Diaschismic family: Difference between revisions

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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 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 itself (and the obvious extension to prime 23 by mapping it as an augmented fourth aka. tritone, na"naa').
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 82: Line 82:
Comma list: 126/125, 176/175, 896/891
Comma list: 126/125, 176/175, 896/891


Mapping: {{mapping| 2 0 11 31 45 | 0 1 -2 -8 -12 }}
{{Mapping|legend=0| 2 0 11 31 45 | 0 1 -2 -8 -12 }}


Optimal tunings:  
Optimal tunings:  
Line 101: Line 101:
Comma list: 126/125, 176/175, 196/195, 364/363
Comma list: 126/125, 176/175, 196/195, 364/363


Mapping: {{mapping| 2 0 11 31 45 55 | 0 1 -2 -8 -12 -15 }}
{{Mapping|legend=0| 2 0 11 31 45 55 | 0 1 -2 -8 -12 -15 }}


Optimal tunings:  
Optimal tunings:  
Line 121: 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: {{mapping| 2 0 11 31 45 55 5 | 0 1 -2 -8 -12 -15 1 }}
{{Mapping|legend=0| 2 0 11 31 45 55 5 | 0 1 -2 -8 -12 -15 1 }}


Optimal tunings:  
Optimal tunings:  
Line 184: Line 184:
Comma list: 50/49, 64/63, 85/84
Comma list: 50/49, 64/63, 85/84


Mapping: {{mapping| 2 0 11 12 5 | 0 1 -2 -2 1 }}
{{Mapping|legend=0| 2 0 11 12 5 | 0 1 -2 -2 1 }}


Optimal tunings:  
Optimal tunings:  
Line 199: Line 199:
Comma list: 50/49, 64/63, 99/98
Comma list: 50/49, 64/63, 99/98


Mapping: {{mapping| 2 0 11 12 26 | 0 1 -2 -2 -6 }}
{{Mapping|legend=0| 2 0 11 12 26 | 0 1 -2 -2 -6 }}


Optimal tunings:  
Optimal tunings:  
Line 218: Line 218:
Comma list: 50/49, 64/63, 85/84, 99/98
Comma list: 50/49, 64/63, 85/84, 99/98


Mapping: {{mapping| 2 0 11 12 26 5 | 0 1 -2 -2 -6 1 }}
{{Mapping|legend=0| 2 0 11 12 26 5 | 0 1 -2 -2 -6 1 }}


Optimal tunings:  
Optimal tunings:  
Line 233: Line 233:
Comma list: 50/49, 64/63, 65/63, 99/98
Comma list: 50/49, 64/63, 65/63, 99/98


Mapping: {{mapping| 2 0 11 12 26 1 | 0 1 -2 -2 -6 2 }}
{{Mapping|legend=0| 2 0 11 12 26 1 | 0 1 -2 -2 -6 2 }}


Optimal tunings:  
Optimal tunings:  
Line 248: 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: {{mapping| 2 0 11 12 26 1 5 | 0 1 -2 -2 -6 2 1 }}
{{Mapping|legend=0| 2 0 11 12 26 1 5 | 0 1 -2 -2 -6 2 1 }}


Optimal tunings:  
Optimal tunings:  
Line 263: Line 263:
Comma list: 50/49, 64/63, 78/77, 99/98
Comma list: 50/49, 64/63, 78/77, 99/98


Mapping: {{mapping| 2 0 11 12 26 36 | 0 1 -2 -2 -6 -9 }}
{{Mapping|legend=0| 2 0 11 12 26 36 | 0 1 -2 -2 -6 -9 }}


Optimal tunings:  
Optimal tunings:  
Line 278: 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: {{mapping| 2 0 11 12 26 36 5 | 0 1 -2 -2 -6 -9 1 }}
{{Mapping|legend=0| 2 0 11 12 26 36 5 | 0 1 -2 -2 -6 -9 1 }}


Optimal tunings:  
Optimal tunings:  
Line 293: Line 293:
Comma list: 40/39, 50/49, 64/63, 66/65
Comma list: 40/39, 50/49, 64/63, 66/65


Mapping: {{mapping| 2 0 11 12 26 17 | 0 1 -2 -2 -6 -3 }}
{{Mapping|legend=0| 2 0 11 12 26 17 | 0 1 -2 -2 -6 -3 }}


Optimal tunings:  
Optimal tunings:  
Line 308: 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: {{mapping| 2 0 11 12 26 17 5 | 0 1 -2 -2 -6 -3 1 }}
{{Mapping|legend=0| 2 0 11 12 26 17 5 | 0 1 -2 -2 -6 -3 1 }}


