Mirkwai family: Difference between revisions

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__FORCETOC__
The '''mirkwai family''' of [[planar temperament]]s tempers out the [[mirkwai comma]], 16875/16807.
The mirkwai family of [[Planar_Temperament|planar temperament]]s tempers out the mirkwai comma, 16875/16807.


=Vital statistics=
= Mirkwai =
[[Comma|Comma]]: mirkwai 16875/16807
[[Comma]]: mirkwai 16875/16807


7-limit minimax
7-limit minimax
Line 10: Line 9:
|0 -3/7 3/7 5/7>, |0 0 0 1>]
|0 -3/7 3/7 5/7>, |0 0 0 1>]


[[Eigenmonzo|Eigenmonzos]]: 2, 8/7, 6/5
[[Eigenmonzo]]s: 2, 8/7, 6/5


9-limit minimax
9-limit minimax
Line 17: Line 16:
|0 -6/11 3/11 10/11>, |0 0 0 1>]
|0 -6/11 3/11 10/11>, |0 0 0 1>]


[[Eigenmonzo|Eigenmonzos]]: 2, 10/9, 8/7
[[Eigenmonzo]]s: 2, 10/9, 8/7


Map: [<1 0 0 0|, <0 1 3 3|, <0 0 -5 -4|]
Map: [<1 0 0 0|, <0 1 3 3|, <0 0 -5 -4|]


[[generator|Generators]]: 2, 3, 7/5
[[Generator]]s: 2, 3, 7/5


[[EDO|Edos]]: [[72edo|72]], [[152edo|152]], [[193edo|193]], [[224edo|224]], [[296edo|296]], [[327edo|327]], [[775edo|775]]
[[EDO|Edos]]: [[72edo|72]], [[152edo|152]], [[193edo|193]], [[224edo|224]], [[296edo|296]], [[327edo|327]], [[775edo|775]]
Line 27: Line 26:
Badness: 0.000342
Badness: 0.000342


[[Projection_pair|Projection pair]]s: 5 84375/16807 7 16875/2401 to 2.3.7/5
[[Projection pair]]s: 5 84375/16807 7 16875/2401 to 2.3.7/5


=Indra=
= Indra =
[[Comma|Commas]]: 540/539, 1375/1372
[[Comma]]s: 540/539, 1375/1372


[[Minimax_tuning|Minimax tuning]]
[[Minimax tuning]]


[|1 0 0 0 0>, |10 10 -3 0 -5>, |0 0 1 0 0>,  
[|1 0 0 0 0>, |10 10 -3 0 -5>, |0 0 1 0 0>,  
|6 6 -1 0 -3>, |20 18 -6 0 -9>]
|6 6 -1 0 -3>, |20 18 -6 0 -9>]


[[Eigenmonzo|Eigenmonzos]]: 2, 11/9, 5/4
[[Eigenmonzo]]s: 2, 11/9, 5/4


Lattice basis: 15/14 length 0.6184 55/36 length 0.7585
Lattice basis: 15/14 length 0.6184 55/36 length 0.7585
Line 47: Line 46:
Map: [<1 0 0 0 2|, <0 1 3 3 0|, <0 0 -5 -4 3|]
Map: [<1 0 0 0 2|, <0 1 3 3 0|, <0 0 -5 -4 3|]


[[generator|Generators]]: 2, 3, 7/5
[[Generator]]s: 2, 3, 7/5


[[EDO|Edos]]: 31, 41, [[72edo|72]], [[152edo|152]], [[224edo|224]], [[296edo|296]], [[703edo|703]]
[[EDO|Edos]]: 31, 41, [[72edo|72]], [[152edo|152]], [[224edo|224]], [[296edo|296]], [[703edo|703]]
Line 53: Line 52:
Badness: 0.000266
Badness: 0.000266


[[Projection_pair|Projection pair]]s: 5 84375/16807 7 16875/2401 11 1372/125 to 2.3.7/5
[[Projection pair]]s: 5 84375/16807 7 16875/2401 11 1372/125 to 2.3.7/5


Scales: [[indra31|indra31]]
Scales: [[indra31]]


==Shibi==
== Shibi ==
Commas: 540/539, 729/728, 1375/1372
Commas: 540/539, 729/728, 1375/1372


Line 66: Line 65:
Badness: 0.000721
Badness: 0.000721


==Yajna==
== Yajna ==
[[Comma|Commas]]: 540/539, 625/624, 1375/1372
[[Comma]]s: 540/539, 625/624, 1375/1372


13-limit minimax
13-limit minimax
Line 77: Line 76:
|8/5 2/5 -8/5 0 0 7/5>]
|8/5 2/5 -8/5 0 0 7/5>]


[[Eigenmonzo|Eigenmonzos]]: 2, 10/9, 13/10
[[Eigenmonzo]]s: 2, 10/9, 13/10


15-limit minimax
15-limit minimax
Line 87: Line 86:
|1 1 0 -5/4 0 5/4>]
|1 1 0 -5/4 0 5/4>]


[[Eigenmonzo|Eigenmonzos]]: 2, 14/13, 4/3
[[Eigenmonzo]]s: 2, 14/13, 4/3


Map: [<1 0 0 0 2 -4|, <0 1 3 3 0 11|, <0 0 -5 -4 3 -20|]
Map: [<1 0 0 0 2 -4|, <0 1 3 3 0 11|, <0 0 -5 -4 3 -20|]


