Diaschismic family: Difference between revisions
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==== Subgroup extensions ==== | ==== Subgroup extensions ==== | ||
Since the diaschisma factors into ([[256/255]])<sup>2</sup>([[289/288]]) in the 17-limit, it extends naturally to the 2.3.5.17 subgroup as ''srutal archagall'', considered in [[#Subgroup extensions_2|#Subgroup extensions]]. The [[S-expression]]-based comma list of this temperament is {[[256/255|S16]], [[289/288|S17]]}. | Since the diaschisma factors into ([[256/255]])<sup>2</sup>([[289/288]]) in the 17-limit, it extends naturally to the 2.3.5.17 subgroup as ''srutal archagall'', considered in [[#Subgroup extensions_2|#Subgroup extensions]]. The [[S-expression]]-based comma list of this temperament is {[[256/255|S16]], [[289/288|S17]]}. | ||
More generally, one may note that since the fifth of diaschismic is sharp in any good tuning, it is compatible with the logic of [[parapyth]] in making ~13/11 a minor third and ~14/11 a major third, leading to the rank-3 temperament [[varda]], which multiple temps here are rank-2 tunings of, such as 17-limit diaschismic and srutal (and their obvious extensions to prime 23, na"naa' and srutaloo, both by mapping ~23/16 as an augmented fourth aka. tritone). | |||
== Septimal diaschismic == | == Septimal diaschismic == | ||
| Line 80: | Line 82: | ||
Comma list: 126/125, 176/175, 896/891 | Comma list: 126/125, 176/175, 896/891 | ||
{{Mapping|legend=0| 2 0 11 31 45 | 0 1 -2 -8 -12 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 99: | Line 101: | ||
Comma list: 126/125, 176/175, 196/195, 364/363 | Comma list: 126/125, 176/175, 196/195, 364/363 | ||
{{Mapping|legend=0| 2 0 11 31 45 55 | 0 1 -2 -8 -12 -15 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 119: | Line 121: | ||
Comma list: 126/125, 136/135, 176/175, 196/195, 256/255 | Comma list: 126/125, 136/135, 176/175, 196/195, 256/255 | ||
{{Mapping|legend=0| 2 0 11 31 45 55 5 | 0 1 -2 -8 -12 -15 1 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 140: | Line 142: | ||
Comma list: 126/125, 136/135, 176/175, 196/195, 231/230, 256/255 | Comma list: 126/125, 136/135, 176/175, 196/195, 231/230, 256/255 | ||
{{Mapping|legend=2| 2 0 11 31 45 55 5 63 | 0 1 -2 -8 -12 -15 1 -17 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 182: | Line 184: | ||
Comma list: 50/49, 64/63, 85/84 | Comma list: 50/49, 64/63, 85/84 | ||
{{Mapping|legend=0| 2 0 11 12 5 | 0 1 -2 -2 1 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 197: | Line 199: | ||
Comma list: 50/49, 64/63, 99/98 | Comma list: 50/49, 64/63, 99/98 | ||
{{Mapping|legend=0| 2 0 11 12 26 | 0 1 -2 -2 -6 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 216: | Line 218: | ||
Comma list: 50/49, 64/63, 85/84, 99/98 | Comma list: 50/49, 64/63, 85/84, 99/98 | ||
{{Mapping|legend=0| 2 0 11 12 26 5 | 0 1 -2 -2 -6 1 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 231: | Line 233: | ||
Comma list: 50/49, 64/63, 65/63, 99/98 | Comma list: 50/49, 64/63, 65/63, 99/98 | ||
{{Mapping|legend=0| 2 0 11 12 26 1 | 0 1 -2 -2 -6 2 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 246: | Line 248: | ||
Comma list: 50/49, 52/51, 64/63, 65/63, 99/98 | Comma list: 50/49, 52/51, 64/63, 65/63, 99/98 | ||
{{Mapping|legend=0| 2 0 11 12 26 1 5 | 0 1 -2 -2 -6 2 1 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 261: | Line 263: | ||
Comma list: 50/49, 64/63, 78/77, 99/98 | Comma list: 50/49, 64/63, 78/77, 99/98 | ||
{{Mapping|legend=0| 2 0 11 12 26 36 | 0 1 -2 -2 -6 -9 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 276: | Line 278: | ||
Comma list: 50/49, 64/63, 78/77, 85/84, 99/98 | Comma list: 50/49, 64/63, 78/77, 85/84, 99/98 | ||
