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Temperaments of the '''Mirkwai clan''' temper out the ''mirkwai comma'' ({{Monzo| 0 3 4 -5 }} = 16875/16807), a no-twos comma. Members of the clan include grendel, kwai, pluto and mirkat considered below, as well as miracle, octokaidecal, nusecond, semisept and bohpier, considered elsewhere.
Temperaments of the '''Mirkwai clan''' temper out the ''mirkwai comma'' ({{Monzo| 0 3 4 -5 }} = 16875/16807), a no-twos comma. Members of the clan include grendel, kwai, pluto and mirkat considered below, as well as [[miracle]], octokaidecal, nusecond, semisept and bohpier, considered elsewhere.


=Grendel=
= Grendel =
Commas: 6144/6125, 16875/16807
[[Comma list]]: 6144/6125, 16875/16807


[[POTE_tuning|POTE generator]]: ~5/4 = 386.863
[[Mapping]]: [{{val|1 9 2 7}}, {{val|0 -23 1 -13}}]


Map: [<1 9 2 7|, <0 -23 1 -13|]
{{Multival|legend=1|23 -1 13 -55 -44 33}}


Wedgie: <<23 -1 13 -55 -44 33||
[[POTE generator]]: ~5/4 = 386.863


EDOs: 31, 90, 121, 152, 335d
{{Val list|legend=1| 31, 90, 121, 152, 335d }}


Badness: 0.051834
[[Badness]]: 0.051834


==11-limit==
== 11-limit ==
Commas: 540/539, 1375/1372, 5632/5625
Comma list: 540/539, 1375/1372, 5632/5625


[[POTE_tuning|POTE generator]]: ~5/4 = 386.856
Mapping: [{{val|1 9 2 7 17}}, {{val|0 -23 1 -13 -42}}]


Map: [<1 9 2 7 17|, <0 -23 1 -13 -42|]
POTE generator: ~5/4 = 386.856


EDOs: 31, 90e, 121, 152, 335d, 487d
Vals: {{Val list| 31, 90e, 121, 152, 335d, 487d }}


Badness: 0.019845
Badness: 0.019845


==13-limit==
== 13-limit ==
Commas: 352/351, 540/539, 625/624, 1375/1372
Comma list: 352/351, 540/539, 625/624, 1375/1372


[[POTE_tuning|POTE generator]]: ~5/4 = 386.826
Map: [{{val|1 9 2 7 17 -5}}, {{val|0 -23 1 -13 -42 27}}]


Map: [<1 9 2 7 17 -5|, <0 -23 1 -13 -42 27|]
POTE generator: ~5/4 = 386.826


EDOs: 31, 121, 152f, 425deff
Vals: {{Val list| 31, 121, 152f, 425deff }}


Badness: 0.024839
Badness: 0.024839


==17-limit==
== 17-limit ==
Commas: 256/255, 352/351, 625/624, 715/714, 1275/1274
Comma list: 256/255, 352/351, 625/624, 715/714, 1275/1274


[[POTE_tuning|POTE generator]]: ~5/4 = 386.812
Mapping: [{{val|1 9 2 7 17 -5 -3}}, {{val|0 -23 1 -13 -42 27 22}}]


Map: [<1 9 2 7 17 -5 -3|, <0 -23 1 -13 -42 27 22|]
POTE generator: ~5/4 = 386.812


EDOs: 31, 121, 273defgg
Vals: {{Val list| 31, 121, 273defgg }}


Badness: 0.021400
Badness: 0.021400


==19-limit==
== 19-limit ==
Commas: 256/255, 352/351, 375/374, 400/399, 456/455, 715/714
Comma list: 256/255, 352/351, 375/374, 400/399, 456/455, 715/714


[[POTE_tuning|POTE generator]]: ~5/4 = 386.819
POTE generator: ~5/4 = 386.819


Map: [<1 9 2 7 17 -5 -3 -8|, <0 -23 1 -13 -42 27 22 38|]
Mapping: [{{val|1 9 2 7 17 -5 -3 -8}}, {{val|0 -23 1 -13 -42 27 22 38}}]


