


Optimal tunings:  
Optimal tunings:  
Line 530: Line 530:
Comma list: 325/324, 352/351, 385/384, 625/624
Comma list: 325/324, 352/351, 385/384, 625/624


Mapping: {{mapping| 1 0 1 11 -5 0 | 0 6 5 -31 32 14 }}
{{Mapping|legend=0| 1 0 1 11 -5 0 | 0 6 5 -31 32 14 }}


Optimal tunings:  
Optimal tunings:  
Line 567: Line 567:
Comma list: 896/891, 2200/2187, 14700/14641
Comma list: 896/891, 2200/2187, 14700/14641


Mapping: {{mapping| 1 0 1 -12 -5 | 0 6 5 56 32 }}
{{Mapping|legend=0| 1 0 1 -12 -5 | 0 6 5 56 32 }}


Optimal tunings:  
Optimal tunings:  
Line 582: Line 582:
Comma list: 325/324, 352/351, 364/363, 625/624
Comma list: 325/324, 352/351, 364/363, 625/624


Mapping: {{mapping| 1 0 1 -12 -5 0 | 0 6 5 56 32 14 }}
{{Mapping|legend=0| 1 0 1 -12 -5 0 | 0 6 5 56 32 14 }}


Optimal tunings:  
Optimal tunings:  
Line 615: Line 615:
Comma list: 121/120, 176/175, 4000/3969
Comma list: 121/120, 176/175, 4000/3969


Mapping: {{mapping| 1 0 1 4 2 | 0 12 10 -9 11 }}
{{Mapping|legend=0| 1 0 1 4 2 | 0 12 10 -9 11 }}


Optimal tunings:  
Optimal tunings:  
Line 630: Line 630:
Comma list: 121/120, 176/175, 275/273, 325/324
Comma list: 121/120, 176/175, 275/273, 325/324


Mapping: {{mapping| 1 0 1 4 2 0 | 0 12 10 -9 11 28 }}
{{Mapping|legend=0| 1 0 1 4 2 0 | 0 12 10 -9 11 28 }}


Optimal tunings:  
Optimal tunings:  
Line 670: Line 670:
Comma list: 245/243, 385/384, 3136/3125
Comma list: 245/243, 385/384, 3136/3125


Mapping: {{mapping| 1 -6 -4 -13 18 | 0 12 10 25 -23 }}
{{Mapping|legend=0| 1 -6 -4 -13 18 | 0 12 10 25 -23 }}


Optimal tunings:  
Optimal tunings:  
Line 685: Line 685:
Comma list: 196/195, 245/243, 385/384, 625/624
Comma list: 196/195, 245/243, 385/384, 625/624


Mapping: {{mapping| 1 -6 -4 -13 18 -14 | 0 12 10 25 -23 28 }}
{{Mapping|legend=0| 1 -6 -4 -13 18 -14 | 0 12 10 25 -23 28 }}


Optimal tunings:  
Optimal tunings:  
Line 729: Line 729:
Comma list: 385/384, 441/440, 4000/3993
Comma list: 385/384, 441/440, 4000/3993


Mapping: {{mapping| 3 0 3 10 8 | 0 6 5 -2 3 }}
{{Mapping|legend=0| 3 0 3 10 8 | 0 6 5 -2 3 }}


Optimal tunings:  
Optimal tunings:  
Line 749: Line 749:
Comma list: 325/324, 364/363, 385/384, 625/624
Comma list: 325/324, 364/363, 385/384, 625/624


Mapping: {{mapping| 3 0 3 10 8 0 | 0 6 5 -2 3 14 }}
{{Mapping|legend=0| 3 0 3 10 8 0 | 0 6 5 -2 3 14 }}


Optimal tunings:  
Optimal tunings:  
Line 764: Line 764:
Comma list: 273/272, 325/324, 364/363, 375/374, 385/384
Comma list: 273/272, 325/324, 364/363, 375/374, 385/384


Mapping: {{mapping| 3 0 3 10 8 0 -2 | 0 6 5 -2 3 14 18 }}
{{Mapping|legend=0| 3 0 3 10 8 0 -2 | 0 6 5 -2 3 14 18 }}


Optimal tunings:  
Optimal tunings:  
Line 799: Line 799:
Comma list: 385/384, 6250/6237, 10976/10935
Comma list: 385/384, 6250/6237, 10976/10935


Mapping: {{mapping| 1 -6 -4 -17 22 | 0 18 15 47 -44 }}
{{Mapping|legend=0| 1 -6 -4 -17 22 | 0 18 15 47 -44 }}