{{Mapping|legend=0| 2 0 11 12 26 36 5 | 0 1 -2 -2 -6 -9 1 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 291: | Line 293: | ||
Comma list: 40/39, 50/49, 64/63, 66/65 | Comma list: 40/39, 50/49, 64/63, 66/65 | ||
{{Mapping|legend=0| 2 0 11 12 26 17 | 0 1 -2 -2 -6 -3 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 306: | Line 308: | ||
Comma list: 40/39, 50/49, 64/63, 66/65, 85/84 | Comma list: 40/39, 50/49, 64/63, 66/65, 85/84 | ||
{{Mapping|legend=0| 2 0 11 12 26 17 5 | 0 1 -2 -2 -6 -3 1 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 321: | Line 323: | ||
Comma list: 50/49, 55/54, 64/63 | Comma list: 50/49, 55/54, 64/63 | ||
{{Mapping|legend=0| 2 0 11 12 -9 | 0 1 -2 -2 5 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 340: | Line 342: | ||
Comma list: 50/49, 52/51, 55/54, 64/63, 65/63 | Comma list: 50/49, 52/51, 55/54, 64/63, 65/63 | ||
{{Mapping|legend=0| 2 0 11 12 -9 1 5 | 0 1 -2 -2 5 2 1 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 355: | Line 357: | ||
Comma list: 50/49, 55/54, 64/63, 65/63 | Comma list: 50/49, 55/54, 64/63, 65/63 | ||
{{Mapping|legend=0| 2 0 11 12 -9 1 | 0 1 -2 -2 5 2 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 370: | Line 372: | ||
Comma list: 50/49, 52/51, 55/54, 64/63, 65/63 | Comma list: 50/49, 52/51, 55/54, 64/63, 65/63 | ||
{{Mapping|legend=0| 2 0 11 12 -9 1 5 | 0 1 -2 -2 5 2 1 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 385: | Line 387: | ||
Comma list: 40/39, 50/49, 55/54, 64/63 | Comma list: 40/39, 50/49, 55/54, 64/63 | ||
{{Mapping|legend=0| 2 0 11 12 -9 17 | 0 1 -2 -2 5 -3 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 400: | Line 402: | ||
Comma list: 40/39, 50/49, 55/54, 64/63, 85/84 | Comma list: 40/39, 50/49, 55/54, 64/63, 85/84 | ||
{{Mapping|legend=0| 2 0 11 12 -9 17 5 | 0 1 -2 -2 5 -3 1 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 415: | Line 417: | ||
Comma list: 45/44, 50/49, 56/55 | Comma list: 45/44, 50/49, 56/55 | ||
{{Mapping|legend=0| 2 0 11 12 7 | 0 1 -2 -2 0 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 430: | Line 432: | ||
Comma list: 40/39, 45/44, 50/49, 56/55 | Comma list: 40/39, 45/44, 50/49, 56/55 | ||
{{Mapping|legend=0| 2 0 11 12 7 17 | 0 1 -2 -2 0 -3 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 445: | Line 447: | ||
Comma list: 34/33, 40/39, 45/44, 50/49, 56/55 | Comma list: 34/33, 40/39, 45/44, 50/49, 56/55 | ||
{{Mapping|legend=0| 2 0 11 12 7 17 5 | 0 1 -2 -2 0 -3 1 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 460: | Line 462: | ||
Comma list: 50/49, 64/63, 121/120 | Comma list: 50/49, 64/63, 121/120 | ||
{{Mapping|legend=0| 2 1 9 10 8 | 0 2 -4 -4 -1 }} | |||
: mapping generators: ~2, ~16/11 | : mapping generators: ~2, ~16/11 | ||
| Line 477: | Line 479: | ||
Comma list: 50/49, 64/63, 243/242 | Comma list: 50/49, 64/63, 243/242 | ||
{{Mapping|legend=0| 2 0 11 12 -1 | 0 2 -4 -4 5 }} | |||
: mapping generators: ~2, ~55/32 | : mapping generators: ~2, ~55/32 | ||
| Line 493: | Line 495: | ||
Comma list: 50/49, 64/63, 78/77, 144/143 | Comma list: 50/49, 64/63, 78/77, 144/143 | ||
{{Mapping|legend=0| 2 0 11 12 -1 9 | 0 2 -4 -4 5 -1 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 508: | Line 510: | ||
Comma list: 50/49, 64/63, 78/77, 85/84, 144/143 | Comma list: 50/49, 64/63, 78/77, 85/84, 144/143 | ||
{{Mapping|legend=0| 2 0 11 12 -1 9 5 | 0 2 -4 -4 5 -1 2 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 548: | Line 550: | ||
Comma list: 176/175, 896/891, 1331/1323 | Comma list: 176/175, 896/891, 1331/1323 | ||
{{Mapping|legend=0| 2 0 11 -42 -28 | 0 1 -2 15 11 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 567: | Line 569: | ||
Comma list: 169/168, 176/175, 325/324, 364/363 | Comma list: 169/168, 176/175, 325/324, 364/363 | ||
