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]], [[Trienstonic clan #Octokaidecal|octokaidecal]], [[Starling temperaments #Nusecond|nusecond]], [[Ragismic microtemperaments #Octoid|octoid]], [[Kleismic family #Sqrtphi|sqrtphi]], [[Schismatic family #Quanharuk|quanharuk]], [[Semicomma family #Rainwell|rainwell]], [[Amity family #Familia|familia]], [[Hemimean clan #Semisept|semisept]], and [[Sensamagic clan #Bohpier|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 these considered elsewhere:
* ''[[octokaidecal]]'', {28/27, 50/49} → [[Trienstonic clan #Octokaidecal]]
* ''[[nusecond]]'', {126/125, 2430/2401} → [[Starling temperaments #Nusecond]]
* [[miracle]], {225/224, 1029/1024} → [[Gamelismic clan #Miracle]]
* ''[[bohpier]]'', {245/243, 3125/3087} → [[Sensamagic clan #Bohpier]]
* ''[[semisept]]'', {1728/1715, 3136/3125} → [[Hemimean clan #Semisept]]
* ''[[octoid]]'', {4375/4374, 16875/16807} → [[Ragismic microtemperaments #Octoid]]
* ''[[sqrtphi]]'', {15625/15552, 16875/16807} → [[Kleismic family #Sqrtphi]]
* ''[[quanharuk]]'', {16875/16807, 32805/32768} → [[Schismatic family #Quanharuk]]
* ''[[familia]]'', {16875/16807, 1600000/1594323} → [[Amity family #Familia]]
* ''[[rainwell]]'', {16875/16807, 2100875/2097152} → [[Semicomma family #Rainwell]]


= Grendel =
= Grendel =
Subgroup: 2.3.5.7
[[Comma list]]: 6144/6125, 16875/16807
[[Comma list]]: 6144/6125, 16875/16807


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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1375/1372, 5632/5625
Comma list: 540/539, 1375/1372, 5632/5625


Line 26: Line 40:


== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 540/539, 625/624, 1375/1372
Comma list: 352/351, 540/539, 625/624, 1375/1372


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== 17-limit ==
== 17-limit ==
Subgroup: 2.3.5.7.11.13.17
Comma list: 256/255, 352/351, 625/624, 715/714, 1275/1274
Comma list: 256/255, 352/351, 625/624, 715/714, 1275/1274


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== 19-limit ==
== 19-limit ==
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 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


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= Kwai =
= Kwai =
Subgroup: 2.3.5.7
[[Comma list]]: 5120/5103, 16875/16807
[[Comma list]]: 5120/5103, 16875/16807


Line 72: Line 94:


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1375/1372, 16384/16335
Comma list: 540/539, 1375/1372, 16384/16335


Line 83: Line 107:


== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 540/539, 729/728, 1375/1372
Comma list: 352/351, 540/539, 729/728, 1375/1372


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== 17-limit ==
== 17-limit ==
Commas: 256/255, 352/351, 540/539, 715/714, 1089/1088
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 256/255, 352/351, 540/539, 715/714, 1089/1088


Mapping: [{{val|1 0 -50 -40 32 27 58}}, {{val|0 1 33 27 -18 -21 -34}}]
Mapping: [{{val|1 0 -50 -40 32 27 58}}, {{val|0 1 33 27 -18 -21 -34}}]
Line 105: Line 133:


== 19-limit ==
== 19-limit ==
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 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


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= Pluto =
= Pluto =
Subgroup: 2.3.5.7
[[Comma list]]: 4000/3969, 10976/10935
[[Comma list]]: 4000/3969, 10976/10935


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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 540/539, 896/891, 1375/1372
Comma list: 540/539, 896/891, 1375/1372


Line 140: Line 174:


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 352/351, 364/363, 540/539
Comma list: 325/324, 352/351, 364/363, 540/539


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==== 17-limit ====
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
Comma list: 256/255, 325/324, 352/351, 364/363, 540/539
Comma list: 256/255, 325/324, 352/351, 364/363, 540/539


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==== 19-limit ====
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 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


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=== Orcus ===
=== Orcus ===
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 196/195, 275/273, 896/891
Comma list: 144/143, 196/195, 275/273, 896/891


