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* [[Diaschismic family #Diaschismic|diaschismic]] ({126/125, 2048/2025}, diaschismic family)
* [[Diaschismic family #Diaschismic|diaschismic]] ({126/125, 2048/2025}, diaschismic family)
* [[Tetracot family #Wollemia|wollemia]] ({126/125, 2240/2187}, tetracot family)
* [[Tetracot family #Wollemia|wollemia]] ({126/125, 2240/2187}, tetracot family)
* [[Unicorn family|unicorn]] ({126/125, 10976/10935}, unicorn family)
* [[Cloudy clan #Coblack|coblack]] ({126/125, 16807/16384}, cloudy clan)
* [[Cloudy clan #Coblack|coblack]] ({126/125, 16807/16384}, cloudy clan)
* [[Schismatic family #Grackle|grackle]] ({126/125, 32805/32768}, schismatic family)
* [[Schismatic family #Grackle|grackle]] ({126/125, 32805/32768}, schismatic family)
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In addition to 126/125, myna tempers out [[1728/1715]], the orwell comma, and [[2401/2400]], the breedsma. It can also be described as the 27&amp;31 temperament. It has 6/5 as a generator, and [[58edo]] can be used as a tuning, with [[89edo]] being a better one, and fans of round amounts in cents may like [[120edo]]. It is also possible to tune myna with pure fifths by taking 6<sup>1/10</sup> as the generator. Myna extends naturally but with much increased complexity to the 11 and 13 limits.
In addition to 126/125, myna tempers out [[1728/1715]], the orwell comma, and [[2401/2400]], the breedsma. It can also be described as the 27&amp;31 temperament. It has 6/5 as a generator, and [[58edo]] can be used as a tuning, with [[89edo]] being a better one, and fans of round amounts in cents may like [[120edo]]. It is also possible to tune myna with pure fifths by taking 6<sup>1/10</sup> as the generator. Myna extends naturally but with much increased complexity to the 11 and 13 limits.
== 5-limit (mynic) ==


Subgroup: 2.3.5
Subgroup: 2.3.5
Line 38: Line 37:
{{Val list|legend=1| 27, 31, 58, 89, 325cc }}
{{Val list|legend=1| 27, 31, 58, 89, 325cc }}


[[Badness]]: 0.2500
[[Badness]]: 0.249965


== 7-limit ==
== 7-limit ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 61: Line 59:
{{Val list|legend=1| 27, 31, 58, 89 }}
{{Val list|legend=1| 27, 31, 58, 89 }}


[[Badness]]: 0.0270
[[Badness]]: 0.027044


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 73: Line 70:
POTE generator: ~6/5 = 310.144
POTE generator: ~6/5 = 310.144


{{Val list|legend=1| 27e, 31, 58, 89 }}
Vals: {{Val list| 27e, 31, 58, 89 }}


Badness: 0.0168
Badness: 0.016842


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 87: Line 83:
POTE generator: ~6/5 = 310.276
POTE generator: ~6/5 = 310.276


{{Val list|legend=1| 27e, 31, 58 }}
Vals: {{Val list| 27e, 31, 58 }}


Badness: 0.0171
Badness: 0.017125


=== Minah ===
=== Minah ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 101: Line 96:
POTE generator: ~6/5 = 310.381
POTE generator: ~6/5 = 310.381


{{Val list|legend=1| 27e, 31f, 58f }}
Vals: {{Val list| 27e, 31f, 58f }}


Badness: 0.0276
Badness: 0.027568


=== Maneh ===
=== Maneh ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 115: Line 109:
POTE generator: ~6/5 = 309.804
POTE generator: ~6/5 = 309.804


{{Val list|legend=1| 27eff, 31 }}
Vals: {{Val list| 27eff, 31 }}


Badness: 0.0299
Badness: 0.029868


== Myno ==
== Myno ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 129: Line 122:
POTE generator: ~6/5 = 309.737
POTE generator: ~6/5 = 309.737


{{Val list|legend=1| 27, 31 }}
Vals: {{Val list| 27, 31 }}


Badness: 0.0334
Badness: 0.033434


== Coleto ==
== Coleto ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 143: Line 135:
POTE generator: ~6/5 = 310.853
POTE generator: ~6/5 = 310.853


{{Val list|legend=1| 4, …, 23bc, 27e }}
Vals: {{Val list| 4, 23bc, 27e }}


Badness: 0.0487
Badness: 0.048687


= Valentine =
= Valentine =
Line 154: Line 146:


Valentine is very closely related to [[Carlos Alpha]], the rank one nonoctave temperament of Wendy Carlos, as the generator chain of valentine is the same thing as Carlos Alpha. Indeed, the way Carlos uses Alpha in ''Beauty in the Beast'' suggests that she really intended Alpha to be the same thing as valentine, and that it is misdescribed as a rank one temperament. Carlos tells us that "[t]he melodic motions of Alpha are amazingly exotic and fresh, like you've never heard before", and since Alpha lives inside valentine this comment carries over and applies to it if you stick close melodically to generator steps, which is almost impossible not to do since the generator step is so small. MOS of 15, 16, 31 and 46 notes are available to explore these exotic and fresh melodies, or the less exotic ones you might cook up otherwise.
Valentine is very closely related to [[Carlos Alpha]], the rank one nonoctave temperament of Wendy Carlos, as the generator chain of valentine is the same thing as Carlos Alpha. Indeed, the way Carlos uses Alpha in ''Beauty in the Beast'' suggests that she really intended Alpha to be the same thing as valentine, and that it is misdescribed as a rank one temperament. Carlos tells us that "[t]he melodic motions of Alpha are amazingly exotic and fresh, like you've never heard before", and since Alpha lives inside valentine this comment carries over and applies to it if you stick close melodically to generator steps, which is almost impossible not to do since the generator step is so small. MOS of 15, 16, 31 and 46 notes are available to explore these exotic and fresh melodies, or the less exotic ones you might cook up otherwise.
== 5-limit ==


Subgroup: 2.3.5
Subgroup: 2.3.5
Line 167: Line 157:
{{Val list|legend=1| 15, 31, 46, 77, 123 }}
{{Val list|legend=1| 15, 31, 46, 77, 123 }}


[[Badness]]: 0.1228
[[Badness]]: 0.122765


== 7-limit ==
== 7-limit ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 193: Line 182:
{{Val list|legend=1| 15, 31, 46, 77, 185, 262cd }}
{{Val list|legend=1| 15, 31, 46, 77, 185, 262cd }}


[[Badness]]: 0.0311
[[Badness]]: 0.031056


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 214: Line 202:
Algebraic generator: positive root of 4''x''<sup>3</sup> + 15''x''<sup>2</sup> - 21, or else Gontrand2, the smallest positive root of 4''x''<sup>7</sup> - 8''x''<sup>6</sup> + 5.
Algebraic generator: positive root of 4''x''<sup>3</sup> + 15''x''<sup>2</sup> - 21, or else Gontrand2, the smallest positive root of 4''x''<sup>7</sup> - 8''x''<sup>6</sup> + 5.


{{Val list|legend=1| 15, 31, 46, 77, 262cdee, 339cdeee }}
Vals: {{Val list| 15, 31, 46, 77, 262cdee, 339cdeee }}


Badness: 0.0167
Badness: 0.016687


=== Dwynwen ===
=== Dwynwen ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 228: Line 215:
POTE generator: ~21/20 = 78.219
POTE generator: ~21/20 = 78.219


{{Val list|legend=1| 15, 31f, 46 }}
Vals: {{Val list| 15, 31f, 46 }}


Badness: 0.0235
Badness: 0.023461


=== Lupercalia ===
=== Lupercalia ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 242: Line 228:
POTE generator: ~21/20 = 77.709
POTE generator: ~21/20 = 77.709


{{Val list|legend=1| 15, 31, 77ff, 108eff, 139efff }}
Vals: {{Val list| 15, 31, 77ff, 108eff, 139efff }}


Badness: 0.0213
Badness: 0.021328


=== Valentino ===
=== Valentino ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 256: Line 241:
POTE generator: ~21/20 = 77.958
POTE generator: ~21/20 = 77.958


{{Val list|legend=1| 15f, 31, 46, 77, 431ccdeeeef }}
Vals: {{Val list| 15f, 31, 46, 77 }}


Badness: 0.0207
Badness: 0.020665


=== Semivalentine ===
=== Semivalentine ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 270: Line 254:
POTE generator: ~21/20 = 77.839
POTE generator: ~21/20 = 77.839


{{Val list|legend=1| 16, 30, 46, 62, 108ef }}
Vals: {{Val list| 16, 30, 46, 62, 108ef }}
 
Badness: 0.0327
 
= Alicorn =
{{see also| Unicorn family #Alicorn }}
 
Subgroup: 2.3.5.7
 
[[Comma list]]: 126/125, 10976/10935
 
[[Mapping]]: [{{val| 1 2 3 4 }}, {{val| 0 -8 -13 -23 }}]
 
