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[[Comma list]]: 2048/2025
[[Comma list]]: 2048/2025


[[Mapping]]: [{{val| 2 0 11 }}, {{val| 0 1 -2 }}]
{{Mapping|legend=1| 2 0 11 | 0 1 -2 }}


Mapping generators: ~45/32, ~3
: mapping generators: ~45/32, ~3


[[Optimal tuning]] ([[POTE]]): ~45/32 = 1\2, ~3/2 = 704.898
[[Optimal tuning]] ([[POTE]]): ~45/32 = 1\2, ~3/2 = 704.898
Line 43: Line 43:
Comma list: 136/135, 256/255
Comma list: 136/135, 256/255


Sval mapping: [{{val| 2 0 11 5 }}], {{val| 0 1 -2 1 }}]
Sval mapping: {{mapping| 2 0 11 5 | 0 1 -2 1 }}


Optimal tuning (CTE): ~17/12 = 1\2, ~3/2 = 705.1272
Optimal tuning (CTE): ~17/12 = 1\2, ~3/2 = 705.1272
Line 58: Line 58:
[[Comma list]]: 2048/2025, 4375/4374
[[Comma list]]: 2048/2025, 4375/4374


[[Mapping]]: [{{val| 2 0 11 -42 }}, {{val| 0 1 -2 15 }}]
{{Mapping|legend=1| 2 0 11 -42 | 0 1 -2 15 }}


{{Multival|legend=1| 2 -4 30 -11 42 81 }}
{{Multival|legend=1| 2 -4 30 -11 42 81 }}
Line 78: Line 78:
Comma list: 176/175, 896/891, 1331/1323
Comma list: 176/175, 896/891, 1331/1323


Mapping: [{{val| 2 0 11 -42 -28 }}, {{val| 0 1 -2 15 11 }}]
Mapping: {{mapping| 2 0 11 -42 -28 | 0 1 -2 15 11 }}


Optimal tuning (POTE): ~45/32 = 1\2, ~3/2 = 704.856
Optimal tuning (POTE): ~45/32 = 1\2, ~3/2 = 704.856
Line 96: Line 96:
Comma list: 169/168, 176/175, 325/324, 364/363
Comma list: 169/168, 176/175, 325/324, 364/363


Mapping: [{{val| 2 0 11 -42 -28 -18 }}, {{val| 0 1 -2 15 11 8 }}]
Mapping: {{mapping| 2 0 11 -42 -28 -18 | 0 1 -2 15 11 8 }}


Optimal tuning (POTE): ~45/32 = 1\2, ~3/2 = 704.881
Optimal tuning (POTE): ~45/32 = 1\2, ~3/2 = 704.881
Line 115: Line 115:
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: [{{val| 2 0 11 -42 -28 -18 5 }}, {{val| 0 1 -2 15 11 8 1 }}]
Mapping: {{mapping| 2 0 11 -42 -28 -18 5 | 0 1 -2 15 11 8 1 }}


Optimal tuning (POTE): ~17/12 = 1\2, ~3/2 = 704.840
Optimal tuning (POTE): ~17/12 = 1\2, ~3/2 = 704.840
Line 129: Line 129:


=== 19-limit ===
=== 19-limit ===
Srutal, Shrutar and Bidia have similar 19-limit properties, tempering 190/189, related rank-3 [[Julius]].
Srutal, shrutar and bidia have similar 19-limit properties, tempering 190/189, related rank-3 [[julius]].


Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19
Line 135: Line 135:
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: [{{val| 2 0 11 -42 -28 -18 5 -55 }}, {{val| 0 1 -2 15 11 8 1 20 }}]
Mapping: {{mapping| 2 0 11 -42 -28 -18 5 -55 | 0 1 -2 15 11 8 1 20 }}


Optimal tuning (POTE): ~17/12 = 1\2, ~3/2 = 704.905
Optimal tuning (POTE): ~17/12 = 1\2, ~3/2 = 704.905
Line 150: Line 150:
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: [{{val| 2 0 11 -42 -28 -18 5 -55 -10 }}, {{val| 0 1 -2 15 11 8 1 20 6 }}]
Mapping: {{mapping| 2 0 11 -42 -28 -18 5 -55 -10 | 0 1 -2 15 11 8 1 20 6 }}


Optimal tuning (POTE): ~17/12 = 1\2, ~3/2 = 704.899
Optimal tuning (POTE): ~17/12 = 1\2, ~3/2 = 704.899
Line 163: Line 163:
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: [{{val| 2 0 11 -42 -28 -18 5 -55 -10 -76 }}, {{val| 0 1 -2 15 11 8 1 20 6 27 }}]
Mapping: {{mapping| 2 0 11 -42 -28 -18 5 -55 -10 -76 | 0 1 -2 15 11 8 1 20 6 27 }}


Optimal tuning (POTE): ~17/12 = 1\2, ~3/2 = 704.906
Optimal tuning (POTE): ~17/12 = 1\2, ~3/2 = 704.906
Line 174: Line 174:
{{Main| Pajara }}
{{Main| Pajara }}


Pajara is closely associated with 22edo (not to mention [[Paul Erlich]]) but other tunings are possible. The 1/2 octave period serves as both a [[10/7]] and a [[7/5]]. Aside from 22edo, 34 with the val {{val| 34 54 79 96 }} and 56 with the val {{val| 56 89 130 158 }} are are interesting alternatives, with more accpetable fifths, and a tetrad which is more clearly a dominant seventh. As such, they are closer to the tuning of 12edo and of common practice Western music in general, while retaining the distictiveness of a sharp fifth.
Pajara is closely associated with 22edo (not to mention [[Paul Erlich]]) but other tunings are possible. The 1/2-octave period serves as both a [[10/7]] and a [[7/5]]. Aside from 22edo, 34 with the val {{val| 34 54 79 96 }} and 56 with the val {{val| 56 89 130 158 }} are are interesting alternatives, with more accpetable fifths, and a tetrad which is more clearly a dominant seventh. As such, they are closer to the tuning of 12edo and of common practice Western music in general, while retaining the distictiveness of a sharp fifth.


