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Starling temperaments: Difference between revisions

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= Starling comma =
This page discusses some of the rank two temperaments tempering out [[126/125]], the starling comma or septimal semicomma. Since (6/5)^3 = 126/125 * 12/7, these temperaments tend to have a relatively small complexity for 6/5. They also possess the [[starling tetrad]], the 6/5-6/5-6/5-7/6 versions of the diminished seventh chord. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before [[12edo]] established itself as the standard tuning, it is arguably more authentic to tune it as three stacked minor thirds and an augmented second, which is what it is in meantone, than as the modern version of four stacked very flat minor thirds.
This page discusses some of the rank two temperaments tempering out [[126/125]], the starling comma or septimal semicomma. Since (6/5)^3 = 126/125 * 12/7, these temperaments tend to have a relatively small complexity for 6/5. They also possess the [[starling tetrad]], the 6/5-6/5-6/5-7/6 versions of the diminished seventh chord. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before [[12edo]] established itself as the standard tuning, it is arguably more authentic to tune it as three stacked minor thirds and an augmented second, which is what it is in meantone, than as the modern version of four stacked very flat minor thirds.


= Myna =
= Myna =
{{main|Myna}}
{{main|Myna}}


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&31 temperament, or in terms of its wedgie <<10 9 7 -9 -17 -9||. 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^(1/10) 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&31 temperament, or in terms of its wedgie <<10 9 7 -9 -17 -9||. 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^(1/10) as the generator. Myna extends naturally but with much increased complexity to the 11 and 13 limits.


==5-limit (Mynic)==
==5-limit (mynic)==
Comma: 10077696/9765625
Comma: 10077696/9765625


Line 16: Line 13:
Map: [<1 9 9|, <0 -10 -9|]
Map: [<1 9 9|, <0 -10 -9|]


EDOs: 27, 31, 58, 89, 325c
EDOs: {{EDOs|27, 31, 58, 89, 325cc}}


Badness: 0.2500
Badness: 0.2500
Line 35: Line 32:
[[Generator]]s: 2, 5/3
[[Generator]]s: 2, 5/3


EDOs: 27, 31, 58, 89
EDOs: {{EDOs|27, 31, 58, 89}}


Badness: 0.0270
Badness: 0.0270
Line 46: Line 43:
Map: [<1 9 9 8 22|, <0 -10 -9 -7 -25|]
Map: [<1 9 9 8 22|, <0 -10 -9 -7 -25|]


EDOs: 27e, 31, 58, 89
EDOs: {{EDOs|27e, 31, 58, 89}}


Badness: 0.0168
Badness: 0.0168


==13-limit==
=== 13-limit ===
Commas: 126/125, 144/143, 176/175, 196/195
Commas: 126/125, 144/143, 176/175, 196/195


Line 57: Line 54:
Map: [<1 9 9 8 22 0|, <0 -10 -9 -7 -25 5|]
Map: [<1 9 9 8 22 0|, <0 -10 -9 -7 -25 5|]


EDOs: 27e, 31, 58
EDOs: {{EDOs|27e, 31, 58}}


Badness: 0.0171
Badness: 0.0171


==Minah==
=== Minah ===
Commas: 78/77, 91/90, 126/125, 176/175
Commas: 78/77, 91/90, 126/125, 176/175


Line 68: Line 65:
Map: [<1 9 9 8 22 20|, <0 -10 -9 -7 -25 -22|]
Map: [<1 9 9 8 22 20|, <0 -10 -9 -7 -25 -22|]


EDOs: 27e, 31f, 58f, 116cef
EDOs: {{EDOs|27e, 31f, 58f}}


Badness: 0.0276
Badness: 0.0276


==Maneh==
=== Maneh ===
Commas: 66/65, 105/104, 126/125, 540/539
Commas: 66/65, 105/104, 126/125, 540/539


Line 79: Line 76:
Map: [<1 9 9 8 22 23|, <0 -10 -9 -7 -25 -26|]
Map: [<1 9 9 8 22 23|, <0 -10 -9 -7 -25 -26|]