{{Multival|legend=1| 8 13 23 2 14 17 }}


[[POTE generator]]: ~28/27 = 62.278
Badness: 0.032749
 
{{Val list|legend=1| 19, 39d, 58, 77, 135c }}
 
[[Badness]]: 0.040913
 
== 11-limit ==
Subgroup: 2.3.5.7.11
 
Comma list: 126/125, 540/539, 896/891
 
Mapping: [{{val| 1 2 3 4 3 }}, {{val| 0 -8 -13 -23 9 }}]
 
POTE generator: ~28/27 = 62.101
 
Vals: {{Val list| 19, 39d, 58 }}
 
Badness: 0.039156
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 126/125, 144/143, 196/195, 676/675
 
Mapping: [{{val| 1 2 3 4 3 5 }}, {{val| 0 -8 -13 -23 9 -25 }}]
 
POTE generator: ~28/27 = 62.119
 
Vals: {{Val list| 19, 39df, 58 }}
 
Badness: 0.023667
 
== Camahueto ==
Subgroup: 2.3.5.7.11
 
Comma list: 126/125, 385/384, 10976/10935
 
Mapping: [{{val| 1 2 3 4 2 }}, {{val| 0 -8 -13 -23 28 }}]
 
POTE generator: ~28/27 = 62.431
 
Vals: {{Val list| 19, 58e, 77, 96d, 173d }}
 
Badness: 0.065940
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 126/125, 196/195, 385/384, 676/675
 
Mapping: [{{val| 1 2 3 4 2 5 }}, {{val| 0 -8 -13 -23 28 -25 }}]
 
POTE generator: ~28/27 = 62.434
 
Vals: {{Val list| 19, 58e, 77, 96d, 173d }}
 
Badness: 0.036155
 
== Qilin ==
Subgroup: 2.3.5.7.11
 
Comma list: 126/125, 176/175, 10976/10935
 
Mapping: [{{val| 1 2 3 4 6 }}, {{val| 0 -8 -13 -23 -49 }}]
 
POTE generator: ~28/27 = 62.196
 
Vals: {{Val list| 58, 77, 135c, 193c, 328cc }}
 
Badness: 0.041426
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 126/125, 176/175, 196/195, 2200/2197
 
Mapping: [{{val| 1 2 3 4 6 5 }}, {{val| 0 -8 -13 -23 -49 -25 }}]
 
POTE generator: ~28/27 = 62.197
 
Vals: {{Val list| 58, 77, 135c, 193cf, 328ccff }}
 
Badness: 0.022842
 
== Monocerus ==
Subgroup: 2.3.5.7.11
 
Comma list: 126/125, 243/242, 5488/5445
 
Mapping: [{{val| 2 4 6 8 9 }}, {{val| 0 -8 -13 -23 -20 }}]
 
POTE generator: ~28/27 = 62.292
 
Vals: {{Val list| 58, 96d, 154, 212ce, 366cce }}
 
Badness: 0.052757
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 126/125, 196/195, 364/363, 676/675
 
Mapping: [{{val| 2 4 6 8 9 10 }}, {{val| 0 -8 -13 -23 -20 -25 }}]
 
POTE generator: ~28/27 = 62.301
 
Vals: {{Val list| 58, 96d, 154, 366ccef }}
 
Badness: 0.028795


= Casablanca =
= Casablanca =
Line 412: Line 275:
{{Val list|legend=1| 11b, 20b, 31, 104c, 135c, 166c }}
{{Val list|legend=1| 11b, 20b, 31, 104c, 135c, 166c }}


[[Badness]]: 0.1012
[[Badness]]: 0.101191


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 424: Line 286:
POTE generator: ~16/11 = 657.923
POTE generator: ~16/11 = 657.923


{{Val list|legend=1| 11b, 20b, 31 }}
Vals: {{Val list| 11b, 20b, 31 }}


Badness: 0.0623
Badness: 0.067291


== Marrakesh ==
== Marrakesh ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 438: Line 299:
POTE generator: ~22/15 = 657.791
POTE generator: ~22/15 = 657.791


{{Val list|legend=1| 31, 73, 104c, 135c }}
Vals: {{Val list| 31, 73, 104c, 135c }}


Badness: 0.0405
Badness: 0.040539


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 452: Line 312:
POTE generator: ~22/15 = 657.756
POTE generator: ~22/15 = 657.756