Pajara extends nicely to an 11-limit version, for which the 56 tuning can be used, but a good alternative is to make the major thirds pure by setting the fifth to be 706.843 cents. Now 99/98, 100/99, 176/175 and 896/891 are being tempered out.
Pajara extends nicely to an 11-limit version, for which the 56 tuning can be used, but a good alternative is to make the major thirds pure by setting the fifth to be 706.843 cents. Now 99/98, 100/99, 176/175 and 896/891 are being tempered out.
Line 182: Line 182:
[[Comma list]]: 50/49, 64/63
[[Comma list]]: 50/49, 64/63


[[Mapping]]: [{{val| 2 0 11 12 }}, {{val| 0 1 -2 -2 }}]
{{Mapping|legend=1| 2 0 11 12 | 0 1 -2 -2 }}


{{Multival|legend=1| 2 -4 -4 -11 -12 2 }}
{{Multival|legend=1| 2 -4 -4 -11 -12 2 }}
Line 202: Line 202:
Comma list: 50/49, 64/63, 99/98
Comma list: 50/49, 64/63, 99/98


Mapping: [{{val| 2 0 11 12 26 }}, {{val| 0 1 -2 -2 -6 }}]
Mapping: {{mapping| 2 0 11 12 26 | 0 1 -2 -2 -6 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 706.885
Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 706.885
Line 220: Line 220:
Comma list: 50/49, 64/63, 65/63, 99/98
Comma list: 50/49, 64/63, 65/63, 99/98


Mapping: [{{val| 2 0 11 12 26 1 }}, {{val| 0 1 -2 -2 -6 2 }}]
Mapping: {{mapping| 2 0 11 12 26 1 | 0 1 -2 -2 -6 2 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 708.919
Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 708.919
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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: [{{val| 2 0 11 12 26 1 5 }}, {{val| 0 1 -2 -2 -6 2 1 }}]
Mapping: {{mapping| 2 0 11 12 26 1 5 | 0 1 -2 -2 -6 2 1 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 708.806
Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 708.806
Line 246: Line 246:
Comma list: 50/49, 64/63, 78/77, 99/98
Comma list: 50/49, 64/63, 78/77, 99/98


Mapping: [{{val| 2 0 11 12 26 36 }}, {{val| 0 1 -2 -2 -6 -9 }}]
Mapping: {{mapping| 2 0 11 12 26 36 | 0 1 -2 -2 -6 -9 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 706.133
Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 706.133
Line 259: Line 259:
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: [{{val| 2 0 11 12 26 36 5 }}, {{val| 0 1 -2 -2 -6 -9 1 }}]
Mapping: {{mapping| 2 0 11 12 26 36 5 | 0 1 -2 -2 -6 -9 1 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 706.410
Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 706.410
Line 272: Line 272:
Comma list: 40/39, 50/49, 64/63, 66/65
Comma list: 40/39, 50/49, 64/63, 66/65


Mapping: [{{val|2 0 11 12 26 17}}, {{val|0 1 -2 -2 -6 -3}}]
Mapping: {{mapping| 2 0 11 12 26 17 | 0 1 -2 -2 -6 -3 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 707.450
Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 707.450
Line 285: Line 285:
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: [{{val|2 0 11 12 26 17 5}}, {{val|0 1 -2 -2 -6 -3 1}}]
Mapping: {{mapping| 2 0 11 12 26 17 5 | 0 1 -2 -2 -6 -3 1 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 707.947
Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 707.947
Line 298: Line 298:
Comma list: 50/49, 55/54, 64/63
Comma list: 50/49, 55/54, 64/63


Mapping: [{{val| 2 0 11 12 -9 }}, {{val| 0 1 -2 -2 5 }}]
Mapping: {{mapping| 2 0 11 12 -9 | 0 1 -2 -2 5 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 709.578
Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 709.578
Line 316: Line 316:
Comma list: 50/49, 55/54, 64/63, 65/63
Comma list: 50/49, 55/54, 64/63, 65/63


Mapping: [{{val| 2 0 11 12 -9 1 }}, {{val| 0 1 -2 -2 5 2 }}]
Mapping: {{mapping| 2 0 11 12 -9 1 | 0 1 -2 -2 5 2 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 710.240
Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 710.240
Line 329: Line 329:
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: [{{val| 2 0 11 12 -9 1 5 }}, {{val| 0 1 -2 -2 5 2 1 }}]
Mapping: {{mapping| 2 0 11 12 -9 1 5 | 0 1 -2 -2 5 2 1 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 710.221
Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 710.221
Line 342: Line 342:
Comma list: 40/39, 50/49, 55/54, 64/63
Comma list: 40/39, 50/49, 55/54, 64/63