EDOs: 31
EDOs: {{EDOs|27eff, 31}}


Badness: 0.0299
Badness: 0.0299
Line 90: Line 87:
Map: [<1 9 9 8 -1|, <0 -10 -9 -7 6|]
Map: [<1 9 9 8 -1|, <0 -10 -9 -7 6|]


EDOs: 27, 31
EDOs: {{EDOs|27, 31}}


Badness: 0.0334
Badness: 0.0334
Line 101: Line 98:
Map: [<1 9 9 8 2|, <0 -10 -9 -7 2|]
Map: [<1 9 9 8 2|, <0 -10 -9 -7 2|]


EDOs: 23bc, 27e
EDOs: {{EDOs|23bc, 27e}}


Badness: 0.0487
Badness: 0.0487
Line 136: Line 133:
[[Generator]]s: 2, 14/9
[[Generator]]s: 2, 14/9


EDOs: 19, 27, 46, 157d, 203cd, 249cdd, 295ccdd
EDOs: {{EDOs|19, 27, 46, 157d, 203cd, 249cdd, 295ccdd}}


Badness: 0.0256
Badness: 0.0256
Line 147: Line 144:
Map: [<1 6 8 11 -6|, <0 -7 -9 -13 15|]
Map: [<1 6 8 11 -6|, <0 -7 -9 -13 15|]


EDOs: 19, 27, 46, 111d, 157d
EDOs: {{EDOs|19, 27, 46, 111d, 157d}}


Badness: 0.0379
Badness: 0.0379
Line 158: Line 155:
Map: [<1 6 8 11 -6 10|, <0 -7 -9 -13 15 -10|]
Map: [<1 6 8 11 -6 10|, <0 -7 -9 -13 15 -10|]


EDOs: 19, 27, 46, 111df, 157df
EDOs: {{EDOs|19, 27, 46, 111df, 157df}}


Badness: 0.0256
Badness: 0.0256
Line 169: Line 166:
Map: [<1 6 8 11 6|, <0 -7 -9 -13 -4|]
Map: [<1 6 8 11 6|, <0 -7 -9 -13 -4|]


EDOs: 19, 27e, 73ee
EDOs: {{EDOs|19, 27e, 73ee}}


Badness: 0.0287
Badness: 0.0287
Line 180: Line 177:
Map: [<1 6 8 11 6 10|, <0 -7 -9 -13 -4 -10|]
Map: [<1 6 8 11 6 10|, <0 -7 -9 -13 -4 -10|]


EDOs: 19, 27e, 46e, 73ee
EDOs: {{EDOs|19, 27e, 46e, 73ee}}


Badness: 0.0200
Badness: 0.0200
Line 191: Line 188:
Map: [<1 6 8 11 23|, <0 -7 -9 -13 -31|]
Map: [<1 6 8 11 23|, <0 -7 -9 -13 -31|]


EDOs: 19e, 27e, 46, 119c, 165c
EDOs: {{EDOs|19e, 27e, 46, 119c, 165c}}


Badness: 0.0295
Badness: 0.0295
Line 202: Line 199:
Map: [<1 6 8 11 23 10|, <0 -7 -9 -13 -31 -10|]
Map: [<1 6 8 11 23 10|, <0 -7 -9 -13 -31 -10|]


EDOs: 19e, 27e, 46, 165cf, 211bccf, 257bccff, 303bccdff
EDOs: {{EDOs|19e, 27e, 46, 165cf, 211bccf, 257bccff, 303bccdff}}


Badness: 0.0208
Badness: 0.0208
Line 236: Line 233:
[[Generator]]s: 2, 21/20
[[Generator]]s: 2, 21/20


EDOs: 15, 31, 46, 77, 185, 262
EDOs: {{EDOs|15, 31, 46, 77, 185, 262cd}}


Badness: 0.0311
Badness: 0.0311
Line 258: Line 255:
Map: [<1 1 2 3 3|, <0 9 5 -3 7|]
Map: [<1 1 2 3 3|, <0 9 5 -3 7|]