{{Val list|legend=1| 31, 73, 104c, 135c, 239ccf }}
Vals: {{Val list| 31, 73, 104c, 135c, 239ccf }}


Badness: 0.0408
Badness: 0.040774


=== Murakuc ===
=== Murakuc ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 466: Line 325:
POTE generator: ~22/15 = 657.700
POTE generator: ~22/15 = 657.700


{{Val list|legend=1| 31, 104cf, 135cf, 166c }}
Vals: {{Val list| 31, 104cff, 135cff }}


Badness: 0.0414
Badness: 0.041395


= Nusecond =
= Nusecond =
Nusecond tempers out 2430/2401 and 16875/16807 in addition to 126/125, and may be described as 31&amp;70. It has a neutral second generator of 49/45, two of which make up a 6/5 minor third since 2430/2401 is tempered out. [[31edo]] can be used as a tuning, or [[132edo]] with a val which is the sum of the [[patent val]]s for 31 and 101. Because 49/45 is flat of 12/11 by only 540/539, nusecond is more naturally thought of as an 11-limit temperament with a combined 12/11 and 11/10 as a generator, tempering out 99/98, 121/120 and 540/539. Because of all the neutral seconds, an exotic Middle Eastern sound comes naturally to nusecond. MOS of 15, 23, or 31 notes are enough to give fuller effect to the harmony, but the 8-note MOS might also be considered from the melodic point of view.
Nusecond tempers out 2430/2401 and 16875/16807 in addition to 126/125, and may be described as 31&amp;70. It has a neutral second generator of 49/45, two of which make up a 6/5 minor third since 2430/2401 is tempered out. [[31edo]] can be used as a tuning, or [[132edo]] with a val which is the sum of the [[patent val]]s for 31 and 101. Because 49/45 is flat of 12/11 by only 540/539, nusecond is more naturally thought of as an 11-limit temperament with a combined 12/11 and 11/10 as a generator, tempering out 99/98, 121/120 and 540/539. Because of all the neutral seconds, an exotic Middle Eastern sound comes naturally to nusecond. MOS of 15, 23, or 31 notes are enough to give fuller effect to the harmony, but the 8-note MOS might also be considered from the melodic point of view.
== 5-limit ==


Subgroup: 2.3.5
Subgroup: 2.3.5
Line 488: Line 345:


== 7-limit ==
== 7-limit ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 514: Line 370:


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 537: Line 392:


== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 551: Line 405:


= Thuja =
= Thuja =
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 567: Line 420:


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 581: Line 433:


== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 595: Line 446:


== 29-limit ==
== 29-limit ==
The ''raison d'etre'' of this entry is the simple and accurate approximation of factor twenty-nine, the 2.5.11.21.29 subgroup being of especially good accuracy and simplicity.
The ''raison d'etre'' of this entry is the simple and accurate approximation of factor twenty-nine, the 2.5.11.21.29 subgroup being of especially good accuracy and simplicity.


Line 607: Line 457:


= Cypress =
= Cypress =
== 5-limit ==
Subgroup: 2.3.5
Subgroup: 2.3.5


Line 622: Line 470:


== 7-limit ==
== 7-limit ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 638: Line 485:


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 652: Line 498:


== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 666: Line 511:


= Bisemidim =
= Bisemidim =
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 682: Line 526:


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 696: Line 539:


== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 710: Line 552:


= Vines =
= Vines =
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 724: Line 565:


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 738: Line 578:


== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 752: Line 591:


= Kumonga =
= Kumonga =
== 5-limit ==
Subgroup: 2.3.5
Subgroup: 2.3.5


Line 767: Line 604:


== 7-limit ==
== 7-limit ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 783: Line 619:


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 797: Line 632:


== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 826: Line 660:


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 840: Line 673:


== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 855: Line 687:
= Oolong =
= Oolong =
{{main|Oolong}}
{{main|Oolong}}
== 5-limit ==


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma list]]: [11 18 -17>
[[Comma list]]: {{monzo|11 18 -17}}


[[Mapping]]: [{{val| 1 6 7 }}, {{val| 0 -17 -18 }}]
[[Mapping]]: [{{val| 1 6 7 }}, {{val| 0 -17 -18 }}]
Line 871: Line 701:


== 7-limit ==
== 7-limit ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 885: Line 714:


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 899: Line 727:


== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Retrieved from "https://en.xen.wiki/w/Starling_temperaments"