Associated temperament: Difference between revisions
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cleanup 7-limit table |
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{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! 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|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 | | | 245/243 | ||
Line 135: | Line 135: | ||
| | 2401/2400, 65625/65536 | | | 2401/2400, 65625/65536 | ||
|- | |- | ||
| 703125/702464 | |||
| [[2185edo]] | |||
| [[Ragismic_microtemperaments#Enneadecal|enneadecal]] | |||
| 4375/4374, 703125/702464 | |||
|- | |- | ||
| 4375/4374 | |||
| [[8419edo]] | |||
| [[Semidimi]] | |||
| 4375/4374, 3955078125/3954653486 | |||
|- | |- | ||
| 250047/250000 | |||
| [[12555edo]] | |||
| | |||
| 250047/250000, 281484423828125/281474976710656 | |||
|} | |} | ||
Revision as of 17:14, 11 September 2020
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 |
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 |
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 |
441/400 | 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 |
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 |