[[generator|Generators]]: 2, 3, 7/5
[[Generator]]s: 2, 3, 7/5


[[EDO|Edos]]: [[31edo|31]], [[72edo|72]], [[103edo|103]], [[193edo|193]], 224, 296, 520, 703
[[EDO|Edos]]: [[31edo|31]], [[72edo|72]], [[103edo|103]], [[193edo|193]], 224, 296, 520, 703
Line 97: Line 96:
Badness: 0.000700
Badness: 0.000700


==Vibhu==
== Vibhu ==
[[Comma|Commas]]: 540/539, 1375/1372, 351/350
[[Comma]]s: 540/539, 1375/1372, 351/350


Map: [<1 0 0 0 2 1|, <0 1 3 3 0 6|, <0 0 -5 -4 3 -14|]
Map: [<1 0 0 0 2 1|, <0 1 3 3 0 6|, <0 0 -5 -4 3 -14|]
Line 106: Line 105:
Badness: 0.000826
Badness: 0.000826


==Vish==
== Vish ==
[[Comma|Commas]]: 325/324, 364/363, 540/539
[[Comma]]s: 325/324, 364/363, 540/539


Map: [<1 0 0 0 2 2], <0 1 3 3 0 -2], <0 0 -5 -4 3 10|]
Map: [<1 0 0 0 2 2], <0 1 3 3 0 -2], <0 0 -5 -4 3 10|]
Line 117: Line 116:
[[Category:Theory]]
[[Category:Theory]]
[[Category:Temperament family]]
[[Category:Temperament family]]
[[Category:Planar temperament]]
[[Category:Mirkwai]]
[[Category:Mirkwai]]
[[Category:Rank 3]]

Revision as of 05:56, 6 January 2021

The mirkwai family of planar temperaments tempers out the mirkwai comma, 16875/16807.

Mirkwai

Comma: mirkwai 16875/16807

7-limit minimax

[|1 0 0 0>, |0 4/7 -4/7 5/7>, |0 -3/7 3/7 5/7>, |0 0 0 1>]

Eigenmonzos: 2, 8/7, 6/5

9-limit minimax

[|1 0 0 0>, |0 8/11 -4/11 5/11>, |0 -6/11 3/11 10/11>, |0 0 0 1>]

Eigenmonzos: 2, 10/9, 8/7

Map: [<1 0 0 0|, <0 1 3 3|, <0 0 -5 -4|]

Generators: 2, 3, 7/5

Edos: 72, 152, 193, 224, 296, 327, 775

Badness: 0.000342

Projection pairs: 5 84375/16807 7 16875/2401 to 2.3.7/5

Indra

Commas: 540/539, 1375/1372

Minimax tuning

[|1 0 0 0 0>, |10 10 -3 0 -5>, |0 0 1 0 0>, |6 6 -1 0 -3>, |20 18 -6 0 -9>]

Eigenmonzos: 2, 11/9, 5/4

Lattice basis: 15/14 length 0.6184 55/36 length 0.7585

Angle(15/14, 55/36) = 68.1048 cents

Map to lattice: [<0 2 1 2 3|, <0 -1 2 1 -3|]

Map: [<1 0 0 0 2|, <0 1 3 3 0|, <0 0 -5 -4 3|]

Generators: 2, 3, 7/5

Edos: 31, 41, 72, 152, 224, 296, 703

Badness: 0.000266

Projection pairs: 5 84375/16807 7 16875/2401 11 1372/125 to 2.3.7/5

Scales: indra31

Shibi

Commas: 540/539, 729/728, 1375/1372

Map: [<1 0 0 0 2 -4 -3|, <0 1 3 3 0 11 3|, <0 0 -5 -4 3 4|]

EDOs: 41, 72, 111, 183, 224, 703

Badness: 0.000721

Yajna

Commas: 540/539, 625/624, 1375/1372

13-limit minimax

[|1 0 0 0 0 0>, |4/5 6/5 -4/5 0 0 1/5>, |8/5 2/5 -3/5 0 0 2/5>, |44/25 26/25 -24/25 0 0 11/25>, |62/25 48/25 -27/25 0 0 3/25>, |8/5 2/5 -8/5 0 0 7/5>]

Eigenmonzos: 2, 10/9, 13/10

15-limit minimax

[|1 0 0 0 0 0>, |0 1 0 0 0 0>, |5/4 1/2 0 -5/16 0 5/16>, |1 1 0 -1/4 0 1/4>, |5/4 3/2 0 3/16 0 -3/16>, |1 1 0 -5/4 0 5/4>]

Eigenmonzos: 2, 14/13, 4/3

Map: [<1 0 0 0 2 -4|, <0 1 3 3 0 11|, <0 0 -5 -4 3 -20|]

Generators: 2, 3, 7/5

Edos: 31, 72, 103, 193, 224, 296, 520, 703

Badness: 0.000700

Vibhu

Commas: 540/539, 1375/1372, 351/350

Map: [<1 0 0 0 2 1|, <0 1 3 3 0 6|, <0 0 -5 -4 3 -14|]

EDOs: 31, 72, 103, 111, 152, 183

Badness: 0.000826

Vish

Commas: 325/324, 364/363, 540/539

Map: [<1 0 0 0 2 2], <0 1 3 3 0 -2], <0 0 -5 -4 3 10|]

EDOs: 41, 72, 121, 193

Badness: 0.000930

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