Mapping: [{{val| 2 0 11 12 -9 17 }}, {{val| 0 1 -2 -2 5 -3 }}]
Mapping: {{mapping| 2 0 11 12 -9 17 | 0 1 -2 -2 5 -3 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 710.818
Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 710.818
Line 355: Line 355:
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: [{{val| 2 0 11 12 -9 17 5 }}, {{val| 0 1 -2 -2 5 -3 1 }}]
Mapping: {{mapping| 2 0 11 12 -9 17 5 | 0 1 -2 -2 5 -3 1 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 710.866
Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 710.866
Line 368: Line 368:
Comma list: 45/44, 50/49, 56/55
Comma list: 45/44, 50/49, 56/55


Mapping: [{{val| 2 0 11 12 7 }}, {{val| 0 1 -2 -2 0 }}]
Mapping: {{mapping| 2 0 11 12 7 | 0 1 -2 -2 0 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 705.524
Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 705.524
Line 381: Line 381:
Comma list: 40/39, 45/44, 50/49, 56/55
Comma list: 40/39, 45/44, 50/49, 56/55


Mapping: [{{val| 2 0 11 12 7 17 }}, {{val| 0 1 -2 -2 0 -3 }}]
Mapping: {{mapping| 2 0 11 12 7 17 | 0 1 -2 -2 0 -3 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 707.442
Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 707.442
Line 394: Line 394:
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: [{{val| 2 0 11 12 7 17 5 }}, {{val| 0 1 -2 -2 0 -3 1 }}]
Mapping: {{mapping| 2 0 11 12 7 17 5 | 0 1 -2 -2 0 -3 1 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 708.544
Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 708.544
Line 407: Line 407:
Comma list: 50/49, 64/63, 121/120  
Comma list: 50/49, 64/63, 121/120  


Mapping: [{{val| 2 1 9 10 8 }}, {{val| 0 2 -4 -4 -1 }}]
Mapping: {{mapping| 2 1 9 10 8 | 0 2 -4 -4 -1 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~11/8 = 546.383
Optimal tuning (POTE): ~7/5 = 1\2, ~11/8 = 546.383
Line 420: Line 420:
Comma list: 50/49, 64/63, 243/242
Comma list: 50/49, 64/63, 243/242


Mapping: [{{val| 2 0 11 12 -1 }}, {{val| 0 2 -4 -4 5 }}]
Mapping: {{mapping| 2 0 11 12 -1 | 0 2 -4 -4 5 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~55/32 = 953.093
Optimal tuning (POTE): ~7/5 = 1\2, ~55/32 = 953.093
Line 433: Line 433:
Comma list: 50/49, 64/63, 78/77, 144/143
Comma list: 50/49, 64/63, 78/77, 144/143


Mapping: [{{val| 2 0 11 12 -1 9 }}, {{val| 0 2 -4 -4 5 -1 }}]
Mapping: {{mapping| 2 0 11 12 -1 9 | 0 2 -4 -4 5 -1 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~26/15 = 953.074
Optimal tuning (POTE): ~7/5 = 1\2, ~26/15 = 953.074
Line 446: Line 446:
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: [{{val| 2 0 11 12 -1 9 5 }}, {{val| 0 2 -4 -4 5 -1 2 }}]
Mapping: {{mapping| 2 0 11 12 -1 9 5 | 0 2 -4 -4 5 -1 2 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~26/15 = 953.210
Optimal tuning (POTE): ~7/5 = 1\2, ~26/15 = 953.210
Line 455: Line 455:


== Diaschismic ==
== Diaschismic ==
{{see also| Srutal vs diaschismic }}
{{See also| Srutal vs diaschismic }}


A simpler characterization than the one given by the normal comma list is that diaschismic adds [[126/125]] or [[5120/5103]] to the set of commas, and it can also be called 46&58. However described, diaschismic has a 1/2 period and a sharp fifth generator like pajara, but not so sharp, giving a more accurate but more complex temperament. [[58edo]] provides an excellent tuning, but an alternative is to make [[7/4]] just by making the fifth 703.897 cents, as opposed to 703.448 cents for 58edo.
A simpler characterization than the one given by the normal comma list is that diaschismic adds [[126/125]] or [[5120/5103]] to the set of commas, and it can also be called 46 & 58. However described, diaschismic has a 1/2-octave period and a sharp fifth generator like pajara, but not so sharp, giving a more accurate but more complex temperament. [[58edo]] provides an excellent tuning, but an alternative is to make [[7/4]] just by making the fifth 703.897 cents, as opposed to 703.448 cents for 58edo.


Diaschismic extends naturally to the 17-limit, for which the same tunings may be used, making it one of the most important of the higher limit rank two temperaments. Adding the 11-limit adds the commas 176/175, 896/891 and 441/440. The 13-limit yields 196/195, 351/350, and 364/363; the 17-limit adds 136/135, 221/220, and 442/441. If you want to explore higher limit harmonies, diaschismic is certainly one excellent way to do it; MOS of 34 notes and even more the 46 note MOS will encompass very great deal of it. Of course 46 or 58 equal provide alternatives which in many ways are similar, particularly in the case of 58.
Diaschismic extends naturally to the 17-limit, for which the same tunings may be used, making it one of the most important of the higher-limit rank-2 temperaments. Adding the 11-limit adds the commas 176/175, 896/891 and 441/440. The 13-limit yields 196/195, 351/350, and 364/363; the 17-limit adds 136/135, 221/220, and 442/441. If you want to explore higher-limit harmonies, diaschismic is certainly one excellent way to do it; Mos of 34 notes and even more the 46-note mos will encompass very great deal of it. Of course 46 or 58 equal provide alternatives which in many ways are similar, particularly in the case of 58.


