Mirkwai family: Difference between revisions

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


7-limit minimax
[[Mapping]]: [<1 0 0 0|, <0 1 3 3|, <0 0 -5 -4|]


[|1 0 0 0>, |0 4/7 -4/7 5/7>,  
Mapping generators: ~2, ~3, ~7/5
|0 -3/7 3/7 5/7>, |0 0 0 1>]


[[Eigenmonzo]]s: 2, 8/7, 6/5
[[Minimax tuning]]:
* [[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>]
: [[Eigenmonzo]]s: 2, 8/7, 6/5
* [[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>]
: [[Eigenmonzo]]s: 2, 10/9, 8/7


9-limit minimax
{{Val list|legend=1| 72, 152, 193, 224, 296, 327, 775 }}


[|1 0 0 0>, |0 8/11 -4/11 5/11>,
[[Badness]]: 0.342 × 10<sup>-3</sup>
|0 -6/11 3/11 10/11&gt;, |0 0 0 1&gt;]
 
[[Eigenmonzo]]s: 2, 10/9, 8/7
 
Map: [&lt;1 0 0 0|, &lt;0 1 3 3|, &lt;0 0 -5 -4|]
 
[[Generator]]s: 2, 3, 7/5
 
[[EDO|Edos]]: [[72edo|72]], [[152edo|152]], [[193edo|193]], [[224edo|224]], [[296edo|296]], [[327edo|327]], [[775edo|775]]
 
Badness: 0.000342


[[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]]s: 540/539, 1375/1372
[[Comma list]]: 540/539, 1375/1372


[[Minimax tuning]]
Mapping: [&lt;1 0 0 0 2|, &lt;0 1 3 3 0|, &lt;0 0 -5 -4 3|]


[|1 0 0 0 0&gt;, |10 10 -3 0 -5&gt;, |0 0 1 0 0&gt;,
Mapping generators: ~2, ~3, ~7/5
|6 6 -1 0 -3&gt;, |20 18 -6 0 -9&gt;]


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


Map to lattice: [&lt;0 2 1 2 3|, &lt;0 -1 2 1 -3|]
Map to lattice: [&lt;0 2 1 2 3|, &lt;0 -1 2 1 -3|]


Map: [&lt;1 0 0 0 2|, &lt;0 1 3 3 0|, &lt;0 0 -5 -4 3|]
Lattice basis:  
: 15/14 length = 0.6184, 55/36 length = 0.7585
: Angle (15/14, 55/36) = 68.1048 deg


[[Generator]]s: 2, 3, 7/5
{{Val list|legend=1| 31, 41, 72, 152, 224, 296, 703 }}


[[EDO|Edos]]: 31, 41, [[72edo|72]], [[152edo|152]], [[224edo|224]], [[296edo|296]], [[703edo|703]]
[[Badness]]: 0.266 × 10<sup>-3</sup>
 
Badness: 0.000266


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


Map: [&lt;1 0 0 0 2 -4 -3|, &lt;0 1 3 3 0 11 3|, &lt;0 0 -5 -4 3 4|]
Mapping: [&lt;1 0 0 0 2 -4 -3|, &lt;0 1 3 3 0 11 3|, &lt;0 0 -5 -4 3 4|]


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


Badness: 0.000721
Badness: 0.721 × 10<sup>-3</sup>


== Yajna ==
== Yajna ==
[[Comma]]s: 540/539, 625/624, 1375/1372
Comma list: 540/539, 625/624, 1375/1372
 
13-limit minimax
 
[|1 0 0 0 0 0&gt;, |4/5 6/5 -4/5 0 0 1/5&gt;,
|8/5 2/5 -3/5 0 0 2/5&gt;,
|44/25 26/25 -24/25 0 0 11/25&gt;,
|62/25 48/25 -27/25 0 0 3/25&gt;,
|8/5 2/5 -8/5 0 0 7/5&gt;]
 
[[Eigenmonzo]]s: 2, 10/9, 13/10
 
15-limit minimax
 
[|1 0 0 0 0 0&gt;, |0 1 0 0 0 0&gt;,
|5/4 1/2 0 -5/16 0 5/16&gt;,
|1 1 0 -1/4 0 1/4&gt;,
|5/4 3/2 0 3/16 0 -3/16&gt;,
|1 1 0 -5/4 0 5/4&gt;]


[[Eigenmonzo]]s: 2, 14/13, 4/3
Mapping: [&lt;1 0 0 0 2 -4|, &lt;0 1 3 3 0 11|, &lt;0 0 -5 -4 3 -20|]


Map: [&lt;1 0 0 0 2 -4|, &lt;0 1 3 3 0 11|, &lt;0 0 -5 -4 3 -20|]
Mapping generators: ~2, ~3, ~7/5


[[Generator]]s: 2, 3, 7/5
Minimax tuning:
* 13-odd-limit
: [|1 0 0 0 0 0&gt;, |4/5 6/5 -4/5 0 0 1/5&gt;, |8/5 2/5 -3/5 0 0 2/5&gt;, |44/25 26/25 -24/25 0 0 11/25&gt;, |62/25 48/25 -27/25 0 0 3/25&gt;, |8/5 2/5 -8/5 0 0 7/5&gt;]
: [[Eigenmonzo]]s: 2, 10/9, 13/10
* 15-odd-limit minimax
: [|1 0 0 0 0 0&gt;, |0 1 0 0 0 0&gt;, |5/4 1/2 0 -5/16 0 5/16&gt;, |1 1 0 -1/4 0 1/4&gt;, |5/4 3/2 0 3/16 0 -3/16&gt;, |1 1 0 -5/4 0 5/4&gt;]
: [[Eigenmonzo]]s: 2, 14/13, 4/3


[[EDO|Edos]]: [[31edo|31]], [[72edo|72]], [[103edo|103]], [[193edo|193]], 224, 296, 520, 703
Vals: {{Val list| 31, 72, 103, 193, 224, 296, 520, 703 }}


Badness: 0.000700
Badness: 0.700 × 10<sup>-3</sup>


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


Map: [&lt;1 0 0 0 2 1|, &lt;0 1 3 3 0 6|, &lt;0 0 -5 -4 3 -14|]
Mapping: [&lt;1 0 0 0 2 1|, &lt;0 1 3 3 0 6|, &lt;0 0 -5 -4 3 -14|]


EDOs: 31, 72, 103, 111, 152, 183
Vals: {{Val list| 31, 72, 103, 111, 152, 183 }}


Badness: 0.000826
Badness: 0.826 × 10<sup>-3</sup>


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


Map: [&lt;1 0 0 0 2 2], &lt;0 1 3 3 0 -2], &lt;0 0 -5 -4 3 10|]
Mapping: [&lt;1 0 0 0 2 2], &lt;0 1 3 3 0 -2], &lt;0 0 -5 -4 3 10|]


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


Badness: 0.000930
Badness: 0.930 × 10<sup>-3</sup>


[[Category:Theory]]
[[Category:Regular temperament theory]]
[[Category:Temperament family]]
[[Category:Temperament family]]
[[Category:Mirkwai]]
[[Category:Mirkwai]]
[[Category:Rank 3]]
[[Category:Rank 3]]

Revision as of 08:05, 30 May 2021

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

Mirkwai

Comma list: 16875/16807 (mirkwai)

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

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

Minimax tuning:

[|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
[|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

Template:Val list

Badness: 0.342 × 10-3

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

Indra

Comma list: 540/539, 1375/1372

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

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

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

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

Lattice basis:

15/14 length = 0.6184, 55/36 length = 0.7585
Angle (15/14, 55/36) = 68.1048 deg

Template:Val list

Badness: 0.266 × 10-3

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

Scales: indra31

Shibi

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|]

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

Badness: 0.721 × 10-3

Yajna

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

Minimax tuning:

  • 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>]
Eigenmonzos: 2, 10/9, 13/10
  • 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>]
Eigenmonzos: 2, 14/13, 4/3

Vals: Template:Val list

Badness: 0.700 × 10-3

Vibhu

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|]

Vals: Template:Val list

Badness: 0.826 × 10-3

Vish

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|]

Vals: Template:Val list

Badness: 0.930 × 10-3

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