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]], [[Trienstonic clan #Octokaidecal|octokaidecal]], [[Starling temperaments #Nusecond|nusecond]], [[Hemimean clan #Semisept|semisept]] and [[Sensamagic clan #Bohpier|bohpier]], considered elsewhere.


= Grendel =
= Grendel =
Line 115: Line 115:
Badness: 0.016957
Badness: 0.016957


=Pluto=
= Pluto =
Commas: 4000/3969, 10976/10935
[[Comma list]]: 4000/3969, 10976/10935


[[POTE_tuning|POTE generator]]: ~7/5 = 585.147
[[Mapping]]: [{{val|1 5 15 15}}, {{val|0 -7 -26 -25}}]


Map: [<1 5 15 15|, <0 -7 -26 -25|]
{{Multival|legend=1|7 26 25 25 20 -15}}


Wedgie: <<7 26 25 25 20 -15||
[[POTE generator]]: ~7/5 = 585.147


EDOs: 39d, 41, 80, 121, 404bd
{{Val list|legend=1| 39d, 41, 80, 121, 404bd }}


Badness: 0.057514
[[Badness]]: 0.057514


==11-limit==
== 11-limit ==
Commas: 540/539, 896/891, 1375/1372
Comma list: 540/539, 896/891, 1375/1372


[[POTE_tuning|POTE generator]]: ~7/5 = 585.114
Mapping: [{{val|1 5 15 15 2}}, {{val|0 -7 -26 -25 3}}]


Map: [<1 5 15 15 2|, <0 -7 -26 -25 3|]
POTE generator: ~7/5 = 585.114


EDOs: 39d, 41, 80, 121
Vals: {{Val list| 39d, 41, 80, 121 }}


Badness: 0.029844
Badness: 0.029844


===13-limit===
=== 13-limit ===
Commas: 325/324, 352/351, 364/363, 540/539
Comma list: 325/324, 352/351, 364/363, 540/539


[[POTE_tuning|POTE generator]]: ~7/5 = 585.123
Mapping: [{{val|1 5 15 15 2 -8}}, {{val|0 -7 -26 -25 3 24}}]


Map: [<1 5 15 15 2 -8|, <0 -7 -26 -25 3 24|]
POTE generator: ~7/5 = 585.123


EDOs: 39d, 41, 80, 121
Vals: {{Val list| 39d, 41, 80, 121 }}


Badness: 0.025717
Badness: 0.025717


===17-limit===
==== 17-limit ====
Commas: 256/255, 325/324, 352/351, 364/363, 540/539
Comma list: 256/255, 325/324, 352/351, 364/363, 540/539


[[POTE_tuning|POTE generator]]: ~7/5 = 585.116
Mapping: [{{val|1 5 15 15 2 -8 -12}}, {{val|0 -7 -26 -25 3 24 33}}]


Map: [<1 5 15 15 2 -8 -12|, <0 -7 -26 -25 3 24 33|]
POTE generator: ~7/5 = 585.116


EDOs: 39d, 41, 80, 121
Vals: {{Val list| 39d, 41, 80, 121 }}


Badness: 0.021463
Badness: 0.021463


===19-limit===
==== 19-limit ====
Commas: 190/189, 256/255, 325/324, 352/351, 361/360, 595/594
Comma list: 190/189, 256/255, 325/324, 352/351, 361/360, 595/594


[[POTE_tuning|POTE generator]]: ~7/5 = 585.109
Mapping: [{{val|1 5 15 15 2 -8 -12 14}}, {{val|0 -7 -26 -25 3 24 33 -20}}]


Map: [<1 5 15 15 2 -8 -12 14|, <0 -7 -26 -25 3 24 33 -20|]
POTE generator: ~7/5 = 585.109


EDOs: 39d, 41, 80, 121
Vals: {{Val list| 39d, 41, 80, 121 }}


Badness: 0.017650
Badness: 0.017650


===Orcus===
=== Orcus ===
Commas: 144/143, 196/195, 275/273, 896/891
Comma list: 144/143, 196/195, 275/273, 896/891
 
Mapping: [{{val|1 5 15 15 2 12}}, {{val|0 -7 -26 -25 3 -17}}]


