Canopic clan: Difference between revisions

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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

Revision as of 22:13, 26 May 2021

Temperaments of the Mirkwai clan temper out the mirkwai comma ([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

Comma list: 6144/6125, 16875/16807

Mapping: [⟨1 9 2 7], ⟨0 -23 1 -13]]

Wedgie: ⟨⟨ 23 -1 13 -55 -44 33 ]]

POTE generator: ~5/4 = 386.863

Template:Val list

Badness: 0.051834

11-limit

Comma list: 540/539, 1375/1372, 5632/5625

Mapping: [⟨1 9 2 7 17], ⟨0 -23 1 -13 -42]]

POTE generator: ~5/4 = 386.856

Vals: Template:Val list

Badness: 0.019845

13-limit

Comma list: 352/351, 540/539, 625/624, 1375/1372

Map: [⟨1 9 2 7 17 -5], ⟨0 -23 1 -13 -42 27]]

POTE generator: ~5/4 = 386.826

Vals: Template:Val list

Badness: 0.024839

17-limit

Comma list: 256/255, 352/351, 625/624, 715/714, 1275/1274

Mapping: [⟨1 9 2 7 17 -5 -3], ⟨0 -23 1 -13 -42 27 22]]

POTE generator: ~5/4 = 386.812

Vals: Template:Val list

Badness: 0.021400

19-limit

Comma list: 256/255, 352/351, 375/374, 400/399, 456/455, 715/714

POTE generator: ~5/4 = 386.819

Mapping: [⟨1 9 2 7 17 -5 -3 -8], ⟨0 -23 1 -13 -42 27 22 38]]

Vals: Template:Val list

Badness: 0.018413

Kwai

Comma list: 5120/5103, 16875/16807

Mapping: [⟨1 0 -50 -40], ⟨0 1 33 27]]

Wedgie: ⟨⟨ 1 33 27 50 40 -30 ]]

POTE generator: ~3/2 = 702.616

Template:Val list

Badness: 0.054476

11-limit

Comma list: 540/539, 1375/1372, 16384/16335

Mapping: [⟨1 0 -50 -40 32], ⟨0 1 33 27 -18]]

POTE generator: ~3/2 = 702.623

Vals: Template:Val list

Badness: 0.026219

13-limit

Comma list: 352/351, 540/539, 729/728, 1375/1372

Mapping: [⟨1 0 -50 -40 32 27], ⟨0 1 33 27 -18 -21]]

POTE generator: ~3/2 = 702.644

Vals: Template:Val list

Badness: 0.024555

17-limit

Commas: 256/255, 352/351, 540/539, 715/714, 1089/1088

Mapping: [⟨1 0 -50 -40 32 27 58], ⟨0 1 33 27 -18 -21 -34]]

POTE generator: ~3/2 = 702.660

Vals: Template:Val list

Badness: 0.021950

19-limit

Comma list: 256/255, 352/351, 400/399, 456/455, 715/714, 847/845

Mapping: [⟨1 0 -50 -40 32 27 58 -56], ⟨0 1 33 27 -18 -21 -34 38]]

POTE generator: ~3/2 = 702.657

Vals: Template:Val list

Badness: 0.016957

Pluto

Commas: 4000/3969, 10976/10935

POTE generator: ~7/5 = 585.147

Map: [<1 5 15 15|, <0 -7 -26 -25|]

Wedgie: <<7 26 25 25 20 -15||

EDOs: 39d, 41, 80, 121, 404bd

Badness: 0.057514

11-limit

Commas: 540/539, 896/891, 1375/1372

POTE generator: ~7/5 = 585.114

Map: [<1 5 15 15 2|, <0 -7 -26 -25 3|]

EDOs: 39d, 41, 80, 121

Badness: 0.029844

13-limit

Commas: 325/324, 352/351, 364/363, 540/539

POTE generator: ~7/5 = 585.123

Map: [<1 5 15 15 2 -8|, <0 -7 -26 -25 3 24|]