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 465: Line 465:
[[Comma list]]: 126/125, 2048/2025
[[Comma list]]: 126/125, 2048/2025


[[Mapping]]: [{{val| 2 0 11 31 }}, {{val| 0 1 -2 -8 }}]
{{Mapping|legend=1| 2 0 11 31 | 0 1 -2 -8 }}


{{Multival|legend=1| 2 -4 -16 -11 -31 -26 }}
{{Multival|legend=1| 2 -4 -16 -11 -31 -26 }}
Line 485: Line 485:
Comma list: 126/125, 176/175, 896/891
Comma list: 126/125, 176/175, 896/891


Mapping: [{{val| 2 0 11 31 45 }}, {{val| 0 1 -2 -8 -12 }}]
Mapping: {{mapping| 2 0 11 31 45 0 1 -2 -8 -12 }}


Optimal tuning (POTE): ~45/32 = 1\2, ~3/2 = 703.714
Optimal tuning (POTE): ~45/32 = 1\2, ~3/2 = 703.714
Line 503: Line 503:
Comma list: 126/125, 176/175, 196/195, 364/363
Comma list: 126/125, 176/175, 196/195, 364/363


Mapping: [{{val| 2 0 11 31 45 55 }}, {{val| 0 1 -2 -8 -12 -15 }}]
Mapping: {{mapping| 2 0 11 31 45 55 | 0 1 -2 -8 -12 -15 }}


Optimal tuning (POTE): ~45/32 = 1\2, ~3/2 = 703.704
Optimal tuning (POTE): ~45/32 = 1\2, ~3/2 = 703.704
Line 522: Line 522:
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: [{{val| 2 0 11 31 45 55 5 }}, {{val| 0 1 -2 -8 -12 -15 1 }}]
Mapping: {{mapping| 2 0 11 31 45 55 5 | 0 1 -2 -8 -12 -15 1 }}


Optimal tuning (POTE): ~17/12 = 1\2, ~3/2 = 703.812
Optimal tuning (POTE): ~17/12 = 1\2, ~3/2 = 703.812
Line 542: Line 542:
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


Sval mapping: [{{val| 2 0 11 31 45 55 5 63 }}, {{val| 0 1 -2 -8 -12 -15 1 -17 }}]
Sval mapping: {{mapping| 2 0 11 31 45 55 5 63 | 0 1 -2 -8 -12 -15 1 -17 }}


Optimal tuning (POTE): ~17/12 = 1\2, ~3/2 = 703.870
Optimal tuning (POTE): ~17/12 = 1\2, ~3/2 = 703.870
Line 549: Line 549:


== Keen ==
== Keen ==
Keen adds 875/864 as well as 2240/2187 to the set of commas. It may also be described as the 22&56 temperament. [[78edo]] is a good tuning choice, and remains a good one in the 11-limit, where keen, {{multival| 2 -4 18 -12 … }}, is really more interesting, adding 100/99 and 385/384 to the commas.
Keen adds 875/864 as well as 2240/2187 to the set of commas. It may also be described as the 22 & 56 temperament. [[78edo]] is a good tuning choice, and remains a good one in the 11-limit, where keen, {{multival| 2 -4 18 -12 … }}, is really more interesting, adding 100/99 and 385/384 to the commas.


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 555: Line 555:
[[Comma list]]: 875/864, 2048/2025
[[Comma list]]: 875/864, 2048/2025


[[Mapping]]: [{{val| 2 0 11 -23 }}, {{val| 0 1 -2 9 }}]
{{Mapping|legend=1| 2 0 11 -23 | 0 1 -2 9 }}


{{Multival|legend=1| 2 -4 18 -11 23 53 }}
{{Multival|legend=1| 2 -4 18 -11 23 53 }}
Line 570: Line 570:
Comma list: 100/99, 385/384, 1232/1215
Comma list: 100/99, 385/384, 1232/1215


Mapping: [{{val|2 0 11 -23 26}}, {{val|0 1 -2 9 -6}}]
Mapping: {{mapping| 2 0 11 -23 26 | 0 1 -2 9 -6 }}


Optimal tuning (POTE): ~45/32 = 1\2, ~3/2 = 707.609
Optimal tuning (POTE): ~45/32 = 1\2, ~3/2 = 707.609
Line 583: Line 583:
Comma list: 100/99, 105/104, 144/143, 1078/1053
Comma list: 100/99, 105/104, 144/143, 1078/1053


Mapping: [{{val|2 0 11 -23 26 -18}}, {{val|0 1 -2 9 -6 8}}]
Mapping: {{mapping| 2 0 11 -23 26 -18 | 0 1 -2 9 -6 8 }}


Optimal tuning (POTE): ~45/32 = 1\2, ~3/2 = 707.167
Optimal tuning (POTE): ~45/32 = 1\2, ~3/2 = 707.167
Line 596: Line 596:
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: [{{val|2 0 11 -23 26 -18 5}}, {{val|0 1 -2 9 -6 8 1}}]
Mapping: {{mapping| 2 0 11 -23 26 -18 5 | 0 1 -2 9 -6 8 }}


Optimal tuning (POTE): ~17/12 = 1\2, ~3/2 = 707.155
Optimal tuning (POTE): ~17/12 = 1\2, ~3/2 = 707.155
Line 609: Line 609:
Comma list: 91/90, 100/99, 352/351, 385/384
Comma list: 91/90, 100/99, 352/351, 385/384


Mapping: [{{val|2 0 11 -23 26 36}}, {{val|0 1 -2 9 -6 -9}}]
Mapping: {{mapping| 2 0 11 -23 26 36 | 0 1 -2 9 -6 -9 }}