{{Mapping|legend=0| 2 0 11 -42 -28 -18 | 0 1 -2 15 11 8 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 587: | Line 589: | ||
Comma list: 136/135, 169/168, 176/175, 221/220, 256/255 | Comma list: 136/135, 169/168, 176/175, 221/220, 256/255 | ||
{{Mapping|legend=0| 2 0 11 -42 -28 -18 5 | 0 1 -2 15 11 8 1 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 606: | Line 608: | ||
Comma list: 136/135, 169/168, 176/175, 190/189, 221/220, 256/255 | Comma list: 136/135, 169/168, 176/175, 190/189, 221/220, 256/255 | ||
{{Mapping|legend=0| 2 0 11 -42 -28 -18 5 -55 | 0 1 -2 15 11 8 1 20 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 623: | Line 625: | ||
Comma list: 136/135, 169/168, 176/175, 190/189, 208/207, 221/220, 256/255 | Comma list: 136/135, 169/168, 176/175, 190/189, 208/207, 221/220, 256/255 | ||
{{Mapping|legend=0| 2 0 11 -42 -28 -18 5 -55 -10 | 0 1 -2 15 11 8 1 20 6 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 638: | Line 640: | ||
Comma list: 136/135, 169/168, 176/175, 190/189, 208/207, 221/220, 232/231, 256/255 | Comma list: 136/135, 169/168, 176/175, 190/189, 208/207, 221/220, 232/231, 256/255 | ||
{{Mapping|legend=0| 2 0 11 -42 -28 -18 5 -55 -10 -76 | 0 1 -2 15 11 8 1 20 6 27 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 653: | Line 655: | ||
Comma list: 136/135, 169/168, 176/175, 190/189, 208/207, 217/216, 221/220, 232/231, 256/255 | Comma list: 136/135, 169/168, 176/175, 190/189, 208/207, 217/216, 221/220, 232/231, 256/255 | ||
{{Mapping|legend=0| 2 0 11 -42 -28 -18 5 -55 -10 -76 48 | 0 1 -2 15 11 8 1 20 6 27 -12 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 687: | Line 689: | ||
Comma list: 100/99, 385/384, 1232/1215 | Comma list: 100/99, 385/384, 1232/1215 | ||
{{Mapping|legend=0| 2 0 11 -23 26 | 0 1 -2 9 -6 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 702: | Line 704: | ||
Comma list: 100/99, 105/104, 144/143, 1078/1053 | Comma list: 100/99, 105/104, 144/143, 1078/1053 | ||
{{Mapping|legend=0| 2 0 11 -23 26 -18 | 0 1 -2 9 -6 8 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 717: | Line 719: | ||
Comma list: 100/99, 105/104, 119/117, 144/143, 154/153 | Comma list: 100/99, 105/104, 119/117, 144/143, 154/153 | ||
{{Mapping|legend=0| 2 0 11 -23 26 -18 5 | 0 1 -2 9 -6 8 1}} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 732: | Line 734: | ||
Comma list: 91/90, 100/99, 352/351, 385/384 | Comma list: 91/90, 100/99, 352/351, 385/384 | ||
{{Mapping|legend=0| 2 0 11 -23 26 36 | 0 1 -2 9 -6 -9 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 747: | Line 749: | ||
Comma list: 91/90, 100/99, 136/135, 154/153, 256/255 | Comma list: 91/90, 100/99, 136/135, 154/153, 256/255 | ||
{{Mapping|legend=0| 2 0 11 -23 26 36 5 | 0 1 -2 9 -6 -9 1 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 782: | Line 784: | ||
Comma list: 176/175, 896/891, 1375/1372 | Comma list: 176/175, 896/891, 1375/1372 | ||
{{Mapping|legend=0| 4 0 22 43 71 | 0 1 -2 -5 -9 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 797: | Line 799: | ||
Comma list: 176/175, 325/324, 640/637, 896/891 | Comma list: 176/175, 325/324, 640/637, 896/891 | ||
{{Mapping|legend=0| 4 0 22 43 71 -36 | 0 1 -2 -5 -9 8 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 812: | Line 814: | ||
Comma list: 136/135, 176/175, 256/255, 325/324, 640/637 | Comma list: 136/135, 176/175, 256/255, 325/324, 640/637 | ||
{{Mapping|legend=0| 4 0 22 43 71 -36 10 | 0 1 -2 -5 -9 8 1 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 827: | Line 829: | ||
Comma list: 136/135, 176/175, 190/189, 256/255, 325/324, 640/637 | Comma list: 136/135, 176/175, 190/189, 256/255, 325/324, 640/637 | ||