[[EDO]]s: [[15edo|15]], [[31edo|31]], [[46edo|46]], [[77edo|77]], [[108edo|108]], [[185edo|185]]
[[EDO]]s: {{EDOs|15, 31, 46, 77}}


Badness: 0.0167
Badness: 0.0167


See also: [[Chords of valentine]]
{{see also|Chords of valentine}}


==Dwynwen==
=== Dwynwen ===
Commas: 91/90, 121/120, 126/125, 176/175
Commas: 91/90, 121/120, 126/125, 176/175


Line 271: Line 268:
Map: [<1 1 2 3 3 2|, <0 9 5 -3 7 26|]
Map: [<1 1 2 3 3 2|, <0 9 5 -3 7 26|]


EDOs: 15, 46
EDOs: {{EDOs|15, 31f, 46}}


Badness: 0.0235
Badness: 0.0235


==Lupercalia==
=== Lupercalia ===
Commas: 66/65, 105/104, 121/120, 126/125
Commas: 66/65, 105/104, 121/120, 126/125


POTE generator: ~22/21 = 77.709
POTE generator: ~21/20 = 77.709


Map: [<1 1 2 3 3 3|, <0 9 5 -3 7 11|]
Map: [<1 1 2 3 3 3|, <0 9 5 -3 7 11|]


EDOs: 15, 31, 108, 139
EDOs: {{EDOs|15, 31, 108eff, 139efff}}


Badness: 0.0213
Badness: 0.0213


==Valentino==
=== Valentino ===
Commas: 121/120, 126/125, 176/175, 196/195
Commas: 121/120, 126/125, 176/175, 196/195


POTE generator: ~22/21 = 77.958
POTE generator: ~21/20 = 77.958


Map: [<1 1 2 3 3 5|, <0 9 5 -3 7 -20|]
Map: [<1 1 2 3 3 5|, <0 9 5 -3 7 -20|]


EDOs: 15, 31, 46, 77, 431
EDOs: {{EDOs|15f, 31, 46, 77, 431ccdeeeef}}


Badness: 0.0207
Badness: 0.0207


==Semivalentine==
=== Semivalentine ===
Commas: 121/120, 126/125, 169/168, 176/175
Commas: 121/120, 126/125, 169/168, 176/175


POTE generator: ~22/21 = ~21/20 = 77.839
POTE generator: ~21/20 = 77.839


Map: [<2 2 4 6 6 7|, <0 9 5 -3 7 3|]
Map: [<2 2 4 6 6 7|, <0 9 5 -3 7 3|]


EDOs: 16, 30, 46, 62, 108ef
EDOs: {{EDOs|16, 30, 46, 62, 108ef}}


Badness: 0.0327
Badness: 0.0327
Line 319: Line 316:
Wedgie: <<8 13 23 2 14 17||
Wedgie: <<8 13 23 2 14 17||


EDOs: 19, 58, 77, 96
EDOs: {{EDOs|19, 39d, 58, 77, 135c}}


Badness: 0.0409
Badness: 0.0409


==11-limit==
== 11-limit ==
Commas: 126/125, 540/539, 896/891
Commas: 126/125, 540/539, 896/891


Line 330: Line 327:
Map: [<1 2 3 4 3|, <0 -8 -13 -23 9|]
Map: [<1 2 3 4 3|, <0 -8 -13 -23 9|]


EDOs: 19, 58
EDOs: {{EDOs|19, 39d, 58}}


Badness: 0.0392
Badness: 0.0392


==13-limit==
=== 13-limit ===
Commas: 126/125, 144/143, 196/195, 676/675
Commas: 126/125, 144/143, 196/195, 676/675


Line 341: Line 338:
Map: [<1 2 3 4 3 5|, <0 -8 -13 -23 9 -25|]
Map: [<1 2 3 4 3 5|, <0 -8 -13 -23 9 -25|]


EDOs: 19, 58
EDOs: {{EDOs|19, 39df, 58}}


Badness: 0.0237
Badness: 0.0237


==Camahueto==
== Camahueto ==
Commas: 126/125, 10976/10935, 385/384
Commas: 126/125, 10976/10935, 385/384


