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Mirkwai family: Difference between revisions

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


= Mirkwai =
= Mirkwai =
Subgroup: 2.3.5.7
[[Comma list]]: 16875/16807 (mirkwai)
[[Comma list]]: 16875/16807 (mirkwai)


[[Mapping]]: [<1 0 0 0|, <0 1 3 3|, <0 0 -5 -4|]
[[Mapping]]: [{{val| 1 0 0 0 }}, {{val| 0 1 3 3 }}, {{val| 0 0 -5 -4 }}]


Mapping generators: ~2, ~3, ~7/5
Mapping generators: ~2, ~3, ~7/5
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[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[7-odd-limit]]
* [[7-odd-limit]]
: [|1 0 0 0>, |0 4/7 -4/7 5/7>, |0 -3/7 3/7 5/7>, |0 0 0 1>]
: [{{monzo| 1 0 0 0 }}, {{monzo| 0 4/7 -4/7 5/7 }}, {{monzo| 0 -3/7 3/7 5/7 }}, {{monzo| 0 0 0 1 }}]
: [[Eigenmonzo]]s: 2, 8/7, 6/5
: [[Eigenmonzo]]s: 2, 8/7, 6/5
* [[9-odd-limit]]
* [[9-odd-limit]]
: [|1 0 0 0>, |0 8/11 -4/11 5/11>, |0 -6/11 3/11 10/11>, |0 0 0 1>]
: [{{monzo| 1 0 0 0 }}, {{monzo| 0 8/11 -4/11 5/11 }}, {{monzo| 0 -6/11 3/11 10/11 }}, {{monzo| 0 0 0 1 }}]
: [[Eigenmonzo]]s: 2, 10/9, 8/7
: [[Eigenmonzo]]s: 2, 10/9, 8/7


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= Indra =
= Indra =
Subgroup: 2.3.5.7.11
[[Comma list]]: 540/539, 1375/1372
[[Comma list]]: 540/539, 1375/1372


Mapping: [<1 0 0 0 2|, <0 1 3 3 0|, <0 0 -5 -4 3|]
Mapping: [{{val| 1 0 0 0 2 }}, {{val| 0 1 3 3 0 }}, {{val| 0 0 -5 -4 3 }}]


Mapping generators: ~2, ~3, ~7/5
Mapping generators: ~2, ~3, ~7/5


[[Minimax tuning]]:
Map to lattice: [{{val| 0 2 1 2 3 }}, {{val| 0 -1 2 1 -3 }}]
* [[11-odd-limit]]
: [|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>]
: [[Eigenmonzo]]s: 2, 11/9, 5/4
 
Map to lattice: [<0 2 1 2 3|, <0 -1 2 1 -3|]


Lattice basis:  
Lattice basis:  
: 15/14 length = 0.6184, 55/36 length = 0.7585
: 15/14 length = 0.6184, 55/36 length = 0.7585
: Angle (15/14, 55/36) = 68.1048 deg
: Angle (15/14, 55/36) = 68.1048 deg
[[Minimax tuning]]:
* [[11-odd-limit]]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 10 10 -3 0 -5 }}, {{monzo| 0 0 1 0 0 }}, {{monzo| 6 6 -1 0 -3 }}, {{monzo| 20 18 -6 0 -9 }}]
: [[Eigenmonzo]]s: 2, 11/9, 5/4


{{Val list|legend=1| 31, 41, 72, 152, 224, 296, 703 }}
{{Val list|legend=1| 31, 41, 72, 152, 224, 296, 703 }}
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== Shibi ==
== Shibi ==
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 729/728, 1375/1372
Comma list: 540/539, 729/728, 1375/1372


Mapping: [<1 0 0 0 2 -4 -3|, <0 1 3 3 0 11 3|, <0 0 -5 -4 3 4|]
Mapping: [{{val| 1 0 0 0 2 -4 -3 }}, {{val| 0 1 3 3 0 11 3 }}, {{val| 0 0 -5 -4 3 4 }}]


EDOs: 41, 72, 111, 183, 224, 703
EDOs: 41, 72, 111, 183, 224, 703
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== Yajna ==
== Yajna ==
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 625/624, 1375/1372
Comma list: 540/539, 625/624, 1375/1372


Mapping: [<1 0 0 0 2 -4|, <0 1 3 3 0 11|, <0 0 -5 -4 3 -20|]
Mapping: [{{val| 1 0 0 0 2 -4 }}, {{val| 0 1 3 3 0 11 }}, {{val| 0 0 -5 -4 3 -20 }}]


Mapping generators: ~2, ~3, ~7/5
Mapping generators: ~2, ~3, ~7/5
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Minimax tuning:  
Minimax tuning:  
* 13-odd-limit  
* 13-odd-limit  
: [|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>]
: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 4/5 6/5 -4/5 0 0 1/5 }}, {{monzo| 8/5 2/5 -3/5 0 0 2/5 }}, {{monzo| 44/25 26/25 -24/25 0 0 11/25 }}, {{monzo| 62/25 48/25 -27/25 0 0 3/25 }}, {{monzo| 8/5 2/5 -8/5 0 0 7/5 }}]
: [[Eigenmonzo]]s: 2, 10/9, 13/10
: [[Eigenmonzo]]s: 2, 10/9, 13/10
* 15-odd-limit minimax
* 15-odd-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>]
: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 0 1 0 0 0 0 }}, {{monzo| 5/4 1/2 0 -5/16 0 5/16 }}, {{monzo| 1 1 0 -1/4 0 1/4 }}, {{monzo| 5/4 3/2 0 3/16 0 -3/16 }}, {{monzo| 1 1 0 -5/4 0 5/4 }}]
: [[Eigenmonzo]]s: 2, 14/13, 4/3
: [[Eigenmonzo]]s: 2, 14/13, 4/3


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== Vibhu ==
== Vibhu ==
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 540/539, 1375/1372
Comma list: 351/350, 540/539, 1375/1372


Mapping: [<1 0 0 0 2 1|, <0 1 3 3 0 6|, <0 0 -5 -4 3 -14|]
Mapping: [{{val| 1 0 0 0 2 1 }}, {{val| 0 1 3 3 0 6 }}, {{val| 0 0 -5 -4 3 -14 }}]


Vals: {{Val list| 31, 72, 103, 111, 152, 183 }}
Vals: {{Val list| 31, 72, 103, 111, 152, 183 }}
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== Vish ==
== Vish ==
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 364/363, 540/539
Comma list: 325/324, 364/363, 540/539


Mapping: [<1 0 0 0 2 2], <0 1 3 3 0 -2], <0 0 -5 -4 3 10|]
Mapping: [{{val| 1 0 0 0 2 2 }}, {{val| 0 1 3 3 0 -2 }}, {{val| 0 0 -5 -4 3 10 }}]


Vals: {{Val list| 41, 72, 121, 193 }}
Vals: {{Val list| 41, 72, 121, 193 }}
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