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| {{Technical data page}}
| | #redirect [[Miscellaneous 7-limit temperaments #Canopic a.k.a. mirkwai]] |
| The '''mirkwai family''' of [[planar temperament]]s tempers out the [[mirkwai comma]], 16875/16807.
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| == Mirkwai ==
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| [[Subgroup]]: 2.3.5.7
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| [[Comma list]]: 16875/16807 (mirkwai)
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| [[Mapping]]: [{{val| 1 0 0 0 }}, {{val| 0 1 3 3 }}, {{val| 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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| : [{{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 }}]
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| : [[Eigenmonzo]]s (unchanged-intervals): 2, 8/7, 6/5
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| * [[9-odd-limit]]
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| : [{{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 }}]
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| : [[Eigenmonzo]]s (unchanged-intervals): 2, 10/9, 8/7
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| {{Optimal ET sequence|legend=1| 31, 41, 72, 152, 224 }}
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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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| [[Subgroup]]: 2.3.5.7.11
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| [[Comma list]]: 540/539, 1375/1372
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| [[Mapping]]: [{{val| 1 0 0 0 2 }}, {{val| 0 1 3 3 0 }}, {{val| 0 0 -5 -4 3 }}]
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| Mapping generators: ~2, ~3, ~7/5
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| [[Mapping to lattice]]: [{{val| 0 2 1 2 3 }}, {{val| 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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| [[Minimax tuning]]:
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| * [[11-odd-limit]]
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| : [{{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 }}]
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| : [[Eigenmonzo]]s (unchanged-intervals): 2, 11/9, 5/4
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| {{Optimal ET sequence|legend=1| 31, 41, 72, 152, 224, 631d, 855d }}
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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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| Subgroup: 2.3.5.7.11.13
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| Comma list: 540/539, 729/728, 1375/1372
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| Mapping: [{{val| 1 0 0 0 2 -3 }}, {{val| 0 1 3 3 0 3 }}, {{val| 0 0 -5 -4 4 }}]
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| {{Optimal ET sequence|legend=1| 31f, 39df, 41, 72, 111, 152f, 183, 224, 631d, 855d }}
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| Badness: 0.721 × 10<sup>-3</sup>
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| === Yajna ===
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 540/539, 625/624, 1375/1372
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| Mapping: [{{val| 1 0 0 0 2 -4 }}, {{val| 0 1 3 3 0 11 }}, {{val| 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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| : [{{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 }}]
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| : [[Eigenmonzo]]s (unchanged-intervals): 2, 10/9, 13/10
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| * 15-odd-limit minimax
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| : [{{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 }}]
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| : [[Eigenmonzo]]s (unchanged-intervals): 2, 14/13, 4/3
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| {{Optimal ET sequence|legend=1| 31, 49f, 72, 103, 121, 152f, 193, 224 }}
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| Badness: 0.700 × 10<sup>-3</sup>
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| === Vibhu ===
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 351/350, 540/539, 1375/1372
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| Mapping: [{{val| 1 0 0 0 2 1 }}, {{val| 0 1 3 3 0 6 }}, {{val| 0 0 -5 -4 3 -14 }}]
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| {{Optimal ET sequence|legend=1| 31, 64cdf, 72, 103, 111, 152, 175f, 183, 469f }}
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| Badness: 0.826 × 10<sup>-3</sup>
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| === Vish ===
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 325/324, 364/363, 540/539
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| Mapping: [{{val| 1 0 0 0 2 2 }}, {{val| 0 1 3 3 0 -2 }}, {{val| 0 0 -5 -4 3 10 }}]
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| {{Optimal ET sequence|legend=1| 31f, 41, 72, 121, 193 }}
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| Badness: 0.930 × 10<sup>-3</sup>
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| [[Category:Temperament families]]
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| [[Category:Mirkwai family]] <!-- main article -->
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| [[Category:Rank 3]]
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