Associated temperament
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By an associated temperament to a p-limit comma is meant a p-limit temperament tempering out that comma which shares the same optimal patent val as the codimension one temperament tempering out that comma. By definition, the optimal patent val defines the unique rank one associated temperament. For rank two temperaments, it is possible for more than one temperament to be associated, and some of these are listed below. The column headings are the comma being associated, the optimal patent val, the rank two temperament, and a comma basis for the rank two temperament.
7-limit
Comma | OPV | Temperament | Basis |
---|---|---|---|
28/27 | 15edo | Blacksmith | 28/27, 49/48 |
1029/1000 | 55edo | Liese | 81/80, 686/675 |
36/35 | 12edo | Diminished | 36/35, 50/49 |
36/35 | 12edo | August | 36/35, 128/125 |
36/35 | 12edo | Dominant | 36/35, 64/63 |
525/512 | 45edo | Flattone | 81/80, 525/512 |
49/48 | 19edo | Keemun | 49/48, 126/125 |
49/48 | 19edo | Godzilla | 49/48, 81/80 |
50/49 | 48edo | Doublewide | 50/49, 875/864 |
64/63 | 49edo | Superpyth | 64/63, 245/243 |
875/864 | 41edo | Magic | 225/224, 245/243 |
875/864 | 41edo | Superkleismic | 875/864, 1029/1024 |
3125/3087 | 94edo | Garibaldi | 225/224, 3125/3087 |
2430/2401 | 137edo | Orwell | 225/224, 1728/1715 |
245/243 | 283edo | Escaped | 245/243, 65625/65536 |
126/125 | 185edo | Valentine | 126/125, 1029/1024 |
1728/1715 | 111edo | Buzzard | 1728/1715, 5120/5103 |
1728/1715 | 111edo | Semisept | 1728/1715, 3136/3125 |
1029/1024 | 190edo | Unidec | 1029/1024, 4375/4374 |
225/224 | 197edo | Catakleismic | 225/224, 4375/4374 |
16875/16807 | 224edo | Octoid | 4375/4374, 16875/16807 |
4802000/4782969 | 1131edo | Amicable | 2401/2400, 1600000/1594323 |
3136/3125 | 446edo | Sengagen | 3136/3125, 420175/419904 |
5120/5103 | 391edo | Alphaquarter | 5120/5103, 29360128/29296875 |
5120/5103 | 391edo | Septiquarter | 5120/5103, 420175/419904 |
6144/6125 | 381edo | Nessafof | 6144/6125, 250047/250000 |
65625/65536 | 171edo | Tertiaseptal | 2401/2400, 65625/65536 |
703125/702464 | 2185edo | Enneadecal | 4375/4374, 703125/702464 |
4375/4374 | 8419edo | Semidimi | 4375/4374, 3955078125/3954653486 |
250047/250000 | 12555edo | 250047/250000, 281484423828125/281474976710656 |
11-limit
Comma | OPV | Temperament | Basis |
---|---|---|---|
33/32 | 16edo | Armodue | 33/32, 36/35, 45/44 |
77/75 | 39edo | Triforce | 49/48, 56/55, 77/75 |
352/343 | 22edo | Hedgehog | 50/49, 55/54, 99/98 |
45/44 | 45edo | Flattone | 45/44, 81/80, 385/384 |
55/54 | 51edo | Porky | 55/54, 100/99, 225/224 |
56/55 | 36edo | Catcall | 56/55, 81/80, 128/125 |
245/242 | 91edo | Septimin | 225/224, 245/242, 385/384 |
99/98 | 127edo | Würschmidt | 99/98, 176/175, 243/242 |
100/99 | 104edo | Magic | 100/99, 225/224, 245/243 |