Optimal tunings:  
Optimal tunings:  
Line 814: Line 814:
Comma list: 325/324, 385/384, 625/624, 10976/10935
Comma list: 325/324, 385/384, 625/624, 10976/10935


Mapping: {{mapping| 1 -6 -4 -17 22 -14 | 0 18 15 47 -44 42 }}
{{Mapping|legend=0| 1 -6 -4 -17 22 -14 | 0 18 15 47 -44 42 }}


Optimal tunings:  
Optimal tunings:  
Line 831: Line 831:
Comma list: 1375/1372, 2200/2187, 5632/5625
Comma list: 1375/1372, 2200/2187, 5632/5625


Mapping: {{mapping| 1 -6 -4 -17 -37 | 0 18 15 47 96 }}
{{Mapping|legend=0| 1 -6 -4 -17 -37 | 0 18 15 47 96 }}


Optimal tunings:  
Optimal tunings:  
Line 846: Line 846:
Comma list: 325/324, 352/351, 625/624, 1375/1372
Comma list: 325/324, 352/351, 625/624, 1375/1372


Mapping: {{mapping| 1 -6 -4 -17 -37 -14 | 0 18 15 47 96 42 }}
{{Mapping|legend=0| 1 -6 -4 -17 -37 -14 | 0 18 15 47 96 42 }}


Optimal tunings:  
Optimal tunings:  
Line 863: Line 863:
Comma list: 540/539, 896/891, 15625/15552
Comma list: 540/539, 896/891, 15625/15552


Mapping: {{mapping| 1 -6 -4 -17 14 | 0 18 15 47 -25 }}
{{Mapping|legend=0| 1 -6 -4 -17 14 | 0 18 15 47 -25 }}


Optimal tunings:  
Optimal tunings:  
Line 878: Line 878:
Comma list: 325/324, 540/539, 625/624, 896/891
Comma list: 325/324, 540/539, 625/624, 896/891


Mapping: {{mapping| 1 -6 -4 -17 14 -14 | 0 18 15 47 -25 42 }}
{{Mapping|legend=0| 1 -6 -4 -17 14 -14 | 0 18 15 47 -25 42 }}


Optimal tunings:  
Optimal tunings:  
Line 911: Line 911:
Comma list: 176/175, 540/539, 3125/3087
Comma list: 176/175, 540/539, 3125/3087


Mapping: {{mapping| 1 -12 -9 -7 -29 | 0 18 15 13 43 }}
{{Mapping|legend=0| 1 -12 -9 -7 -29 | 0 18 15 13 43 }}


Optimal tunings:  
Optimal tunings:  
Line 926: Line 926:
Comma list: 176/175, 275/273, 325/324, 540/539
Comma list: 176/175, 275/273, 325/324, 540/539


Mapping: {{mapping| 1 -12 -9 -7 -29 -28 | 0 18 15 13 43 42 }}
{{Mapping|legend=0| 1 -12 -9 -7 -29 -28 | 0 18 15 13 43 42 }}


Optimal tunings:  
Optimal tunings:  
Line 959: Line 959:
Comma list: 385/384, 1375/1372, 6250/6237
Comma list: 385/384, 1375/1372, 6250/6237


Mapping: {{mapping| 4 0 4 7 17 | 0 6 5 4 -3 }}
{{Mapping|legend=0| 4 0 4 7 17 | 0 6 5 4 -3 }}


Optimal tunings:  
Optimal tunings:  
Line 974: Line 974:
Comma list: 325/324, 385/384, 625/624, 1375/1372
Comma list: 325/324, 385/384, 625/624, 1375/1372


Mapping: {{mapping| 4 0 4 7 17 0 | 0 6 5 4 -3 14 }}
{{Mapping|legend=0| 4 0 4 7 17 0 | 0 6 5 4 -3 14 }}


Optimal tunings:  
Optimal tunings:  
Line 989: Line 989:
Comma list: 289/288, 325/324, 385/384, 442/441, 625/624
Comma list: 289/288, 325/324, 385/384, 442/441, 625/624


Mapping: {{mapping| 4 0 4 7 17 0 10 | 0 6 5 4 -3 14 6 }}
{{Mapping|legend=0| 4 0 4 7 17 0 10 | 0 6 5 4 -3 14 6 }}