Line 352: Line 349:
Map: [<1 2 3 4 2|, <0 -8 -13 -23 28|]
Map: [<1 2 3 4 2|, <0 -8 -13 -23 28|]


EDOs: 19, 58, 77, 96
EDOs: {{EDOs|19, 58e, 77, 96d, 173d}}


Badness: 0.0659
Badness: 0.0659


===13-limit===
=== 13-limit ===
Commas: 126/125, 196/195, 385/384, 676/675
Commas: 126/125, 196/195, 385/384, 676/675


Line 363: Line 360:
Map: [<1 2 3 4 2 5|, <0 -8 -13 -23 28 -25|]
Map: [<1 2 3 4 2 5|, <0 -8 -13 -23 28 -25|]


EDOs: 19, 58, 77
EDOs: {{EDOs|19, 58e, 77, 96d, 173d}}


Badness: 0.0362
Badness: 0.0362


= Coblack =
= Coblack =
In addition to 126/125, the [[Trisedodge family|coblack temperament]] tempers out the cloudy comma, 16807/16384, which is the amount by which five septimal supermajor seconds ([[8/7]]) fall short of an octave.
{{see also|Trisedodge family #Coblack}}
 
In addition to 126/125, the coblack temperament tempers out the cloudy comma, 16807/16384, which is the amount by which five septimal supermajor seconds ([[8/7]]) fall short of an octave.


Commas: 126/125, 16807/16384
Commas: 126/125, 16807/16384
Line 376: Line 375:
Map: [<5 1 7 14|, <0 3 2 0|]
Map: [<5 1 7 14|, <0 3 2 0|]


EDOs: 15, 35, 50, 65
EDOs: {{EDOs|15, 35, 50, 65, 115d}}


Badness: 0.1073
Badness: 0.1073
Line 387: Line 386:
Map: [<5 1 7 14 15|, <0 3 2 0 1|]
Map: [<5 1 7 14 15|, <0 3 2 0 1|]


EDOs: 15, 35, 50, 65
EDOs: {{EDOs|15, 35, 50, 65, 115d}}


= Casablanca =
= Casablanca =
Aside from 126/125, casablanca tempers out the no-threes comma 823543/819200 and also 589824/588245, and may also be described by its wedgie, <<19 14 4 -22 -47 -30||, or as 31&73. 74/135 or 91/166 supply good tunings for the generator, and 20 and 31 note MOS are available.
Aside from 126/125, casablanca tempers out the no-threes comma 823543/819200 and also 589824/588245, and may also be described by its wedgie, <<19 14 4 -22 -47 -30||, or as 31&73. 74\135 or 91\166 supply good tunings for the generator, and 20 and 31 note MOS are available.


It may not seem like casablanca has much to offer, but peering under the hood a bit harder suggests otherwise. For one thing, the 35/24 generator is particularly interesting; like 15/14 and 21/20, it represents an interval between one vertex of a [[hexany]] and the opposite vertex, which makes it particularly simple with regard to the cubic lattice of tetrads. For another, if we add 385/384 to the list of commas, 35/24 is identified with 16/11, and casablanca is revealed as an 11-limit temperament with a very low complexity for 11 and not too high a one for 7; we might compare 1, 4, 14, 19, the generator steps to 11, 7, 5 and 3 respectively, with 1, 4, 10, 18, the steps to 3, 5, 7 and 11 in 11-limit meantone.
It may not seem like casablanca has much to offer, but peering under the hood a bit harder suggests otherwise. For one thing, the 35/24 generator is particularly interesting; like 15/14 and 21/20, it represents an interval between one vertex of a [[hexany]] and the opposite vertex, which makes it particularly simple with regard to the cubic lattice of tetrads. For another, if we add 385/384 to the list of commas, 35/24 is identified with 16/11, and casablanca is revealed as an 11-limit temperament with a very low complexity for 11 and not too high a one for 7; we might compare 1, 4, 14, 19, the generator steps to 11, 7, 5 and 3 respectively, with 1, 4, 10, 18, the steps to 3, 5, 7 and 11 in 11-limit meantone.
Line 400: Line 399:
Map: [<1 12 10 5|, <0 -19 -14 -4|]
Map: [<1 12 10 5|, <0 -19 -14 -4|]