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== Plutino ==
== Plutino ==
Subgroup: 2.3.5.7.11
Comma list: 100/99, 245/242, 10976/10935
Comma list: 100/99, 245/242, 10976/10935


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


Vals: {{Val list| 2cde, 39dee, 41 }}
Vals: {{Val list| 39dee, 41 }}


Badness: 0.057966
Badness: 0.057966


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 196/195, 245/242, 729/728
Comma list: 100/99, 196/195, 245/242, 729/728


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


Vals: {{Val list| 2cde, 39deef, 41 }}
Vals: {{Val list| 39deef, 41 }}


Badness: 0.040182
Badness: 0.040182


= Eris =
= Eris =
Subgroup: 2.3.5.7
[[Comma list]]: 16875/16807, 65625/65536
[[Comma list]]: 16875/16807, 65625/65536


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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1375/1372, 65625/65536
Comma list: 540/539, 1375/1372, 65625/65536


Line 230: Line 280:


== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 625/624, 1375/1372, 4096/4095
Comma list: 540/539, 625/624, 1375/1372, 4096/4095


Line 241: Line 293:


= Mirkat =
= Mirkat =
Subgroup: 2.3.5.7
[[Comma list]]: 16875/16807, 19683/19600
[[Comma list]]: 16875/16807, 19683/19600


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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1375/1372, 8019/8000
Comma list: 540/539, 1375/1372, 8019/8000


Line 265: Line 321:


== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 540/539, 676/675, 1375/1372
Comma list: 351/350, 540/539, 676/675, 1375/1372


Line 276: Line 334:


== 17-limit ==
== 17-limit ==
Subgroup: 2.3.5.7.11.13.17
Comma list: 351/350, 442/441, 540/539, 561/560, 715/714
Comma list: 351/350, 442/441, 540/539, 561/560, 715/714


Line 287: Line 347:


= Subsemifourth =
= Subsemifourth =
Subgroup: 2.3.5.7
[[Comma list]]: 16875/16807, 26873856/26796875
[[Comma list]]: 16875/16807, 26873856/26796875


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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1375/1372, 234375/234256
Comma list: 540/539, 1375/1372, 234375/234256


Line 311: Line 375:


== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 847/845, 1375/1372, 1575/1573
Comma list: 540/539, 847/845, 1375/1372, 1575/1573


Line 317: Line 383:
POTE generator: ~15/13 = 244.714
POTE generator: ~15/13 = 244.714


Vals: {{Val list| 103, 152f, 255, 407f, 662df }}
Vals: {{Val list| 49f, 103, 152f, 255, 407f, 662df }}


Badness: 0.028387
Badness: 0.028387


[[Category:Theory]]
[[Category:Regular temperament theory]]
[[Category:Temperament clan]]
[[Category:Temperament clan]]
[[Category:Mirkwai]]
[[Category:Mirkwai]]
[[Category:Rank 2]]

Revision as of 08:50, 30 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 these considered elsewhere:

Grendel

Subgroup: 2.3.5.7

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

Subgroup: 2.3.5.7.11

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

Subgroup: 2.3.5.7.11.13

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

Subgroup: 2.3.5.7.11.13.17

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

Subgroup: 2.3.5.7.11.13.17.19

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

Subgroup: 2.3.5.7

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

Subgroup: 2.3.5.7.11

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

Subgroup: 2.3.5.7.11.13

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

Subgroup: 2.3.5.7.11.13.17

Comma list: 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

Subgroup: 2.3.5.7.11.13.17.19

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

Subgroup: 2.3.5.7

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

Subgroup: 2.3.5.7.11

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

Subgroup: 2.3.5.7.11.13

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

Subgroup: 2.3.5.7.11.13.17

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

Subgroup: 2.3.5.7.11.13.17.19

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

Subgroup: 2.3.5.7.11.13

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

Subgroup: 2.3.5.7.11

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

Subgroup: 2.3.5.7.11.13

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

Subgroup: 2.3.5.7

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

Subgroup: 2.3.5.7.11

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

Subgroup: 2.3.5.7.11.13

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

Subgroup: 2.3.5.7

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

Subgroup: 2.3.5.7.11

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

Subgroup: 2.3.5.7.11.13

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

Subgroup: 2.3.5.7.11.13.17

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

Subgroup: 2.3.5.7

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

Subgroup: 2.3.5.7.11

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

Subgroup: 2.3.5.7.11.13

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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