EDOs: 31, 121, 152fg, 273defgg
Vals: {{Val list| 31, 121, 152fg, 273defgg }}


Badness: 0.018413
Badness: 0.018413


=Kwai=
= Kwai =
Commas: 5120/5103, 16875/16807
[[Comma list]]: 5120/5103, 16875/16807


[[POTE_tuning|POTE generator]]: ~3/2 = 702.616
[[Mapping]]: [{{val|1 0 -50 -40}}, {{val|0 1 33 27}}]


Map: [<1 0 -50 -40|, <0 1 33 27|]
{{Multival|legend=1|1 33 27 50 40 -30}}


Wedgie: <<1 33 27 50 40 -30||
[[POTE generator]]: ~3/2 = 702.616


EDOs: 41, 111, 152, 345, 497d
{{Val list|legend=1| 41, 111, 152, 345, 497d }}


Badness: 0.054476
[[Badness]]: 0.054476


==11-limit==
== 11-limit ==
Commas: 540/539, 1375/1372, 16384/16335
Comma list: 540/539, 1375/1372, 16384/16335


[[POTE_tuning|POTE generator]]: ~3/2 = 702.623
Mapping: [{{val|1 0 -50 -40 32}}, {{val|0 1 33 27 -18}}]


Map: [<1 0 -50 -40 32|, <0 1 33 27 -18|]
POTE generator: ~3/2 = 702.623


EDOs: 29cd, 41, 111, 152
Vals: {{Val list| 29cd, 41, 111, 152 }}


Badness: 0.026219
Badness: 0.026219


==13-limit==
== 13-limit ==
Commas: 352/351, 540/539, 729/728, 1375/1372
Comma list: 352/351, 540/539, 729/728, 1375/1372


[[POTE_tuning|POTE generator]]: ~3/2 = 702.644
Mapping: [{{val|1 0 -50 -40 32 27}}, {{val|0 1 33 27 -18 -21}}]


Map: [<1 0 -50 -40 32 27|, <0 1 33 27 -18 -21|]
POTE generator: ~3/2 = 702.644


EDOs: 29cd, 41, 111, 152f
Vals: {{Val list| 29cd, 41, 111, 152f }}


Badness: 0.024555
Badness: 0.024555


==17-limit==
== 17-limit ==
Commas: 256/255, 352/351, 540/539, 715/714, 1089/1088
Commas: 256/255, 352/351, 540/539, 715/714, 1089/1088


[[POTE_tuning|POTE generator]]: ~3/2 = 702.660
Mapping: [{{val|1 0 -50 -40 32 27 58}}, {{val|0 1 33 27 -18 -21 -34}}]


Map: [<1 0 -50 -40 32 27 58|, <0 1 33 27 -18 -21 -34|]
POTE generator: ~3/2 = 702.660


EDOs: 29cdg, 41, 111, 152fg, 263dfg
Vals: {{Val list| 29cdg, 41, 111, 152fg, 263dfg }}


Badness: 0.021950
Badness: 0.021950


==19-limit==
== 19-limit ==
Commas: 256/255, 352/351, 400/399, 456/455, 715/714, 847/845
Comma list: 256/255, 352/351, 400/399, 456/455, 715/714, 847/845


[[POTE_tuning|POTE generator]]: ~3/2 = 702.657
Mapping: [{{val|1 0 -50 -40 32 27 58 -56}}, {{val|0 1 33 27 -18 -21 -34 38}}]


Map: [<1 0 -50 -40 32 27 58 -56|, <0 1 33 27 -18 -21 -34 38|]
POTE generator: ~3/2 = 702.657


EDOs: 29cdgh, 41, 111, 152fg, 263dfgh
Vals: {{Val list| 29cdgh, 41, 111, 152fg, 263dfgh }}


Badness: 0.016957
Badness: 0.016957
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