POTE generator: ~7/5 = 585.111
POTE generator: ~7/5 = 585.111


Map: [<1 5 15 15 2 12|, <0 -7 -26 -25 3 -17|]
Vals: {{Val list| 41, 80f, 121ff}}


EDOs: 41, 80f, 121ff
Badness: 0.033441


Badness: 0.033441
== Plutino ==
Comma list: 100/99, 245/242, 10976/10935


==Plutino==
Mapping: [{{val|1 5 15 15 22}}, {{val|0 -7 -26 -25 -38}}]
Commas: 100/99, 245/242, 10976/10935


POTE generator: ~7/5 = 585.283
POTE generator: ~7/5 = 585.283


Map: [<1 5 15 15 22|, <0 -7 -26 -25 -38|]
Vals: {{Val list| 2cde, 39dee, 41 }}


EDOs: 2cde, 39dee, 41
Badness: 0.057966


Badness: 0.057966
=== 13-limit ===
Comma list: 100/99, 196/195, 245/242, 729/728


===13-limit===
Mapping: [{{val|1 5 15 15 22 12}}, {{val|0 -7 -26 -25 -38 -17}}]
Commas: 100/99, 196/195, 245/242, 729/728


POTE generator: ~7/5 = 585.232
POTE generator: ~7/5 = 585.232


Map: [<1 5 15 15 22 12|, <0 -7 -26 -25 -38 -17|]
Vals: {{Val list| 2cde, 39deef, 41 }}
 
EDOs: 2cde, 39deef, 41


Badness: 0.040182
Badness: 0.040182


=Eris=
= Eris =
Commas: 16875/16807, 65625/65536
[[Comma list]]: 16875/16807, 65625/65536


POTE generator: ~60/49 = 348.216
[[Mapping]]: [{{val|1 10 0 6}}, {{val|0 -29 8 -11}}]


Map: [<1 10 0 6|, <0 -29 8 -11|]
{{Multival|legend=1|29 -8 11 -80 -64 48}}


Wedgie: <<29 -8 11 -80 -64 48}}
[[POTE generator]]: ~60/49 = 348.216


EDOs: 31, 131, 162, 193, 224, 1823cd, 2271cd
{{Val list|legend=1| 31, 131, 162, 193, 224, 1823cd, 2271cd }}


Badness: 0.0747
[[Badness]]: 0.074719


==11-limit==
== 11-limit ==
Commas: 540/539, 1375/1372, 65625/65536
Comma list: 540/539, 1375/1372, 65625/65536
 
Mapping: [{{val|1 10 0 6 20}}, {{val|0 -29 8 -11 -57}}]


POTE generator: ~11/9 = 348.219
POTE generator: ~11/9 = 348.219


Map: [<1 10 0 6 20|, <0 -29 8 -11 -57|]
Vals: {{Val list| 31, 193, 224, 703, 927d, 1151cd }}
 
Badness: 0.027621
 
== 13-limit ==
Comma list: 540/539, 625/624, 1375/1372, 4096/4095
 
Mapping: [{{val|1 10 0 6 20 -14}}, {{val|0 -29 8 -11 -57 61}}]
 
POTE generator: ~11/9 = 348.213
 
Vals: {{Val list| 31, 193, 224 }}


EDOs: 31, 193, 224, 703, 927d, 1151cd
Badness: 0.025137


Badness: 0.0276
= Mirkat =
[[Comma list]]: 16875/16807, 19683/19600


=Mirkat=
[[Mapping]]: [{{val|3 2 1 2}}, {{val|0 6 13 14}}]
Commas: 16875/16807, 19683/19600


POTE generator: ~10/9 = 183.539
{{Multival|legend=1|18 39 42 20 16 -12}}


Map: [<3 2 1 2|, <0 6 13 14|]
[[POTE generator]]: ~10/9 = 183.539


Wedgie: <<18 39 42 20 16 -12||
{{Val list|legend=1| 39d, 72, 111, 183, 255 }}


EDOs: 39d, 72, 111, 183, 255
[[Badness]]: 0.059376


Badness: 0.0594
== 11-limit ==
Comma list: 540/539, 1375/1372, 8019/8000


==11-limit==
Mapping: [{{val|3 2 1 2 9}}, {{val|0 6 13 14 3}}]
Commas: 540/539, 1375/1372, 8019/8000