EDOs: 9bc, 11b, 31, 135c, 166c
EDOs: {{EDOs|11b, 20b, 31, 104c, 135c, 166c}}


Badness: 0.1012
Badness: 0.1012
Line 411: Line 410:
Map: [<1 12 10 5 4|, |0 -19 -14 -4 -1>]
Map: [<1 12 10 5 4|, |0 -19 -14 -4 -1>]


EDOs: 9bc, 11b, 31, 259bce, 549bce
EDOs: {{EDOs|11b, 20b, 31}}


Badness: 0.0623
Badness: 0.0623


==Marrakesh==
== Marrakesh ==
Commas: 126/125, 176/175, 14641/14580
Commas: 126/125, 176/175, 14641/14580


Line 422: Line 421:
Map: [<1 12 10 5 21|, |0 -19 -14 -4 -32>]
Map: [<1 12 10 5 21|, |0 -19 -14 -4 -32>]


EDOs: 9bce, 11be, 20be, 31, 42e, 73
EDOs: {{EDOs|31, 73, 104c, 135c}}


Badness: 0.0405
Badness: 0.0405


===13-limit===
=== 13-limit ===
126/125, 176/175, 196/195, 17303/17280
Commas: 126/125, 176/175, 196/195, 14641/14580


POTE generator: ~22/15 = 657.756
POTE generator: ~22/15 = 657.756
Line 433: Line 432:
Map: [<1 12 10 5 21 -10|, |0 -19 -14 -4 -32 25>]
Map: [<1 12 10 5 21 -10|, |0 -19 -14 -4 -32 25>]


EDOs: 31, 73, 104c, 135c, 239cf
EDOs: {{EDOs|31, 73, 104c, 135c, 239ccf}}


Badness: 0.0408
Badness: 0.0408


===Murakuc===
=== Murakuc ===
Commas: 126/125, 144/143, 176/175, 1540/1521
Commas: 126/125, 144/143, 176/175, 1540/1521


Line 444: Line 443:
Map: [<1 12 10 5 21 7|, |0 -19 -14 -4 -32 -6>]
Map: [<1 12 10 5 21 7|, |0 -19 -14 -4 -32 -6>]


EDOs: 31, 73f, 104cf
EDOs: {{EDOs|31, 104cf, 135cf, 166c}}


Badness: 0.0414
Badness: 0.0414
Line 451: Line 450:
Nusecond tempers out 2430/2401 and 16875/16807 in addition to 126/125, and may be described as 31&70, or in terms of its wedgie as <<11 13 17 -5 -4 3||. 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&70, or in terms of its wedgie as <<11 13 17 -5 -4 3||. 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==
== 5-limit ==
Comma: 51018336/48828125
Comma: 51018336/48828125


Line 458: Line 457:
Map: [<1 3 4|, <0 -11 -13|]
Map: [<1 3 4|, <0 -11 -13|]


EDOs: 8, 23, 31, 70, 101, 132c, 233c, 365bc
EDOs: {{EDOs|8, 23, 31, 70, 101, 132c, 233c, 365bcc}}


Badness: 0.4665
Badness: 0.4665
Line 483: Line 482:
[[Generator]]s: 2, 49/45
[[Generator]]s: 2, 49/45


EDOs: 7, 8, 31, 101, 132, 163
EDOs: {{EDOs|8d, 23d, 31, 101, 132c, 163c}}


Badness: 0.0504
Badness: 0.0504
Line 506: Line 505:
[[Generator]]s: 2, 11/10
[[Generator]]s: 2, 11/10


EDOs: 7, 8, 31, 101, 194
EDOs: {{EDOs|8d, 23de, 31, 101, 132ce, 163ce, 194cee}}


Badness: 0.0256
Badness: 0.0256


==13-limit==
==13-limit==
Commas: 66/65 99/98 121/120 126/125
Commas: 66/65, 99/98, 121/120, 126/125


