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| {{Technical data page}}
| | #redirect [[Miscellaneous 7-limit temperaments #Canopic a.k.a. mirkwai]] |
| The '''canopic family''' of [[rank-3 temperament|rank-3]] [[regular temperament|temperaments]] tempers out the [[canopic comma]] ({{monzo|legend=1| 0 3 4 -5 }}, [[ratio]]: 16875/16807), a no-twos comma.
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| == Canopic a.k.a. mirkwai ==
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| [[Subgroup]]: 2.3.5.7
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| [[Comma list]]: 16875/16807
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| {{Mapping|legend=1| 1 0 -5 -4 | 0 1 3 3 | 0 0 5 4 }}
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| : Mapping generators: ~2, ~3, ~10/7
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| [[Optimal tuning]]s:
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| * [[WE]]: ~2 = 1199.9999{{c}}, ~3/2 = 701.7827{{c}}, ~10/7 = 616.0944{{c}}
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| : [[error map]]: {{val| -0.000 -0.172 -0.493 +0.900 }}
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| * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.7827{{c}}, ~10/7 = 616.0945{{c}}
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| : error map: {{val| 0.000 -0.172 -0.493 +0.900 }}
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| [[Minimax tuning]]:
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| * [[7-odd-limit]]
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| : {{monzo list| 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 basis|eigenmonzo (unchanged-interval) basis]]: 2.5/3.7
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| * [[9-odd-limit]]
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| : {{monzo list| 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 (unchanged-interval) basis: 2.9/5.7
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| {{Optimal ET sequence|legend=1| 31, 41, 72, 152, 224 }}
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| [[Badness]] (Sintel): 1.51
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| [[Projection pair]]s: <code>5 84375/16807 7 16875/2401</code> 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|legend=1| 1 0 -5 -4 5 | 0 1 3 3 0 | 0 0 5 4 -3 }}
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| : Mapping generators: ~2, ~3, ~10/7
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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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| [[Optimal tuning]]s:
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| * [[WE]]: ~2 = 1199.9693{{c}}, ~3/2 = 701.7444{{c}}, ~10/7 = 616.1152{{c}}
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| : [[error map]]: {{val| -0.031 -0.241 -0.443 +0.899 +0.183 }}
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| * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.7342{{c}}, ~10/7 = 616.1422{{c}}
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| : error map: {{val| 0.000 -0.221 -0.400 +0.946 +0.256 }}
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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 basis|eigenmonzo (unchanged-interval) basis]]: 2.5.11/9
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| {{Optimal ET sequence|legend=1| 31, 41, 72, 152, 224, 631d, 855d }}
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| [[Badness]] (Sintel): 0.320
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| [[Projection pair]]s: <code>5 84375/16807 7 16875/2401 11 1372/125</code> 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: {{mapping| 1 0 -5 -4 5 1 | 0 1 3 3 0 3 | 0 0 5 4 -3 -4 }}
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| Optimal tunings:
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| * WE: ~2 = 1199.9762{{c}}, ~3/2 = 701.7232{{c}}, ~10/7 = 616.1317{{c}}
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| * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.7261{{c}}, ~10/7 = 616.1467{{c}}
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| {{Optimal ET sequence|legend=0| 31f, 39df, 41, 72, 111, 152f, 183, 224, 631d, 855d }}
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| Badness (Sintel): 0.674
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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: {{mapping| 1 0 -5 -4 5 -24 | 0 1 3 3 0 11 | 0 0 5 4 -3 20 }}
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| Optimal tunings:
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| * WE: ~2 = 1200.0073{{c}}, ~3/2 = 701.7067{{c}}, ~10/7 = 616.1052{{c}}
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| * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.7089{{c}}, ~10/7 = 616.0986{{c}}
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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 (unchanged-interval) basis: 2.9/5.13/5
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| * 15-odd-limit
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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 (unchanged-interval) basis: 2.3.13/7
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| {{Optimal ET sequence|legend=0| 31, 49f, 72, 103, 121, 152f, 193, 224 }}
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| Badness (Sintel): 0.655
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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: {{mapping| 1 0 -5 -4 5 -13 | 0 1 3 3 0 6 | 0 0 5 4 -3 14 }}
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| Optimal tunings:
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| * WE: ~2 = 1200.1587{{c}}, ~3/2 = 701.2394{{c}}, ~10/7 = 616.6507{{c}}
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| * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.2689{{c}}, ~10/7 = 616.5306{{c}}
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| {{Optimal ET sequence|legend=0| 31, 64cdf, 72, 103, 111, 152, 175f, 183, 469f }}
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| Badness (Sintel): 0.772
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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: {{mapping| 1 0 0 0 2 2 | 0 1 3 3 0 -2 | 0 0 5 4 -3 -10 }}
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| Optimal tunings:
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| * WE: ~2 = 1199.9463{{c}}, ~3/2 = 702.3912{{c}}, ~10/7 = 615.5733{{c}}
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| * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.3742{{c}}, ~10/7 = 615.6198{{c}}
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| {{Optimal ET sequence|legend=0| 31f, 41, 72, 121, 193 }}
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| Badness (Sintel): 0.870
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| [[Category:Temperament families]]
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| [[Category:Canopic family]] <!-- main article -->
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| [[Category:Rank 3]]
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