121/120 | 99edo | Hitchcock | 121/120, 176/175, 2200/2187 |
121/120 | 99edo | Hemiwur | 121/120, 176/175, 1375/1372 |
176/175 | 111edo | Semisept | 176/175, 540/539, 1331/1323 |
896/891 | 208edo | Metakleismic | 896/891, 2200/2187, 14700/14641 |
65536/65219 | 282edo | Septisuperfourth | 540/539, 4000/3993, 5632/5625 |
14641/14580 | 410edo | Floral | 2401/2400, 9801/9800, 14641/14580 |
243/242 | 202edo | Harry | 243/242, 441/440, 4000/3993 |
243/242 | 202edo | Tertiaseptal | 243/242, 441/440, 65625/65536 |
3388/3375 | 316edo | Semiparakleismic | 3025/3024, 3136/3125, 4375/4374 |
385/384 | 284edo | Quadritikleismic | 385/384, 1375/1372, 6250/6237 |
441/440 | 320edo | Octowerck | 441/440, 8019/8000, 41503/41472 |
540/539 | 578edo | Pogo | 540/539, 4000/3993, 32805/32768 |
4000/3993 | 665edo | Brahmagupta | 4000/3993, 4375/4374, 131072/130977 |
5632/5625 | 1092edo | Sextile | 5632/5625, 9801/9800, 151263/151250 |
3025/3024 | 2554edo | Semisupermajor | 3025/3024, 4375/4374, 35156250/35153041 |
13-limit
Comma | OPV | Temperament | Basis |
---|---|---|---|
26/25 | 12edo | Augustus | 26/25, 36/35, 45/44, 56/55 |
27/26 | 35edo | Secund | 27/26, 45/44, 99/98, 385/384 |
27/26 | 35edo | Greenwood | 27/26, 45/44, 99/98, 640/637 |
40/39 | 15edo | Blacksmith | 28/27, 40/39, 49/48, 55/54 |
65/64 | 29edo | Negril | 49/48, 65/64, 91/90, 875/858 |
65/64 | 29edo | Coendou | 55/54, 65/64, 100/99, 105/104 |
66/65 | 31edo | Winston | 66/65, 99/98, 105/104, 121/120 |
66/65 | 31edo | Mohajira | 66/65, 81/80, 105/104, 121/120 |
66/65 | 31edo | Squares | 66/65, 81/80, 99/98, 121/120 |
78/77 | 43edo | Amavil | 78/77, 99/98, 144/143, 176/175 |
78/77 | 43edo | Jerome | 78/77, 81/80, 99/98, 144/143 |
91/90 | 102edo | Echidnic | 91/90, 169/168, 385/384, 441/440 |
105/104 | 91edo | Septimin | 105/104, 144/143, 196/195, 245/242 |
275/273 | 94edo | Garibaldi | 225/224, 275/273, 325/324, 385/384 |
144/143 | 84edo | Merman | 144/143, 225/224, 364/363, 441/440 |
144/143 | 84edo | Secant | 144/143, 351/350, 364/363, 441/440 |
169/168 | 152edo | Octopus | 169/168, 325/324, 364/363, 540/539 |
196/195 | 232edo | Mystery | 196/195, 352/351, 364/363, 676/675 |
640/637 | 205edo | Quanic | 352/351, 540/539, 729/728, 1331/1323 |
1188/1183 | 255edo | Subsemifourth | 540/539, 847/845, 1375/1372, 1575/1573 |
1573/1568 | 323edo | Stockhausenic | 676/675, 1001/1000, 1375/1372, 4096/4095 |
325/324 | 333edo | Novemkleismic | 325/324, 625/624, 1375/1372, 4000/3993 |
351/350 | 546edo | Fermionic | 351/350, 540/539, 40656/40625, 142884/142805 |
352/351 | 198edo | Semihemi | 352/351, 676/675, 847/845, 1716/1715 |
352/351 | 198edo | Hemimist | 352/351, 676/675, 847/845, 3025/3024 |
847/845 | 388edo | Neusec | 847/845, 1001/1000, 3025/3024, 4375/4374 |
676/675 | 940edo | Decoid | 676/675, 1001/1000, 1716/1715, 4225/4224 |
2200/2197 | 836edo | Quasithird | 2200/2197, 3025/3024, 4375/4374, 468512/468195 |