POTE generator: ~11/10 = 154.478
POTE generator: ~11/10 = 154.478
Line 517: Line 516:
Map: [<1 3 4 5 5 5|, <0 -11 -13 -17 -12 -10|]
Map: [<1 3 4 5 5 5|, <0 -11 -13 -17 -12 -10|]


EDOs: 31, 70f, 101f
EDOs: {{EDOs|8d, 23de, 31, 70f, 101ff}}


Badness: 0.0233
Badness: 0.0233
Line 530: Line 529:
Wedgie: <<12 5 -9 -20 -48 -35||
Wedgie: <<12 5 -9 -20 -48 -35||


EDOs: 15, 43, 58
EDOs: {{EDOs|15, 43, 58}}


Badness: 0.0884
Badness: 0.0884
Line 541: Line 540:
Map: [<1 8 5 -2 4|, <0 -12 -5 9 -1|]
Map: [<1 8 5 -2 4|, <0 -12 -5 9 -1|]


EDOs: 13, 15, 28, 43, 58
EDOs: {{EDOs|15, 43, 58}}


Badness: 0.0331
Badness: 0.0331
Line 552: Line 551:
Map: [<1 8 5 -2 4 16|, <0 -12 -5 9 -1 -23|]
Map: [<1 8 5 -2 4 16|, <0 -12 -5 9 -1 -23|]


EDOs: 15, 43, 58
EDOs: {{EDOs|15, 43, 58}}


Badness: 0.0228
Badness: 0.0228
Line 561: Line 560:
Map: [<1 -4 0 7 3 -7 12 1 5 3|, <0 12 5 -9 1 23 -17 7 -1 4|]
Map: [<1 -4 0 7 3 -7 12 1 5 3|, <0 12 5 -9 1 23 -17 7 -1 4|]


EDOs: 43, 58
EDOs: {{EDOs|43, 58hi}}


(''Raison d'etre'' of this entry being the simple and accurate approximation of factor twenty-nine, the 2.5.11.21.29 subgroup being of especially good accuracy and simplicity.)
(''Raison d'etre'' of this entry being the simple and accurate approximation of factor twenty-nine, the 2.5.11.21.29 subgroup being of especially good accuracy and simplicity.)


=Cypress=
= Cypress =
== 5-limit ==
Comma: 258280326/244140625
Comma: 258280326/244140625


Line 572: Line 572:
Map: [<1 7 10|, <0 -12 -17|]
Map: [<1 7 10|, <0 -12 -17|]


EDOs: 20c, 31, 113c, 144c, 175c, 381bc
EDOs: {{EDOs|11c, 20c, 31, 113c, 144c, 175c, 381bcc}}


Badness: 0.8166
Badness: 0.8166
Line 585: Line 585:
Wedgie: <<12 17 27 -1 9 15||
Wedgie: <<12 17 27 -1 9 15||


EDOs: 31, 206bcd, 237bcd, 268bcd, 299bcd, 330bcd
EDOs: {{EDOs|11cd, 20cd, 31, 206bcd, 237bcd, 268bcd, 299bcd, 330bbcd}}


Badness: 0.0998
Badness: 0.0998
Line 596: Line 596:
Map: [<1 7 10 15 17|, <0 -12 -17 -27 -30|]
Map: [<1 7 10 15 17|, <0 -12 -17 -27 -30|]


EDOs: 31, 144cd, 175cd, 206bcde, 237bcde
EDOs: {{EDOs|11cdee, 20cde, 31, 144cd, 175cd, 206bcde, 237bcde}}


Badness: 0.0427
Badness: 0.0427


==13-limit==
== 13-limit ==
Commas: 66/65, 99/98. 126/125, 243/242
Commas: 66/65, 99/98. 126/125, 243/242


Line 607: Line 607:
Map: [<1 7 10 15 17 15|, <0 -12 -17 -27 -30 -25|]
Map: [<1 7 10 15 17 15|, <0 -12 -17 -27 -30 -25|]