Optimal tunings:  
Optimal tunings:  
Line 323: Line 323:
Comma list: 50/49, 55/54, 64/63
Comma list: 50/49, 55/54, 64/63


Mapping: {{mapping| 2 0 11 12 -9 | 0 1 -2 -2 5 }}
{{Mapping|legend=0| 2 0 11 12 -9 | 0 1 -2 -2 5 }}


Optimal tunings:  
Optimal tunings:  
Line 342: 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: {{mapping| 2 0 11 12 -9 1 5 | 0 1 -2 -2 5 2 1 }}
{{Mapping|legend=0| 2 0 11 12 -9 1 5 | 0 1 -2 -2 5 2 1 }}


Optimal tunings:  
Optimal tunings:  
Line 357: Line 357:
Comma list: 50/49, 55/54, 64/63, 65/63
Comma list: 50/49, 55/54, 64/63, 65/63


Mapping: {{mapping| 2 0 11 12 -9 1 | 0 1 -2 -2 5 2 }}
{{Mapping|legend=0| 2 0 11 12 -9 1 | 0 1 -2 -2 5 2 }}


Optimal tunings:  
Optimal tunings:  
Line 372: 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: {{mapping| 2 0 11 12 -9 1 5 | 0 1 -2 -2 5 2 1 }}
{{Mapping|legend=0| 2 0 11 12 -9 1 5 | 0 1 -2 -2 5 2 1 }}


Optimal tunings:  
Optimal tunings:  
Line 387: Line 387:
Comma list: 40/39, 50/49, 55/54, 64/63
Comma list: 40/39, 50/49, 55/54, 64/63


Mapping: {{mapping| 2 0 11 12 -9 17 | 0 1 -2 -2 5 -3 }}
{{Mapping|legend=0| 2 0 11 12 -9 17 | 0 1 -2 -2 5 -3 }}


Optimal tunings:  
Optimal tunings:  
Line 402: 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: {{mapping| 2 0 11 12 -9 17 5 | 0 1 -2 -2 5 -3 1 }}
{{Mapping|legend=0| 2 0 11 12 -9 17 5 | 0 1 -2 -2 5 -3 1 }}


Optimal tunings:  
Optimal tunings:  
Line 417: Line 417:
Comma list: 45/44, 50/49, 56/55
Comma list: 45/44, 50/49, 56/55


Mapping: {{mapping| 2 0 11 12 7 | 0 1 -2 -2 0 }}
{{Mapping|legend=0| 2 0 11 12 7 | 0 1 -2 -2 0 }}


Optimal tunings:  
Optimal tunings:  
Line 432: Line 432:
Comma list: 40/39, 45/44, 50/49, 56/55
Comma list: 40/39, 45/44, 50/49, 56/55


Mapping: {{mapping| 2 0 11 12 7 17 | 0 1 -2 -2 0 -3 }}
{{Mapping|legend=0| 2 0 11 12 7 17 | 0 1 -2 -2 0 -3 }}


Optimal tunings:  
Optimal tunings:  
Line 447: 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: {{mapping| 2 0 11 12 7 17 5 | 0 1 -2 -2 0 -3 1 }}
{{Mapping|legend=0| 2 0 11 12 7 17 5 | 0 1 -2 -2 0 -3 1 }}


Optimal tunings:  
Optimal tunings:  
Line 462: Line 462:
Comma list: 50/49, 64/63, 121/120  
Comma list: 50/49, 64/63, 121/120  


Mapping: {{mapping| 2 1 9 10 8 | 0 2 -4 -4 -1 }}
{{Mapping|legend=0| 2 1 9 10 8 | 0 2 -4 -4 -1 }}


: mapping generators: ~2, ~16/11
: mapping generators: ~2, ~16/11
Line 479: Line 479:
Comma list: 50/49, 64/63, 243/242
Comma list: 50/49, 64/63, 243/242


Mapping: {{mapping| 2 0 11 12 -1 | 0 2 -4 -4 5 }}
{{Mapping|legend=0| 2 0 11 12 -1 | 0 2 -4 -4 5 }}
: mapping generators: ~2, ~55/32
: mapping generators: ~2, ~55/32


Line 495: Line 495:
Comma list: 50/49, 64/63, 78/77, 144/143
Comma list: 50/49, 64/63, 78/77, 144/143


Mapping: {{mapping| 2 0 11 12 -1 9 | 0 2 -4 -4 5 -1 }}
{{Mapping|legend=0| 2 0 11 12 -1 9 | 0 2 -4 -4 5 -1 }}