Optimal tuning (POTE): ~45/32 = 1\2, ~3/2 = 707.257
Optimal tuning (POTE): ~45/32 = 1\2, ~3/2 = 707.257
Line 622: Line 622:
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: [{{val|2 0 11 -23 26 36 5}}, {{val|0 1 -2 9 -6 -9 1}}]
Mapping: {{mapping| 2 0 11 -23 26 36 5 | 0 1 -2 9 -6 -9 1 }}


Optimal tuning (POTE): ~17/12 = 1\2, ~3/2 = 707.252
Optimal tuning (POTE): ~17/12 = 1\2, ~3/2 = 707.252
Line 631: Line 631:


== Bidia ==
== Bidia ==
Bidia adds [[3136/3125]] to the commas, splitting the period into 1/4 octave. It may be called the 12&56 temperament.
Bidia adds [[3136/3125]] to the commas, splitting the period into 1/4 octave. It may be called the 12 & 56 temperament.


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 637: Line 637:
[[Comma list]]: 2048/2025, 3136/3125
[[Comma list]]: 2048/2025, 3136/3125


[[Mapping]]: [{{val| 4 0 22 43 }}, {{val| 0 1 -2 -5 }}]
{{Mapping|legend=1| 4 0 22 43 | 0 1 -2 -5 }}


{{Multival|legend=1| 4 -8 -20 -22 -43 -24 }}
{{Multival|legend=1| 4 -8 -20 -22 -43 -24 }}
Line 652: Line 652:
Comma list: 176/175, 896/891, 1375/1372
Comma list: 176/175, 896/891, 1375/1372


Mapping: [{{val| 4 0 22 43 71 }}, {{val| 0 1 -2 -5 -9 }}]
Mapping: {{mapping| 4 0 22 43 71 | 0 1 -2 -5 -9 }}


Optimal tuning (POTE): ~25/21 = 1\4, ~3/2 = 705.087
Optimal tuning (POTE): ~25/21 = 1\4, ~3/2 = 705.087
Line 665: Line 665:
Comma list: 176/175, 325/324, 640/637, 896/891
Comma list: 176/175, 325/324, 640/637, 896/891


Mapping: [{{val| 4 0 22 43 71 -36 }}, {{val| 0 1 -2 -5 -9 8 }}]
Mapping: {{mapping| 4 0 22 43 71 -36 | 0 1 -2 -5 -9 8 }}


Optimal tuning (POTE): ~25/21 = 1\4, ~3/2 = 705.301
Optimal tuning (POTE): ~25/21 = 1\4, ~3/2 = 705.301
Line 678: Line 678:
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: [{{val| 4 0 22 43 71 -36 10 }}, {{val| 0 1 -2 -5 -9 8 1 }}]
Mapping: {{mapping| 4 0 22 43 71 -36 10 | 0 1 -2 -5 -9 8 1 }}


Optimal tuning (POTE): ~25/21 = 1\4, ~3/2 = 705.334
Optimal tuning (POTE): ~25/21 = 1\4, ~3/2 = 705.334
Line 691: Line 691:
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: [{{val| 4 0 22 43 71 -36 10 17 }}, {{val| 0 1 -2 -5 -9 8 1 0 }}]
Mapping: {{mapping| 4 0 22 43 71 -36 10 17 | 0 1 -2 -5 -9 8 1 0 }}


Optimal tuning (POTE): ~19/16 = 1\4, ~3/2 = 705.339
Optimal tuning (POTE): ~19/16 = 1\4, ~3/2 = 705.339
Line 700: Line 700:


== Echidna ==
== Echidna ==
Echidna adds 1728/1715 to the commas and takes 9/7 as a generator. It may be called the 22&58 temperament. [[58edo]] or [[80edo]] make for good tunings, or their vals can be add to {{val| 138 219 321 388 }}.
Echidna adds 1728/1715 to the commas and takes 9/7 as a generator. It may be called the 22 & 58 temperament. [[58edo]] or [[80edo]] make for good tunings, or their vals can be added to {{val| 138 219 321 388 }}.


Echidna becomes more interesting when extended to be an 11-limit temperament by adding 176/175, 896/891 or 540/539 to the commas, where the same tunings can be used as before. It then is able to represent the entire 11-limit diamond to within about six cents of error, within a compass of 24 notes. The 28 note 2MOS gives scope for this, and the 36 note MOS much more.
Echidna becomes more interesting when extended to be an 11-limit temperament by adding 176/175, 896/891 or 540/539 to the commas, where the same tunings can be used as before. It then is able to represent the entire 11-limit diamond to within about six cents of error, within a compass of 24 notes. The 28 note 2MOS gives scope for this, and the 36 note MOS much more.
Line 708: Line 708:
[[Comma list]]: 1728/1715, 2048/2025
[[Comma list]]: 1728/1715, 2048/2025


[[Mapping]]: [{{val| 2 1 9 2 }}, {{val| 0 3 -6 5 }}]
{{Mapping|legend=1| 2 1 9 2 | 0 3 -6 5 }}


{{Multival|legend=1| 6 -12 10 -33 -1 57 }}
{{Multival|legend=1| 6 -12 10 -33 -1 57 }}
Line 723: Line 723:
Comma list: 176/175, 540/539, 896/891
Comma list: 176/175, 540/539, 896/891


Mapping: [{{val| 2 1 9 2 12 }}, {{val| 0 3 -6 5 -7 }}]
Mapping: {{mapping| 2 1 9 2 12 | 0 3 -6 5 -7 }}


