Associated temperament: Difference between revisions
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| Line 82: | Line 82: | ||
| 245/243 | | 245/243 | ||
| [[283edo]] | | [[283edo]] | ||
| [[Escapade family#Escaped| | | [[Escapade family#Escaped|Escaped]] | ||
| 245/243, 65625/65536 | | 245/243, 65625/65536 | ||
|- | |- | ||
| Line 92: | Line 92: | ||
| 1728/1715 | | 1728/1715 | ||
| [[111edo]] | | [[111edo]] | ||
| [[Hemifamity temperaments#Buzzard| | | [[Hemifamity temperaments#Buzzard|Buzzard]] | ||
| 1728/1715, 5120/5103 | | 1728/1715, 5120/5103 | ||
|- | |- | ||
| Line 107: | Line 107: | ||
| 225/224 | | 225/224 | ||
| [[197edo]] | | [[197edo]] | ||
| [[ | | [[Catakleismic]] | ||
| 225/224, 4375/4374 | | 225/224, 4375/4374 | ||
|- | |- | ||
| 3136/3125 | | 3136/3125 | ||
| [[446edo]] | | [[446edo]] | ||
| [[Hemimean clan#Sengagen| | | [[Hemimean clan#Sengagen|Sengagen]] | ||
| 3136/3125, 420175/419904 | | 3136/3125, 420175/419904 | ||
|- | |- | ||
| 5120/5103 | | 5120/5103 | ||
| [[391edo]] | | [[391edo]] | ||
| [[Hemifamity temperaments#Alphaquarter| | | [[Hemifamity temperaments#Alphaquarter|Alphaquarter]] | ||
| 5120/5103, 29360128/29296875 | | 5120/5103, 29360128/29296875 | ||
|- | |- | ||
| 5120/5103 | | 5120/5103 | ||
| [[391edo]] | | [[391edo]] | ||
| [[Hemifamity temperaments#Septiquarter| | | [[Hemifamity temperaments#Septiquarter|Septiquarter]] | ||
| 5120/5103, 420175/419904 | | 5120/5103, 420175/419904 | ||
|- | |- | ||
| 6144/6125 | | 6144/6125 | ||
| [[381edo]] | | [[381edo]] | ||
| [[ | | [[Nessafof]] | ||
| 6144/6125, 250047/250000 | | 6144/6125, 250047/250000 | ||
|- | |- | ||
| 65625/65536 | | 65625/65536 | ||
| [[171edo]] | | [[171edo]] | ||
| [[Breedsmic temperaments#Tertiaseptal| | | [[Breedsmic temperaments#Tertiaseptal|Tertiaseptal]] | ||
| 2401/2400, 65625/65536 | | 2401/2400, 65625/65536 | ||
|- | |- | ||
| 4802000/4782969 | | 4802000/4782969 | ||
| [[1131edo]] | | [[1131edo]] | ||
| [[ | | [[Amicable]] | ||
| 2401/2400, 1600000/1594323 | | 2401/2400, 1600000/1594323 | ||
|- | |- | ||
| 703125/702464 | | 703125/702464 | ||
| [[2185edo]] | | [[2185edo]] | ||
| [[Ragismic microtemperaments#Enneadecal| | | [[Ragismic microtemperaments#Enneadecal|Enneadecal]] | ||
| 4375/4374, 703125/702464 | | 4375/4374, 703125/702464 | ||
|- | |- | ||
Revision as of 13:06, 21 February 2021
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 |
| 4802000/4782969 | 1131edo | Amicable | 2401/2400, 1600000/1594323 |
| 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 |