Optimal tunings:  
Optimal tunings:  
Line 510: 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: {{mapping| 2 0 11 12 -1 9 5 | 0 2 -4 -4 5 -1 2 }}
{{Mapping|legend=0| 2 0 11 12 -1 9 5 | 0 2 -4 -4 5 -1 2 }}


Optimal tunings:  
Optimal tunings:  
Line 550: Line 550:
Comma list: 176/175, 896/891, 1331/1323
Comma list: 176/175, 896/891, 1331/1323


Mapping: {{mapping| 2 0 11 -42 -28 | 0 1 -2 15 11 }}
{{Mapping|legend=0| 2 0 11 -42 -28 | 0 1 -2 15 11 }}


Optimal tunings:  
Optimal tunings:  
Line 569: Line 569:
Comma list: 169/168, 176/175, 325/324, 364/363
Comma list: 169/168, 176/175, 325/324, 364/363


Mapping: {{mapping| 2 0 11 -42 -28 -18 | 0 1 -2 15 11 8 }}
{{Mapping|legend=0| 2 0 11 -42 -28 -18 | 0 1 -2 15 11 8 }}


Optimal tunings:  
Optimal tunings:  
Line 589: 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: {{mapping| 2 0 11 -42 -28 -18 5 | 0 1 -2 15 11 8 1 }}
{{Mapping|legend=0| 2 0 11 -42 -28 -18 5 | 0 1 -2 15 11 8 1 }}


Optimal tunings:  
Optimal tunings:  
Line 608: 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: {{mapping| 2 0 11 -42 -28 -18 5 -55 | 0 1 -2 15 11 8 1 20 }}
{{Mapping|legend=0| 2 0 11 -42 -28 -18 5 -55 | 0 1 -2 15 11 8 1 20 }}


Optimal tunings:  
Optimal tunings:  
Line 625: 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: {{mapping| 2 0 11 -42 -28 -18 5 -55 -10 | 0 1 -2 15 11 8 1 20 6 }}
{{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 640: 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: {{mapping| 2 0 11 -42 -28 -18 5 -55 -10 -76 | 0 1 -2 15 11 8 1 20 6 27 }}
{{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 655: 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: {{mapping| 2 0 11 -42 -28 -18 5 -55 -10 -76 48 | 0 1 -2 15 11 8 1 20 6 27 -12 }}
{{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 689: Line 689:
Comma list: 100/99, 385/384, 1232/1215
Comma list: 100/99, 385/384, 1232/1215


Mapping: {{mapping| 2 0 11 -23 26 | 0 1 -2 9 -6 }}
{{Mapping|legend=0| 2 0 11 -23 26 | 0 1 -2 9 -6 }}


Optimal tunings:  
Optimal tunings:  
Line 704: Line 704:
Comma list: 100/99, 105/104, 144/143, 1078/1053
Comma list: 100/99, 105/104, 144/143, 1078/1053


Mapping: {{mapping| 2 0 11 -23 26 -18 | 0 1 -2 9 -6 8 }}
{{Mapping|legend=0| 2 0 11 -23 26 -18 | 0 1 -2 9 -6 8 }}


Optimal tunings:  
Optimal tunings:  
Line 719: 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: {{mapping| 2 0 11 -23 26 -18 5 | 0 1 -2 9 -6 8 1}}
{{Mapping|legend=0| 2 0 11 -23 26 -18 5 | 0 1 -2 9 -6 8 1}}


Optimal tunings:  
Optimal tunings:  
Line 734: Line 734:
Comma list: 91/90, 100/99, 352/351, 385/384
Comma list: 91/90, 100/99, 352/351, 385/384


Mapping: {{mapping| 2 0 11 -23 26 36 | 0 1 -2 9 -6 -9 }}
{{Mapping|legend=0| 2 0 11 -23 26 36 | 0 1 -2 9 -6 -9 }}


Optimal tunings:  
Optimal tunings:  
Line 749: 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: {{mapping| 2 0 11 -23 26 36 5 | 0 1 -2 9 -6 -9 1 }}
{{Mapping|legend=0| 2 0 11 -23 26 36 5 | 0 1 -2 9 -6 -9 1 }}


Optimal tunings:  
Optimal tunings:  
Line 784: Line 784:
Comma list: 176/175, 896/891, 1375/1372
Comma list: 176/175, 896/891, 1375/1372


Mapping: {{mapping| 4 0 22 43 71 | 0 1 -2 -5 -9 }}
{{Mapping|legend=0| 4 0 22 43 71 | 0 1 -2 -5 -9 }}


Optimal tunings:  
Optimal tunings:  
Line 799: Line 799:
Comma list: 176/175, 325/324, 640/637, 896/891
Comma list: 176/175, 325/324, 640/637, 896/891