Optimal tuning (POTE): ~45/32 = 1\2, ~9/7 = 434.852
Optimal tuning (POTE): ~45/32 = 1\2, ~9/7 = 434.852
Line 730: Line 730:
* 11-odd-limit: ~9/7 = {{monzo| 5/12 0 0 1/12 -1/12 }}
* 11-odd-limit: ~9/7 = {{monzo| 5/12 0 0 1/12 -1/12 }}
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 7/4 0 0 1/4 -1/4 }}, {{monzo| 2 0 0 -1/2 1/2 }}, {{monzo| 37/12 0 0 5/12 -5/12 }}, {{monzo| 37/12 0 0 -7/12 7/12 }}]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 7/4 0 0 1/4 -1/4 }}, {{monzo| 2 0 0 -1/2 1/2 }}, {{monzo| 37/12 0 0 5/12 -5/12 }}, {{monzo| 37/12 0 0 -7/12 7/12 }}]
: Eigenmonzo subgroup (unchanged-interval basis): 2.11/7
: Eigenmonzo (unchanged-interval) basis: 2.11/7


{{Optimal ET sequence|legend=1| 22, 58, 80, 138cde, 218cde }}
{{Optimal ET sequence|legend=1| 22, 58, 80, 138cde, 218cde }}
Line 741: Line 741:
Comma list: 176/175, 351/350, 364/363, 540/539
Comma list: 176/175, 351/350, 364/363, 540/539


Mapping: [{{val| 2 1 9 2 12 19 }}, {{val| 0 3 -6 5 -7 -16 }}]
Mapping: {{mapping| 2 1 9 2 12 19 | 0 3 -6 5 -7 -16 }}


Optimal tuning (POTE): ~45/32 = 1\2, ~9/7 = 434.756
Optimal tuning (POTE): ~45/32 = 1\2, ~9/7 = 434.756
Line 754: Line 754:
Comma list: 136/135, 176/175, 221/220, 256/255, 540/539
Comma list: 136/135, 176/175, 221/220, 256/255, 540/539


Mapping: [{{val| 2 1 9 2 12 19 6 }}, {{val| 0 3 -6 5 -7 -16 3 }}]
Mapping: {{mapping| 2 1 9 2 12 19 6 | 0 3 -6 5 -7 -16 3 }}


Optimal tuning (POTE): ~17/12 = 1\2, ~9/7 = 434.816
Optimal tuning (POTE): ~17/12 = 1\2, ~9/7 = 434.816
Line 767: Line 767:
[[Comma list]]: 686/675, 1029/1024
[[Comma list]]: 686/675, 1029/1024


[[Mapping]]: [{{val| 2 2 7 6 }}, {{val| 0 3 -6 -1 }}]
{{Mapping|legend=1| 2 2 7 6 | 0 3 -6 -1 }}


{{Multival|legend=1| 6 -12 -2 -33 -20 29 }}
{{Multival|legend=1| 6 -12 -2 -33 -20 29 }}
Line 782: Line 782:
Comma list: 385/384, 441/440, 686/675
Comma list: 385/384, 441/440, 686/675


Mapping: [{{val| 2 2 7 6 3 }}, {{val| 0 3 -6 -1 10 }}]
Mapping: {{mapping| 2 2 7 6 3 | 0 3 -6 -1 10 }}


Optimal tuning (POTE): ~45/32 = 1\2, ~8/7 = 235.096
Optimal tuning (POTE): ~45/32 = 1\2, ~8/7 = 235.096
Line 795: Line 795:
Comma list: 91/90, 169/168, 385/384, 441/440
Comma list: 91/90, 169/168, 385/384, 441/440


Mapping: [{{val| 2 2 7 6 3 7 }}, {{val| 0 3 -6 -1 10 1 }}]
Mapping: {{mapping| 2 2 7 6 3 7 | 0 3 -6 -1 10 1 }}


Optimal tuning (POTE): ~45/32 = 1\2, ~8/7 = 235.088
Optimal tuning (POTE): ~45/32 = 1\2, ~8/7 = 235.088
Line 808: Line 808:
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: [{{val| 2 2 7 6 3 7 7 }}, {{val| 0 3 -6 -1 10 1 3 }}]
Mapping: {{mapping| 2 2 7 6 3 7 7 | 0 3 -6 -1 10 1 3 }}


Optimal tuning (POTE): ~17/12 = 1\2, ~8/7 = 235.088
Optimal tuning (POTE): ~17/12 = 1\2, ~8/7 = 235.088
Line 828: Line 828:
[[Comma list]]: 245/243, 2048/2025
[[Comma list]]: 245/243, 2048/2025


[[Mapping]]: [{{val| 2 1 9 -2 }}, {{val| 0 2 -4 7 }}]
{{Mapping|legend=1| 2 1 9 -2 | 0 2 -4 7 }}


{{Multival|legend=1| 4 -8 14 -22 11 55 }}
{{Multival|legend=1| 4 -8 14 -22 11 55 }}
Line 843: Line 843:
Comma list: 121/120, 176/175, 245/243
Comma list: 121/120, 176/175, 245/243


Mapping: [{{val| 2 1 9 -2 8 }}, {{val| 0 2 -4 7 -1 }}]
Mapping: {{mapping| 2 1 9 -2 8 | 0 2 -4 7 -1 }}


Optimal tuning (POTE): ~45/32 = 1\2, ~16/11 = 652.680
Optimal tuning (POTE): ~45/32 = 1\2, ~16/11 = 652.680
Line 856: Line 856:
Comma list: 121/120, 176/175, 196/195, 245/243
Comma list: 121/120, 176/175, 196/195, 245/243