EDOs: 31
EDOs: {{EDOs|11cdeef, 20cdef, 31}}


Badness: 0.0378
Badness: 0.0378


=Bisemidim=
= Bisemidim =
Commas: 126/125, 118098/117649
Commas: 126/125, 118098/117649


Line 620: Line 620:
Wedgie: <<18 22 30 -7 -3 8||
Wedgie: <<18 22 30 -7 -3 8||


EDOs: 50, 58, 108, 166c, 408c
EDOs: {{EDOs|50, 58, 108, 166c, 408ccc}}


Badness: 0.0978
Badness: 0.0978


==11-limit==
== 11-limit ==
Commas: 126/125, 540/539, 1344/1331
Commas: 126/125, 540/539, 1344/1331


Line 631: Line 631:
Map: [<2 1 2 2 5|, <0 9 11 15 8|]
Map: [<2 1 2 2 5|, <0 9 11 15 8|]


EDOs: 50, 58, 108, 166ce, 224ce
EDOs: {{EDOs|50, 58, 108, 166ce, 224cee}}


Badness: 0.0412
Badness: 0.0412


==13-limit==
== 13-limit ==
Commas: 126/125, 144/143, 196/195, 364/363
Commas: 126/125, 144/143, 196/195, 364/363


Line 642: Line 642:
Map: [<2 1 2 2 5 5|, <0 9 11 15 8 10|]
Map: [<2 1 2 2 5 5|, <0 9 11 15 8 10|]


EDOs: 50, 58, 166cef, 224cef
EDOs: {{EDOs|50, 58, 166cef, 224ceeff}}


Badness: 0.0239
Badness: 0.0239


=Vines=
= Vines =
Commas: 126/125, 84035/82944
Commas: 126/125, 84035/82944


Line 653: Line 653:
Map: [<2 7 8 8|, <0 -8 -7 -5|]
Map: [<2 7 8 8|, <0 -8 -7 -5|]


EDOs: 4, 42, 46, 96d, 142d, 238d
EDOs: {{EDOs|42, 46, 96d, 142d, 238dd}}


Badness: 0.0780
Badness: 0.0780
Line 664: Line 664:
Map: [<2 7 8 8 5|, <0 -8 -7 -5 4|]
Map: [<2 7 8 8 5|, <0 -8 -7 -5 4|]


EDOs: 4, 42, 46, 96d, 142d, 238d
EDOs: {{EDOs|42, 46, 96d, 142d, 238dd}}


Badness: 0.0445
Badness: 0.0445
Line 675: Line 675:
Map: [<2 7 8 8 5 5|, <0 -8 -7 -5 4 5|]
Map: [<2 7 8 8 5 5|, <0 -8 -7 -5 4 5|]


EDOs: 4, 42, 46, 96d, 238df
EDOs: {{EDOs|42, 46, 96d, 238ddf}}


Badness: 0.0297
Badness: 0.0297


=Kumonga=
= Kumonga =
== 5-limit ==
Comma: 1289945088/1220703125
Comma: 1289945088/1220703125


Line 686: Line 687:
Map: [<1 4 4|, <0 -13 -9|]
Map: [<1 4 4|, <0 -13 -9|]


EDOs: 16, 27, 43, 70, 183c
EDOs: {{EDOs|16, 27, 43, 70, 183cc}}


Badness: 0.7296
Badness: 0.7296


==7-limit==
== 7-limit ==
Commas: 126/125, 12288/12005
Commas: 126/125, 12288/12005


Line 699: Line 700:
Wedgie: <<13 9 1 -16 -35 -23||
Wedgie: <<13 9 1 -16 -35 -23||


EDOs: 16, 27, 43, 70, 167cd
EDOs: {{EDOs|16, 27, 43, 70, 167ccdd}}


Badness: 0.0875
Badness: 0.0875


==11-limit==
== 11-limit ==
Commas: 126/125, 176/175, 864/847
Commas: 126/125, 176/175, 864/847


Line 710: Line 711:
Map: [<1 4 4 3 7|, <0 -13 -9 -1 -19|]
Map: [<1 4 4 3 7|, <0 -13 -9 -1 -19|]