POTE generator: ~10/9 = 183.528
POTE generator: ~10/9 = 183.528


Map: [<3 2 1 2 9|, <0 6 13 14 3|]
Vals: {{Val list| 39d, 72, 111, 183, 255 }}


EDOs: 39d, 72, 111, 183, 255
Badness: 0.022126


Badness: 0.0221
== 13-limit ==
Comma list: 351/350, 540/539, 676/675, 1375/1372


==13-limit==
Mapping: [{{val|3 2 1 2 9 1}}, {{val|0 6 13 14 3 22}}]
Commas: 351/350, 540/539, 676/675, 1375/1372


POTE generator: ~10/9 = 183.577
POTE generator: ~10/9 = 183.577


Map: [<3 2 1 2 9 1|, <0 6 13 14 3 22|]
Vals: {{Val list| 39df, 72, 111, 183, 255f }}


EDOs: 39df, 72, 111, 183, 255f
Badness: 0.018632


Badness: 0.0186
== 17-limit ==
Comma list: 351/350, 442/441, 540/539, 561/560, 715/714


==17-limit==
Mapping: [{{val|3 2 1 2 9 1 4}}, {{val|0 6 13 14 3 22 18}}]
Commas: 351/350, 442/441, 540/539, 561/560, 715/714


POTE generator: ~10/9 = 183.579
POTE generator: ~10/9 = 183.579


Map: [<3 2 1 2 9 1 4|, <0 6 13 14 3 22 18|]
Vals: {{Val list| 39dfg, 72, 111, 183, 255f }}


EDOs: 39dfg, 72, 111, 183, 255f
Badness: 0.011775


=Subsemifourth=
= Subsemifourth =
Commas: 16875/16807, 26873856/26796875
[[Comma list]]: 16875/16807, 26873856/26796875


POTE generator: ~144/125 = 244.719
[[Mapping]]: [{{val|1 -8 -4 -8}}, {{val|0 47 31 53}}]


Map: [<1 39 27 45|, <0 -47 -31 -53|]
{{Multival|legend=1|47 31 53 -60 -48 36}}


Wedgie: <<47 31 53 -60 -48 36||
[[POTE generator]]: ~144/125 = 244.719


EDOs: 49, 103, 152, 255, 407
{{Val list|legend=1| 49, 103, 152, 255, 407 }}


Badness: 0.1352
[[Badness]]: 0.135173


==11-limit==
== 11-limit ==
Commas: 540/539, 1375/1372, 234375/234256
Comma list: 540/539, 1375/1372, 234375/234256
 
Mapping: [{{val|1 -8 -4 -8 -10}}, {{val|0 47 31 53 66}}]


POTE generator: ~121/105 = 244.719
POTE generator: ~121/105 = 244.719


Map: [<1 39 27 45 56|, <0 -47 -31 -53 -66|]
Vals: {{Val list| 49, 103, 152, 255, 407, 966d }}


EDOs: 49, 103, 152, 255, 407, 966d
Badness: 0.034276


Badness: 0.0343
== 13-limit ==
Comma list: 540/539, 847/845, 1375/1372, 1575/1573


==13-limit==
Mapping: [{{val|1 -8 -4 -8 -10 -12}}, {{val|0 47 31 53 66 77}}]
Commas: 540/539, 847/845, 1375/1372, 1575/1573


POTE generator: ~15/13 = 244.714
POTE generator: ~15/13 = 244.714


Map: [<1 39 27 45 56 65|, <0 -47 -31 -53 -66 -77|]
Vals: {{Val list| 103, 152f, 255, 407f, 662df }}
 
EDOs: 103, 152f, 255, 407f, 662df


Badness: 0.0284
Badness: 0.028387


[[Category:Theory]]
[[Category:Theory]]
[[Category:Temperament clan]]
[[Category:Temperament clan]]
[[Category:Mirkwai]]
[[Category:Mirkwai]]

Revision as of 03:49, 27 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

Comma list: 4000/3969, 10976/10935

Mapping: [⟨1 5 15 15], ⟨0 -7 -26 -25]]

Wedgie: ⟨⟨ 7 26 25 25 20 -15 ]]

POTE generator: ~7/5 = 585.147

Template:Val list

Badness: 0.057514

11-limit

Comma list: 540/539, 896/891, 1375/1372

Mapping: [⟨1 5 15 15 2], ⟨0 -7 -26 -25 3]]