Mapping: {{mapping| 4 0 22 43 71 -36 | 0 1 -2 -5 -9 8 }}
{{Mapping|legend=0| 4 0 22 43 71 -36 | 0 1 -2 -5 -9 8 }}


Optimal tunings:  
Optimal tunings:  
Line 814: 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: {{mapping| 4 0 22 43 71 -36 10 | 0 1 -2 -5 -9 8 1 }}
{{Mapping|legend=0| 4 0 22 43 71 -36 10 | 0 1 -2 -5 -9 8 1 }}


Optimal tunings:  
Optimal tunings:  
Line 829: 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: {{mapping| 4 0 22 43 71 -36 10 17 | 0 1 -2 -5 -9 8 1 0 }}
{{Mapping|legend=0| 4 0 22 43 71 -36 10 17 | 0 1 -2 -5 -9 8 1 0 }}


Optimal tunings:  
Optimal tunings:  
Line 844: 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: {{mapping| 4 0 22 43 71 -36 10 17 -20 | 0 1 -2 -5 -9 8 1 0 6 }}
{{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 883: Line 883:
Comma list: 121/120, 176/175, 245/243
Comma list: 121/120, 176/175, 245/243


Mapping: {{mapping| 2 1 9 -2 8 | 0 2 -4 7 -1 }}
{{Mapping|legend=0| 2 1 9 -2 8 | 0 2 -4 7 -1 }}


Optimal tunings:
Optimal tunings:
Line 894: 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 one could consider a 22- or 24-note half-octave-period MOS scale as relevant, with an ~11/8 gen.
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 900: Line 900:
Comma list: 121/120, 176/175, 196/195, 245/243
Comma list: 121/120, 176/175, 196/195, 245/243


Mapping: {{mapping| 2 1 9 -2 8 -10 | 0 2 -4 7 -1 16 }}
{{Mapping|legend=0| 2 1 9 -2 8 -10 | 0 2 -4 7 -1 16 }}


Optimal tunings:
Optimal tunings:
Line 915: 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: {{mapping| 2 1 9 -2 8 -10 6 | 0 2 -4 7 -1 16 2 }}
{{Mapping|legend=0| 2 1 9 -2 8 -10 6 | 0 2 -4 7 -1 16 2 }}


Optimal tunings:
Optimal tunings:
Line 930: 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: {{mapping| 2 1 9 -2 8 -10 6 -10 | 0 2 -4 7 -1 16 2 17 }}
{{Mapping|legend=0| 2 1 9 -2 8 -10 6 -10 | 0 2 -4 7 -1 16 2 17 }}


Optimal tunings:
Optimal tunings:
Line 945: 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: {{mapping| 2 1 9 -2 8 -10 6 -10 -4 | 0 2 -4 7 -1 16 2 17 12 }}
{{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 982: Line 982:
Comma list: 56/55, 77/75, 1323/1280
Comma list: 56/55, 77/75, 1323/1280


Mapping: {{mapping| 2 1 9 11 8 | 0 2 -4 -5 -1 }}
{{Mapping|legend=0| 2 1 9 11 8 | 0 2 -4 -5 -1 }}


Optimal tunings:
Optimal tunings:
Line 997: Line 997:
Comma list: 56/55, 77/75, 105/104, 507/500
Comma list: 56/55, 77/75, 105/104, 507/500


Mapping: {{mapping| 2 1 9 11 8 15 | 0 2 -4 -5 -1 -7 }}
{{Mapping|legend=0| 2 1 9 11 8 15 | 0 2 -4 -5 -1 -7 }}


Optimal tunings:
Optimal tunings:
Line 1,034: Line 1,034:
Comma list: 176/175, 243/242, 896/891
Comma list: 176/175, 243/242, 896/891


Mapping: {{mapping| 2 0 11 -15 -1 | 0 2 -4 13 5 }}
{{Mapping|legend=0| 2 0 11 -15 -1 | 0 2 -4 13 5 }}


Optimal tunings:
Optimal tunings:
Line 1,049: Line 1,049:
Comma list: 144/143, 176/175, 351/350, 676/675
Comma list: 144/143, 176/175, 351/350, 676/675


Mapping: {{mapping| 2 0 11 -15 -1 9 | 0 2 -4 13 5 -1 }}
{{Mapping|legend=0| 2 0 11 -15 -1 9 | 0 2 -4 13 5 -1 }}


Optimal tunings:
Optimal tunings:
Line 1,064: 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: {{mapping| 2 0 11 -15 -1 9 5 | 0 2 -4 13 5 -1 2 }}
{{Mapping|legend=0| 2 0 11 -15 -1 9 5 | 0 2 -4 13 5 -1 2 }}