Mapping: [{{val| 2 1 9 -2 8 -10 }}, {{val| 0 2 -4 7 -1 16 }}]
Mapping: {{mapping| 2 1 9 -2 8 -10 | 0 2 -4 7 -1 16 }}


Optimal tuning (POTE): ~45/32 = 1\2, ~16/11 = 652.654
Optimal tuning (POTE): ~45/32 = 1\2, ~16/11 = 652.654
Line 869: Line 869:
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: [{{val| 2 1 9 -2 8 -10 6 }}, {{val| 0 2 -4 7 -1 16 2 }}]
Mapping: {{mapping| 2 1 9 -2 8 -10 6 | 0 2 -4 7 -1 16 2 }}


Optimal tuning (POTE): ~17/12 = 1\2, ~16/11 = 652.647
Optimal tuning (POTE): ~17/12 = 1\2, ~16/11 = 652.647
Line 882: Line 882:
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: [{{val| 2 1 9 -2 8 -10 6 -10 }}, {{val| 0 2 -4 7 -1 16 2 17 }}]
Mapping: {{mapping| 2 1 9 -2 8 -10 6 -10 | 0 2 -4 7 -1 16 2 17 }}


Optimal tuning (POTE): ~17/12 = 1\2, ~16/11 = 652.730
Optimal tuning (POTE): ~17/12 = 1\2, ~16/11 = 652.730
Line 895: Line 895:
[[Comma list]]: 2048/2025, 19683/19600
[[Comma list]]: 2048/2025, 19683/19600


[[Mapping]]: [{{val| 2 0 11 -15 }}, {{val| 0 2 -4 13 }}]
{{Mapping|legend=1| 2 0 11 -15 | 0 2 -4 13 }}


{{Multival|legend=1| 4 -8 26 -22 30 83 }}
{{Multival|legend=1| 4 -8 26 -22 30 83 }}
Line 910: Line 910:
Comma list: 176/175, 243/242, 896/891
Comma list: 176/175, 243/242, 896/891


Mapping: [{{val| 2 0 11 -15 -1 }}, {{val| 0 2 -4 13 5 }}]
Mapping: {{mapping| 2 0 11 -15 -1 | 0 2 -4 13 5 }}


Optimal tuning (POTE): ~45/32 = 1\2, ~121/70 = 951.863
Optimal tuning (POTE): ~45/32 = 1\2, ~121/70 = 951.863
Line 923: Line 923:
Comma list: 144/143, 176/175, 351/350, 676/675
Comma list: 144/143, 176/175, 351/350, 676/675


Mapping: [{{val| 2 0 11 -15 -1 9 }}, {{val| 0 2 -4 13 5 -1 }}]
Mapping: {{mapping| 2 0 11 -15 -1 9 | 0 2 -4 13 5 -1 }}


Optimal tuning (POTE): ~45/32 = 1\2, ~26/15 = 951.886
Optimal tuning (POTE): ~45/32 = 1\2, ~26/15 = 951.886
Line 936: Line 936:
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: [{{val| 2 0 11 -15 -1 9 5 }}, {{val| 0 2 -4 13 5 -1 2 }}]
Mapping: {{mapping| 2 0 11 -15 -1 9 5 | 0 2 -4 13 5 -1 2 }}


Optimal tuning (POTE): ~17/12 = 1\2, ~26/15 = 951.857
Optimal tuning (POTE): ~17/12 = 1\2, ~26/15 = 951.857
Line 949: Line 949:
[[Comma list]]: 49/48, 2048/2025
[[Comma list]]: 49/48, 2048/2025


[[Mapping]]: [{{val| 2 0 11 4 }}, {{val| 0 2 -4 1 }}]
{{Mapping|legend=1| 2 0 11 4 | 0 2 -4 1 }}


{{Multival|legend=1| 4 -8 2 -22 -8 27 }}
{{Multival|legend=1| 4 -8 2 -22 -8 27 }}
Line 964: Line 964:
Comma list: 49/48, 56/55, 243/242
Comma list: 49/48, 56/55, 243/242


Mapping: [{{val| 2 0 11 4 -1 }}, {{val| 0 2 -4 1 5 }}]
Mapping: {{mapping| 2 0 11 4 -1 | 0 2 -4 1 5 }}


Optimal tuning (POTE): ~45/32 = 1\2, ~7/4 = 952.184
Optimal tuning (POTE): ~45/32 = 1\2, ~7/4 = 952.184
Line 977: Line 977:
Comma list: 49/48, 56/55, 91/90, 243/242
Comma list: 49/48, 56/55, 91/90, 243/242


Mapping: [{{val| 2 0 11 4 -1 9 }}, {{val| 0 2 -4 1 5 -1 }}]
Mapping: {{mapping| 2 0 11 4 -1 9 | 0 2 -4 1 5 -1 }}


Optimal tuning (POTE): ~45/32 = 1\2, ~7/4 = 952.309
Optimal tuning (POTE): ~45/32 = 1\2, ~7/4 = 952.309
Line 990: Line 990:
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: [{{val| 2 0 11 4 -1 9 5 }}, {{val| 0 2 -4 1 5 -1 2 }}]
Mapping: {{mapping| 2 0 11 4 -1 9 5 | 0 2 -4 1 5 -1 2 }}


Optimal tuning (POTE): ~17/12 = 1\2, ~7/4 = 952.330
Optimal tuning (POTE): ~17/12 = 1\2, ~7/4 = 952.330
Line 1,003: Line 1,003:
[[Comma list]]: 392/375, 1323/1280
[[Comma list]]: 392/375, 1323/1280