POTE generator: ~7/5 = 585.114

Vals: Template:Val list

Badness: 0.029844

13-limit

Comma list: 325/324, 352/351, 364/363, 540/539

Mapping: [⟨1 5 15 15 2 -8], ⟨0 -7 -26 -25 3 24]]

POTE generator: ~7/5 = 585.123

Vals: Template:Val list

Badness: 0.025717

17-limit

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

Mapping: [⟨1 5 15 15 2 -8 -12], ⟨0 -7 -26 -25 3 24 33]]

POTE generator: ~7/5 = 585.116

Vals: Template:Val list

Badness: 0.021463

19-limit

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

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

POTE generator: ~7/5 = 585.109

Vals: Template:Val list

Badness: 0.017650

Orcus

Comma list: 144/143, 196/195, 275/273, 896/891

Mapping: [⟨1 5 15 15 2 12], ⟨0 -7 -26 -25 3 -17]]

POTE generator: ~7/5 = 585.111

Vals: Template:Val list

Badness: 0.033441

Plutino

Comma list: 100/99, 245/242, 10976/10935

Mapping: [⟨1 5 15 15 22], ⟨0 -7 -26 -25 -38]]

POTE generator: ~7/5 = 585.283

Vals: Template:Val list

Badness: 0.057966

13-limit

Comma list: 100/99, 196/195, 245/242, 729/728

Mapping: [⟨1 5 15 15 22 12], ⟨0 -7 -26 -25 -38 -17]]

POTE generator: ~7/5 = 585.232

Vals: Template:Val list

Badness: 0.040182

Eris

Comma list: 16875/16807, 65625/65536

Mapping: [⟨1 10 0 6], ⟨0 -29 8 -11]]

Wedgie: ⟨⟨ 29 -8 11 -80 -64 48 ]]

POTE generator: ~60/49 = 348.216

Template:Val list

Badness: 0.074719

11-limit

Comma list: 540/539, 1375/1372, 65625/65536

Mapping: [⟨1 10 0 6 20], ⟨0 -29 8 -11 -57]]

POTE generator: ~11/9 = 348.219

Vals: Template:Val list

Badness: 0.027621

13-limit

Comma list: 540/539, 625/624, 1375/1372, 4096/4095

Mapping: [⟨1 10 0 6 20 -14], ⟨0 -29 8 -11 -57 61]]

POTE generator: ~11/9 = 348.213

Vals: Template:Val list

Badness: 0.025137

Mirkat

Comma list: 16875/16807, 19683/19600

Mapping: [⟨3 2 1 2], ⟨0 6 13 14]]

Wedgie: ⟨⟨ 18 39 42 20 16 -12 ]]

POTE generator: ~10/9 = 183.539

Template:Val list

Badness: 0.059376

11-limit

Comma list: 540/539, 1375/1372, 8019/8000

Mapping: [⟨3 2 1 2 9], ⟨0 6 13 14 3]]

POTE generator: ~10/9 = 183.528

Vals: Template:Val list

Badness: 0.022126

13-limit

Comma list: 351/350, 540/539, 676/675, 1375/1372

Mapping: [⟨3 2 1 2 9 1], ⟨0 6 13 14 3 22]]

POTE generator: ~10/9 = 183.577

Vals: Template:Val list

Badness: 0.018632

17-limit

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

Mapping: [⟨3 2 1 2 9 1 4], ⟨0 6 13 14 3 22 18]]

POTE generator: ~10/9 = 183.579

Vals: Template:Val list

Badness: 0.011775

Subsemifourth

Comma list: 16875/16807, 26873856/26796875

Mapping: [⟨1 -8 -4 -8], ⟨0 47 31 53]]

Wedgie: ⟨⟨ 47 31 53 -60 -48 36 ]]

POTE generator: ~144/125 = 244.719

Template:Val list

Badness: 0.135173

11-limit

Comma list: 540/539, 1375/1372, 234375/234256

Mapping: [⟨1 -8 -4 -8 -10], ⟨0 47 31 53 66]]

POTE generator: ~121/105 = 244.719

Vals: Template:Val list

Badness: 0.034276

13-limit

Comma list: 540/539, 847/845, 1375/1372, 1575/1573

Mapping: [⟨1 -8 -4 -8 -10 -12], ⟨0 47 31 53 66 77]]

POTE generator: ~15/13 = 244.714

Vals: Template:Val list

Badness: 0.028387

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