Optimal tunings:  
Optimal tunings:  
Line 1,024: Line 1,024:
Comma list: 1375/1372, 15625/15552, 19712/19683
Comma list: 1375/1372, 15625/15552, 19712/19683


Mapping: {{mapping| 1 -6 -4 -19 -43 | 0 24 20 69 147 }}
{{Mapping|legend=0| 1 -6 -4 -19 -43 | 0 24 20 69 147 }}


Optimal tunings:  
Optimal tunings:  
Line 1,039: Line 1,039:
Comma list: 325/324, 625/624, 1375/1372, 19712/19683
Comma list: 325/324, 625/624, 1375/1372, 19712/19683


Mapping: {{mapping| 1 -6 -4 -19 -43 -14 | 0 24 20 69 147 56 }}
{{Mapping|legend=0| 1 -6 -4 -19 -43 -14 | 0 24 20 69 147 56 }}


Optimal tunings:  
Optimal tunings:  
Line 1,078: Line 1,078:
Comma list: 540/539, 1375/1372, 4375/4356
Comma list: 540/539, 1375/1372, 4375/4356


Mapping: {{mapping| 1 -18 -14 -22 -22 | 0 30 25 38 39 }}
{{Mapping|legend=0| 1 -18 -14 -22 -22 | 0 30 25 38 39 }}


Optimal tunings:  
Optimal tunings:  
Line 1,093: Line 1,093:
Comma list: 325/324, 364/363, 625/624, 1375/1372
Comma list: 325/324, 364/363, 625/624, 1375/1372


Mapping: {{mapping| 1 -18 -14 -22 -22 -42 | 0 30 25 38 39 70 }}
{{Mapping|legend=0| 1 -18 -14 -22 -22 -42 | 0 30 25 38 39 70 }}


Optimal tunings:  
Optimal tunings:  
Line 1,108: Line 1,108:
Comma list: 325/324, 364/363, 375/374, 540/539, 595/594
Comma list: 325/324, 364/363, 375/374, 540/539, 595/594


Mapping: {{mapping| 1 -18 -14 -22 -22 -42 -39 | 0 30 25 38 39 70 66 }}
{{Mapping|legend=0| 1 -18 -14 -22 -22 -42 -39 | 0 30 25 38 39 70 66 }}


Optimal tunings:  
Optimal tunings:  
Line 1,123: Line 1,123:
Comma list: 325/324, 364/363, 375/374, 400/399, 442/441, 595/594
Comma list: 325/324, 364/363, 375/374, 400/399, 442/441, 595/594


Mapping: {{mapping| 1 -18 -14 -22 -22 -42 -39 16 | 0 30 25 38 39 70 66 -18 }}
{{Mapping|legend=0| 1 -18 -14 -22 -22 -42 -39 16 | 0 30 25 38 39 70 66 -18 }}


Optimal tunings:  
Optimal tunings:  
Line 1,158: Line 1,158:
Comma list: 385/384, 6250/6237, 67228/66825
Comma list: 385/384, 6250/6237, 67228/66825


Mapping: {{mapping| 1 0 1 1 5 | 0 36 30 41 -35 }}
{{Mapping|legend=0| 1 0 1 1 5 | 0 36 30 41 -35 }}


Optimal tunings:  
Optimal tunings:  
Line 1,173: Line 1,173:
Comma list: 325/324, 385/384, 625/624, 16807/16731
Comma list: 325/324, 385/384, 625/624, 16807/16731


Mapping: {{mapping| 1 0 1 1 5 0 | 0 36 30 41 -35 84 }}
{{Mapping|legend=0| 1 0 1 1 5 0 | 0 36 30 41 -35 84 }}


Optimal tunings:  
Optimal tunings:  
Line 1,206: Line 1,206:
Comma list: 1375/1372, 4000/3993, 15625/15552
Comma list: 1375/1372, 4000/3993, 15625/15552


Mapping: {{mapping| 9 0 9 11 24 | 0 6 5 6 3 }}
{{Mapping|legend=0| 9 0 9 11 24 | 0 6 5 6 3 }}


Optimal tunings:  
Optimal tunings:  
Line 1,221: Line 1,221:
Comma list: 325/324, 625/624, 1375/1372, 4000/3993
Comma list: 325/324, 625/624, 1375/1372, 4000/3993


Mapping: {{mapping| 9 0 9 11 24 0 | 0 6 5 6 3 14 }}
{{Mapping|legend=0| 9 0 9 11 24 0 | 0 6 5 6 3 14 }}


Optimal tunings:  
Optimal tunings:  
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