[[Mapping]]: [{{val| 2 1 9 11 }}, {{val| 0 2 -4 -5 }}]
{{Mapping|legend=1| 2 1 9 11 | 0 2 -4 -5 }}


{{Multival|legend=1| 4 -8 -10 -22 -27 -1 }}
{{Multival|legend=1| 4 -8 -10 -22 -27 -1 }}
Line 1,018: Line 1,018:
Comma list: 56/55, 77/75, 1323/1280
Comma list: 56/55, 77/75, 1323/1280


Mapping: [{{val| 2 1 9 11 8 }}, {{val| 0 2 -4 -5 -1 }}]
Mapping: {{mapping| 2 1 9 11 8 | 0 2 -4 -5 -1 }}


Optimal tuning (POTE): ~45/32 = 1\2, ~10/7 = 650.130
Optimal tuning (POTE): ~45/32 = 1\2, ~10/7 = 650.130
Line 1,031: Line 1,031:
Comma list: 56/55, 77/75, 105/104, 507/500
Comma list: 56/55, 77/75, 105/104, 507/500


Mapping: [{{val| 2 1 9 11 8 15 }}, {{val| 0 2 -4 -5 -1 -7 }}]
Mapping: {{mapping| 2 1 9 11 8 15 | 0 2 -4 -5 -1 -7 }}


Optimal tuning (POTE): ~45/32 = 1\2, ~10/7 = 650.535
Optimal tuning (POTE): ~45/32 = 1\2, ~10/7 = 650.535
Line 1,044: Line 1,044:
[[Comma list]]: 2048/2025, 2401/2400
[[Comma list]]: 2048/2025, 2401/2400


[[Mapping]]: [{{val| 2 0 11 8 }}, {{val| 0 4 -8 -3 }}]
{{Mapping|legend=1| 2 0 11 8 | 0 4 -8 -3 }}


{{Multival|legend=1| 8 -16 -6 -44 -32 31 }}
{{Multival|legend=1| 8 -16 -6 -44 -32 31 }}
Line 1,059: Line 1,059:
Comma list: 176/175, 896/891, 2401/2400
Comma list: 176/175, 896/891, 2401/2400


Mapping: [{{val| 2 0 11 8 22 }}, {{val| 0 4 -8 -3 -19 }}]
Mapping: {{mapping| 2 0 11 8 22 | 0 4 -8 -3 -19 }}


Optimal tuning (POTE): ~45/32 = 1\2, ~21/16 = 476.118
Optimal tuning (POTE): ~45/32 = 1\2, ~21/16 = 476.118
Line 1,072: Line 1,072:
Comma list: 176/175, 196/195, 512/507, 676/675
Comma list: 176/175, 196/195, 512/507, 676/675


Mapping: [{{val| 2 0 11 8 22 9 }}, {{val| 0 4 -8 -3 -19 -2 }}]
Mapping: {{mapping| 2 0 11 8 22 9 | 0 4 -8 -3 -19 -2 }}


Optimal tuning (POTE): ~45/32 = 1\2, ~21/16 = 476.099
Optimal tuning (POTE): ~45/32 = 1\2, ~21/16 = 476.099
Line 1,085: Line 1,085:
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: [{{val| 2 0 11 8 22 9 5 }}, {{val| 0 4 -8 -3 -19 -2 4 }}]
Mapping: {{mapping| 2 0 11 8 22 9 5 | 0 4 -8 -3 -19 -2 4 }}


Optimal tuning (POTE): ~17/12 = 1\2, ~21/16 = 476.162
Optimal tuning (POTE): ~17/12 = 1\2, ~21/16 = 476.162
Line 1,098: Line 1,098:
Comma list: 243/242, 441/440, 2048/2025
Comma list: 243/242, 441/440, 2048/2025


Mapping: [{{val| 2 0 11 8 -1 }}, {{val| 0 4 -8 -3 10 }}]
Mapping: {{mapping| 2 0 11 8 -1 | 0 4 -8 -3 10 }}


Optimal tuning (POTE): ~45/32 = 1\2, ~21/16 = 476.017
Optimal tuning (POTE): ~45/32 = 1\2, ~21/16 = 476.017
Line 1,111: Line 1,111:
Comma list: 144/143, 196/195, 243/242, 676/675
Comma list: 144/143, 196/195, 243/242, 676/675


Mapping: [{{val| 2 0 11 8 -1 9 }}, {{val| 0 4 -8 -3 10 -2 }}]
Mapping: {{mapping| 2 0 11 8 -1 9 | 0 4 -8 -3 10 -2 }}


Optimal tuning (POTE): ~45/32 = 1\2, ~21/16 = 476.028
Optimal tuning (POTE): ~45/32 = 1\2, ~21/16 = 476.028
Line 1,124: Line 1,124:
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: [{{val| 2 0 11 8 -1 9 5 }}, {{val| 0 4 -8 -3 10 -2 4 }}]
Mapping: {{mapping| 2 0 11 8 -1 9 5 | 0 4 -8 -3 10 -2 4 }}


Optimal tuning (POTE): ~17/12 = 1\2, ~21/16 = 476.077
Optimal tuning (POTE): ~17/12 = 1\2, ~21/16 = 476.077
Line 1,132: Line 1,132:
Badness: 0.022239
Badness: 0.022239


[[Category:Temperament families]]
[[Category:Diaschismic family| ]] <!-- main article -->
[[Category:Diaschismic family| ]] <!-- main article -->
[[Category:Temperament families]]
[[Category:Diaschismic| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Diaschismic_family"