EDOs: 39d, 41, 80, 121

Badness: 0.025717

17-limit

Commas: 256/255, 325/324, 352/351, 364/363, 540/539

POTE generator: ~7/5 = 585.116

Map: [<1 5 15 15 2 -8 -12|, <0 -7 -26 -25 3 24 33|]

EDOs: 39d, 41, 80, 121

Badness: 0.021463

19-limit

Commas: 190/189, 256/255, 325/324, 352/351, 361/360, 595/594

POTE generator: ~7/5 = 585.109

Map: [<1 5 15 15 2 -8 -12 14|, <0 -7 -26 -25 3 24 33 -20|]

EDOs: 39d, 41, 80, 121

Badness: 0.017650

Orcus

Commas: 144/143, 196/195, 275/273, 896/891

POTE generator: ~7/5 = 585.111

Map: [<1 5 15 15 2 12|, <0 -7 -26 -25 3 -17|]

EDOs: 41, 80f, 121ff

Badness: 0.033441

Plutino

Commas: 100/99, 245/242, 10976/10935

POTE generator: ~7/5 = 585.283

Map: [<1 5 15 15 22|, <0 -7 -26 -25 -38|]

EDOs: 2cde, 39dee, 41

Badness: 0.057966

13-limit

Commas: 100/99, 196/195, 245/242, 729/728

POTE generator: ~7/5 = 585.232

Map: [<1 5 15 15 22 12|, <0 -7 -26 -25 -38 -17|]

EDOs: 2cde, 39deef, 41

Badness: 0.040182

Eris

Commas: 16875/16807, 65625/65536

POTE generator: ~60/49 = 348.216

Map: [<1 10 0 6|, <0 -29 8 -11|]

Wedgie: <<29 -8 11 -80 -64 48}}

EDOs: 31, 131, 162, 193, 224, 1823cd, 2271cd

Badness: 0.0747

11-limit

Commas: 540/539, 1375/1372, 65625/65536

POTE generator: ~11/9 = 348.219

Map: [<1 10 0 6 20|, <0 -29 8 -11 -57|]

EDOs: 31, 193, 224, 703, 927d, 1151cd

Badness: 0.0276

Mirkat

Commas: 16875/16807, 19683/19600

POTE generator: ~10/9 = 183.539

Map: [<3 2 1 2|, <0 6 13 14|]

Wedgie: <<18 39 42 20 16 -12||

EDOs: 39d, 72, 111, 183, 255

Badness: 0.0594

11-limit

Commas: 540/539, 1375/1372, 8019/8000

POTE generator: ~10/9 = 183.528

Map: [<3 2 1 2 9|, <0 6 13 14 3|]

EDOs: 39d, 72, 111, 183, 255

Badness: 0.0221

13-limit

Commas: 351/350, 540/539, 676/675, 1375/1372

POTE generator: ~10/9 = 183.577

Map: [<3 2 1 2 9 1|, <0 6 13 14 3 22|]

EDOs: 39df, 72, 111, 183, 255f

Badness: 0.0186

17-limit

Commas: 351/350, 442/441, 540/539, 561/560, 715/714

POTE generator: ~10/9 = 183.579

Map: [<3 2 1 2 9 1 4|, <0 6 13 14 3 22 18|]

EDOs: 39dfg, 72, 111, 183, 255f

Subsemifourth

Commas: 16875/16807, 26873856/26796875

POTE generator: ~144/125 = 244.719

Map: [<1 39 27 45|, <0 -47 -31 -53|]

Wedgie: <<47 31 53 -60 -48 36||

EDOs: 49, 103, 152, 255, 407

Badness: 0.1352

11-limit

Commas: 540/539, 1375/1372, 234375/234256

POTE generator: ~121/105 = 244.719

Map: [<1 39 27 45 56|, <0 -47 -31 -53 -66|]

EDOs: 49, 103, 152, 255, 407, 966d

Badness: 0.0343

13-limit

Commas: 540/539, 847/845, 1375/1372, 1575/1573

POTE generator: ~15/13 = 244.714

Map: [<1 39 27 45 56 65|, <0 -47 -31 -53 -66 -77|]

EDOs: 103, 152f, 255, 407f, 662df

Badness: 0.0284

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