EDOs: 16, 27e, 43, 70e
EDOs: {{EDOs|16, 27e, 43, 70e}}


Badness: 0.0433
Badness: 0.0433


==13-limit==
== 13-limit ==
Commas: 78/77, 126/125, 144/143, 176/175
Commas: 78/77, 126/125, 144/143, 176/175


Line 721: Line 722:
Map: [<1 4 4 3 7 5|, <0 -13 -9 -1 -19 -7|]
Map: [<1 4 4 3 7 5|, <0 -13 -9 -1 -19 -7|]


EDOs: 16, 27e, 43, 70e, 113cde
EDOs: {{EDOs|16, 27e, 43, 70e, 113cdee}}


Badness: 0.0289
Badness: 0.0289


=Amigo=
= Amigo =
Commas: 126/125, 2097152/2083725
Commas: 126/125, 2097152/2083725


Line 732: Line 733:
Map: [<1 9 3 -10|, <0 -11 -1 19|]
Map: [<1 9 3 -10|, <0 -11 -1 19|]


EDOs: 43, 46, 89, 135c, 359c
EDOs: {{EDOs|43, 46, 89, 135c, 359cc}}


Badness: 0.1109
Badness: 0.1109


==11-limit==
== 11-limit ==
Commas: 126/125, 176/175, 16384/16335
Commas: 126/125, 176/175, 16384/16335


Line 743: Line 744:
Map: [<1 9 3 -10 -8|, <0 -11 -1 19 17|]
Map: [<1 9 3 -10 -8|, <0 -11 -1 19 17|]


EDOs: 43, 46, 89, 135c, 224c
EDOs: {{EDOs|43, 46, 89, 135c, 224c}}


Badness: 0.0434
Badness: 0.0434


==13-limit==
== 13-limit ==
Commas: 126/125, 169/168, 176/175, 364/363
Commas: 126/125, 169/168, 176/175, 364/363


Line 754: Line 755:
Map: [<1 9 3 -10 -8 1|, <0 -11 -1 19 17 4|]
Map: [<1 9 3 -10 -8 1|, <0 -11 -1 19 17 4|]


EDOs: 43, 46, 89, 135cf, 224cf
EDOs: {{EDOs|43, 46, 89, 135cf, 224cf}}


Badness: 0.0307
Badness: 0.0307


=Oolong=
= Oolong =
{{main|Oolong}}
{{main|Oolong}}
== 5-limit ==
== 5-limit ==
Line 767: Line 768:
Map: [<1 6 7|, <0 -17 -18|]
Map: [<1 6 7|, <0 -17 -18|]


EDOs: 23, 27, 50, 77
EDOs: {{EDOs|23, 27, 50, 77}}


Badness: 0.9428
Badness: 0.9428
Line 778: Line 779:
Map: [&lt;1 6 7 8|, &lt;0 -17 -18 -20|]
Map: [&lt;1 6 7 8|, &lt;0 -17 -18 -20|]


EDOs: 27, 50, 77
EDOs: {{EDOs|27, 50, 77}}


Badness: 0.0735
Badness: 0.0735
Line 789: Line 790:
Map: [<1 6 7 8 18|, <0 -17 -18 -20 -56|]
Map: [<1 6 7 8 18|, <0 -17 -18 -20 -56|]


EDOs: 27e, 77, 104c, 181c
EDOs: {{EDOs|27e, 77, 104c, 181c}}


Badness: 0.0569
Badness: 0.0569
Line 800: Line 801:
Map: [<1 6 7 8 18 5|, <0 -17 -18 -20 -56 -5|]
Map: [<1 6 7 8 18 5|, <0 -17 -18 -20 -56 -5|]


EDOs: 27e, 77, 104c, 181c
EDOs: {{EDOs|27e, 77, 104c, 181c}}


Badness: 0.0356
Badness: 0.0356
Line 809: Line 810:
[[Category:Myna]]
[[Category:Myna]]
[[Category:Listen]]
[[Category:Listen]]
[[Category:Todo:improve layout]]
[[Category:Todo:review]]
Retrieved from "https://en.xen.wiki/w/Starling_temperaments"