{{Mapping|legend=0| 4 0 22 43 71 -36 10 17 | 0 1 -2 -5 -9 8 1 0 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 842: | Line 844: | ||
Comma list: 136/135, 176/175, 190/189, 253/252, 256/255, 325/324, 640/637 | Comma list: 136/135, 176/175, 190/189, 253/252, 256/255, 325/324, 640/637 | ||
{{Mapping|legend=0| 4 0 22 43 71 -36 10 17 -20 | 0 1 -2 -5 -9 8 1 0 6 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 881: | Line 883: | ||
Comma list: 121/120, 176/175, 245/243 | Comma list: 121/120, 176/175, 245/243 | ||
{{Mapping|legend=0| 2 1 9 -2 8 | 0 2 -4 7 -1 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 892: | Line 894: | ||
=== 13-limit === | === 13-limit === | ||
Note that an alternative, simpler mapping for prime 13 exists at -7 gens, as in [[#Shru]]. This mapping is especially valuable when considering shrutar as a no-7's 17-limit temperament (22 & 24, supported by 46, 68f and 70), as the complexity from mapping 7 at +7 gens is one of the motivations for picking a +16 gen mapping for 13. This temperament isn't as accurate, but it is simple, and | Note that an alternative, simpler mapping for prime 13 exists at -7 gens, as in [[#Shru]]. This mapping is especially valuable when considering shrutar as a no-7's 17-limit temperament (22 & 24, supported by 46, 68f and 70), as the complexity from mapping 7 at +7 gens is one of the motivations for picking a +16 gen mapping for 13. This temperament isn't as accurate, but it is simple, and makes many [[MOS]]es, specifically 2L 2''n''s for ''n'' up to [[2L 20s|10]], followed by [[22L 2s]] for the 24-note MOS, with a quarter-tone generator equivalent to ~11/8. | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 898: | Line 900: | ||
Comma list: 121/120, 176/175, 196/195, 245/243 | Comma list: 121/120, 176/175, 196/195, 245/243 | ||
{{Mapping|legend=0| 2 1 9 -2 8 -10 | 0 2 -4 7 -1 16 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 913: | Line 915: | ||
Comma list: 121/120, 136/135, 154/153, 176/175, 196/195 | Comma list: 121/120, 136/135, 154/153, 176/175, 196/195 | ||
{{Mapping|legend=0| 2 1 9 -2 8 -10 6 | 0 2 -4 7 -1 16 2 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 928: | Line 930: | ||
Comma list: 121/120, 136/135, 154/153, 176/175, 196/195, 343/342 | Comma list: 121/120, 136/135, 154/153, 176/175, 196/195, 343/342 | ||
{{Mapping|legend=0| 2 1 9 -2 8 -10 6 -10 | 0 2 -4 7 -1 16 2 17 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 943: | Line 945: | ||
Comma list: 121/120, 136/135, 154/153, 176/175, 196/195, 253/252, 343/342 | Comma list: 121/120, 136/135, 154/153, 176/175, 196/195, 253/252, 343/342 | ||
{{Mapping|legend=0| 2 1 9 -2 8 -10 6 -10 -4 | 0 2 -4 7 -1 16 2 17 12 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 954: | Line 956: | ||
== Shru == | == Shru == | ||
Shru tempers out 392/375 and slices the compound semitone into two generators of ~10/7. Its ploidacot is diploid alpha-dicot, the same as shrutar. | Shru tempers out 392/375 and slices the compound semitone into two generators of ~10/7. Its ploidacot is diploid alpha-dicot, the same as shrutar. It can be seen as one way of merging [[parapyth]] with [[diaschismic]] (and hence as a lower-accuracy rank 2 tuning of [[varda]]). | ||
Note that shru is especially efficient as a no-7's 17-limit temperament, as its 7 is the highest damage, and without it, the other primes can be tuned more accurately. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
| Line 978: | Line 982: | ||
Comma list: 56/55, 77/75, 1323/1280 | Comma list: 56/55, 77/75, 1323/1280 | ||
{{Mapping|legend=0| 2 1 9 11 8 | 0 2 -4 -5 -1 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 993: | Line 997: | ||
Comma list: 56/55, 77/75, 105/104, 507/500 | Comma list: 56/55, 77/75, 105/104, 507/500 | ||