Optimal tunings:
Optimal tunings:
Line 1,099: Line 1,099:
Comma list: 49/48, 56/55, 243/242
Comma list: 49/48, 56/55, 243/242


Mapping: {{mapping| 2 0 11 4 -1 | 0 2 -4 1 5 }}
{{Mapping|legend=0| 2 0 11 4 -1 | 0 2 -4 1 5 }}


Optimal tunings:
Optimal tunings:
Line 1,114: Line 1,114:
Comma list: 49/48, 56/55, 91/90, 243/242
Comma list: 49/48, 56/55, 91/90, 243/242


Mapping: {{mapping| 2 0 11 4 -1 9 | 0 2 -4 1 5 -1 }}
{{Mapping|legend=0| 2 0 11 4 -1 9 | 0 2 -4 1 5 -1 }}


Optimal tunings:
Optimal tunings:
Line 1,129: 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: {{mapping| 2 0 11 4 -1 9 5 | 0 2 -4 1 5 -1 2 }}
{{Mapping|legend=0| 2 0 11 4 -1 9 5 | 0 2 -4 1 5 -1 2 }}


Optimal tunings:
Optimal tunings:
Line 1,164: Line 1,164:
Comma list: 385/384, 441/440, 686/675
Comma list: 385/384, 441/440, 686/675


Mapping: {{mapping| 2 2 7 6 3 | 0 3 -6 -1 10 }}
{{Mapping|legend=0| 2 2 7 6 3 | 0 3 -6 -1 10 }}


Optimal tunings:
Optimal tunings:
Line 1,179: Line 1,179:
Comma list: 91/90, 169/168, 385/384, 441/440
Comma list: 91/90, 169/168, 385/384, 441/440


Mapping: {{mapping| 2 2 7 6 3 7 | 0 3 -6 -1 10 1 }}
{{Mapping|legend=0| 2 2 7 6 3 7 | 0 3 -6 -1 10 1 }}


Optimal tunings:
Optimal tunings:
Line 1,194: 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: {{mapping| 2 2 7 6 3 7 7 | 0 3 -6 -1 10 1 3 }}
{{Mapping|legend=0| 2 2 7 6 3 7 7 | 0 3 -6 -1 10 1 3 }}


Optimal tunings:
Optimal tunings:
Line 1,233: Line 1,233:
Comma list: 176/175, 896/891, 2401/2400
Comma list: 176/175, 896/891, 2401/2400


Mapping: {{mapping| 2 0 11 8 22 | 0 4 -8 -3 -19 }}
{{Mapping|legend=0| 2 0 11 8 22 | 0 4 -8 -3 -19 }}


Optimal tunings:
Optimal tunings:
Line 1,248: Line 1,248:
Comma list: 176/175, 196/195, 512/507, 676/675
Comma list: 176/175, 196/195, 512/507, 676/675


Mapping: {{mapping| 2 0 11 8 22 9 | 0 4 -8 -3 -19 -2 }}
{{Mapping|legend=0| 2 0 11 8 22 9 | 0 4 -8 -3 -19 -2 }}


Optimal tunings:
Optimal tunings:
Line 1,263: 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: {{mapping| 2 0 11 8 22 9 5 | 0 4 -8 -3 -19 -2 4 }}
{{Mapping|legend=0| 2 0 11 8 22 9 5 | 0 4 -8 -3 -19 -2 4 }}


Optimal tunings:
Optimal tunings:
Line 1,278: Line 1,278:
Comma list: 243/242, 441/440, 2048/2025
Comma list: 243/242, 441/440, 2048/2025


Mapping: {{mapping| 2 0 11 8 -1 | 0 4 -8 -3 10 }}
{{Mapping|legend=0| 2 0 11 8 -1 | 0 4 -8 -3 10 }}


Optimal tunings:
Optimal tunings:
Line 1,293: Line 1,293:
Comma list: 144/143, 196/195, 243/242, 676/675
Comma list: 144/143, 196/195, 243/242, 676/675


Mapping: {{mapping| 2 0 11 8 -1 9 | 0 4 -8 -3 10 -2 }}
{{Mapping|legend=0| 2 0 11 8 -1 9 | 0 4 -8 -3 10 -2 }}


Optimal tunings:
Optimal tunings:
Line 1,308: 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: {{mapping| 2 0 11 8 -1 9 5 | 0 4 -8 -3 10 -2 4 }}
{{Mapping|legend=0| 2 0 11 8 -1 9 5 | 0 4 -8 -3 10 -2 4 }}


Optimal tunings:
Optimal tunings: