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| The '''mirkwai family''' of [[planar temperament]]s tempers out the [[mirkwai comma]], 16875/16807.
| | #redirect [[Miscellaneous 7-limit temperaments #Canopic a.k.a. mirkwai]] |
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| = Mirkwai =
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| [[Comma list]]: 16875/16807 (mirkwai)
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| [[Mapping]]: [<1 0 0 0|, <0 1 3 3|, <0 0 -5 -4|]
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| Mapping generators: ~2, ~3, ~7/5
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| [[Minimax tuning]]:
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| * [[7-odd-limit]]
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| : [|1 0 0 0>, |0 4/7 -4/7 5/7>, |0 -3/7 3/7 5/7>, |0 0 0 1>]
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| : [[Eigenmonzo]]s: 2, 8/7, 6/5
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| * [[9-odd-limit]]
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| : [|1 0 0 0>, |0 8/11 -4/11 5/11>, |0 -6/11 3/11 10/11>, |0 0 0 1>]
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| : [[Eigenmonzo]]s: 2, 10/9, 8/7
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| {{Val list|legend=1| 72, 152, 193, 224, 296, 327, 775 }}
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| [[Badness]]: 0.342 × 10<sup>-3</sup>
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| [[Projection pair]]s: 5 84375/16807 7 16875/2401 to 2.3.7/5
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| = Indra =
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| [[Comma list]]: 540/539, 1375/1372
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| Mapping: [<1 0 0 0 2|, <0 1 3 3 0|, <0 0 -5 -4 3|]
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| Mapping generators: ~2, ~3, ~7/5
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| [[Minimax tuning]]:
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| * [[11-odd-limit]]
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| : [|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>]
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| : [[Eigenmonzo]]s: 2, 11/9, 5/4
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| Map to lattice: [<0 2 1 2 3|, <0 -1 2 1 -3|]
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| Lattice basis:
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| : 15/14 length = 0.6184, 55/36 length = 0.7585
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| : Angle (15/14, 55/36) = 68.1048 deg
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| {{Val list|legend=1| 31, 41, 72, 152, 224, 296, 703 }}
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| [[Badness]]: 0.266 × 10<sup>-3</sup>
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| [[Projection pair]]s: 5 84375/16807 7 16875/2401 11 1372/125 to 2.3.7/5
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| Scales: [[indra31]]
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| == Shibi ==
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| Comma list: 540/539, 729/728, 1375/1372
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| Mapping: [<1 0 0 0 2 -4 -3|, <0 1 3 3 0 11 3|, <0 0 -5 -4 3 4|]
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| EDOs: 41, 72, 111, 183, 224, 703
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| Badness: 0.721 × 10<sup>-3</sup>
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| == Yajna ==
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| Comma list: 540/539, 625/624, 1375/1372
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| Mapping: [<1 0 0 0 2 -4|, <0 1 3 3 0 11|, <0 0 -5 -4 3 -20|]
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| Mapping generators: ~2, ~3, ~7/5
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| Minimax tuning:
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| * 13-odd-limit
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| : [|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>]
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| : [[Eigenmonzo]]s: 2, 10/9, 13/10
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| * 15-odd-limit minimax
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| : [|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>]
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| : [[Eigenmonzo]]s: 2, 14/13, 4/3
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| Vals: {{Val list| 31, 72, 103, 193, 224, 296, 520, 703 }}
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| Badness: 0.700 × 10<sup>-3</sup>
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| == Vibhu ==
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| Comma list: 351/350, 540/539, 1375/1372
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| Mapping: [<1 0 0 0 2 1|, <0 1 3 3 0 6|, <0 0 -5 -4 3 -14|]
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| Vals: {{Val list| 31, 72, 103, 111, 152, 183 }}
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| Badness: 0.826 × 10<sup>-3</sup>
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| == Vish ==
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| Comma list: 325/324, 364/363, 540/539
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| Mapping: [<1 0 0 0 2 2], <0 1 3 3 0 -2], <0 0 -5 -4 3 10|]
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| Vals: {{Val list| 41, 72, 121, 193 }}
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| Badness: 0.930 × 10<sup>-3</sup>
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| [[Category:Regular temperament theory]]
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| [[Category:Temperament family]]
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| [[Category:Mirkwai]]
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| [[Category:Rank 3]]
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