{{Mapping|legend=0| 2 1 9 11 8 15 | 0 2 -4 -5 -1 -7 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,030: | Line 1,034: | ||
Comma list: 176/175, 243/242, 896/891 | Comma list: 176/175, 243/242, 896/891 | ||
{{Mapping|legend=0| 2 0 11 -15 -1 | 0 2 -4 13 5 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,045: | Line 1,049: | ||
Comma list: 144/143, 176/175, 351/350, 676/675 | Comma list: 144/143, 176/175, 351/350, 676/675 | ||
{{Mapping|legend=0| 2 0 11 -15 -1 9 | 0 2 -4 13 5 -1 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,060: | Line 1,064: | ||
Comma list: 136/135, 144/143, 170/169, 176/175, 221/220 | Comma list: 136/135, 144/143, 170/169, 176/175, 221/220 | ||
{{Mapping|legend=0| 2 0 11 -15 -1 9 5 | 0 2 -4 13 5 -1 2 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,095: | Line 1,099: | ||
Comma list: 49/48, 56/55, 243/242 | Comma list: 49/48, 56/55, 243/242 | ||
{{Mapping|legend=0| 2 0 11 4 -1 | 0 2 -4 1 5 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,110: | Line 1,114: | ||
Comma list: 49/48, 56/55, 91/90, 243/242 | Comma list: 49/48, 56/55, 91/90, 243/242 | ||
{{Mapping|legend=0| 2 0 11 4 -1 9 | 0 2 -4 1 5 -1 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,125: | Line 1,129: | ||
Comma list: 49/48, 56/55, 91/90, 119/117, 154/153 | Comma list: 49/48, 56/55, 91/90, 119/117, 154/153 | ||
{{Mapping|legend=0| 2 0 11 4 -1 9 5 | 0 2 -4 1 5 -1 2 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,160: | Line 1,164: | ||
Comma list: 385/384, 441/440, 686/675 | Comma list: 385/384, 441/440, 686/675 | ||
{{Mapping|legend=0| 2 2 7 6 3 | 0 3 -6 -1 10 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,175: | Line 1,179: | ||
Comma list: 91/90, 169/168, 385/384, 441/440 | Comma list: 91/90, 169/168, 385/384, 441/440 | ||
{{Mapping|legend=0| 2 2 7 6 3 7 | 0 3 -6 -1 10 1 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,190: | Line 1,194: | ||
Comma list: 91/90, 136/135, 154/153, 169/168, 256/255 | Comma list: 91/90, 136/135, 154/153, 169/168, 256/255 | ||
{{Mapping|legend=0| 2 2 7 6 3 7 7 | 0 3 -6 -1 10 1 3 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,229: | Line 1,233: | ||
Comma list: 176/175, 896/891, 2401/2400 | Comma list: 176/175, 896/891, 2401/2400 | ||
{{Mapping|legend=0| 2 0 11 8 22 | 0 4 -8 -3 -19 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,244: | Line 1,248: | ||
Comma list: 176/175, 196/195, 512/507, 676/675 | Comma list: 176/175, 196/195, 512/507, 676/675 | ||
{{Mapping|legend=0| 2 0 11 8 22 9 | 0 4 -8 -3 -19 -2 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,259: | Line 1,263: | ||
Comma list: 136/135, 170/169, 176/175, 196/195, 256/255 | Comma list: 136/135, 170/169, 176/175, 196/195, 256/255 | ||
{{Mapping|legend=0| 2 0 11 8 22 9 5 | 0 4 -8 -3 -19 -2 4 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,274: | Line 1,278: | ||
Comma list: 243/242, 441/440, 2048/2025 | Comma list: 243/242, 441/440, 2048/2025 | ||
{{Mapping|legend=0| 2 0 11 8 -1 | 0 4 -8 -3 10 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,289: | Line 1,293: | ||
Comma list: 144/143, 196/195, 243/242, 676/675 | Comma list: 144/143, 196/195, 243/242, 676/675 | ||
{{Mapping|legend=0| 2 0 11 8 -1 9 | 0 4 -8 -3 10 -2 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,304: | Line 1,308: | ||
Comma list: 136/135, 144/143, 170/169, 196/195, 221/220 | Comma list: 136/135, 144/143, 170/169, 196/195, 221/220 | ||
{{Mapping|legend=0| 2 0 11 8 -1 9 5 | 0 4 -8 -3 10 -2 4 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,324: | Line 1,328: | ||
Comma list: 136/135, 256/255 | Comma list: 136/135, 256/255 | ||
{{Mapping|legend=2| 2 0 11 5 | 0 1 -2 1 }} | |||
: mapping generators: ~17/12, ~3 | : mapping generators: ~17/12, ~3 | ||