Canopic clan: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
m Cleanup
Xenwolf (talk | contribs)
m fix heading structure
Line 11: Line 11:
* ''[[rainwell]]'', {16875/16807, 2100875/2097152} → [[Semicomma family #Rainwell]]
* ''[[rainwell]]'', {16875/16807, 2100875/2097152} → [[Semicomma family #Rainwell]]


= Grendel =
== Grendel ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 26: Line 26:
[[Badness]]: 0.051834
[[Badness]]: 0.051834


== 11-limit ==
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 39: Line 39:
Badness: 0.019845
Badness: 0.019845


== 13-limit ==
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 52: Line 52:
Badness: 0.024839
Badness: 0.024839


== 17-limit ==
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Line 65: Line 65:
Badness: 0.021400
Badness: 0.021400


== 19-limit ==
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19


Line 78: Line 78:
Badness: 0.018413
Badness: 0.018413


= Kwai =
== Kwai ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 93: Line 93:
[[Badness]]: 0.054476
[[Badness]]: 0.054476


== 11-limit ==
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 106: Line 106:
Badness: 0.026219
Badness: 0.026219


== 13-limit ==
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 119: Line 119:
Badness: 0.024555
Badness: 0.024555


== 17-limit ==
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Line 132: Line 132:
Badness: 0.021950
Badness: 0.021950


== 19-limit ==
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19


Line 145: Line 145:
Badness: 0.016957
Badness: 0.016957


= Pluto =
== Pluto ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 160: Line 160:
[[Badness]]: 0.057514
[[Badness]]: 0.057514


== 11-limit ==
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 173: Line 173:
Badness: 0.029844
Badness: 0.029844


=== 13-limit ===
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 186: Line 186:
Badness: 0.025717
Badness: 0.025717


==== 17-limit ====
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Line 199: Line 199:
Badness: 0.021463
Badness: 0.021463


==== 19-limit ====
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19


Line 212: Line 212:
Badness: 0.017650
Badness: 0.017650


=== Orcus ===
==== Orcus ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 225: Line 225:
Badness: 0.033441
Badness: 0.033441


== Plutino ==
=== Plutino ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 238: Line 238:
Badness: 0.057966
Badness: 0.057966


=== 13-limit ===
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 251: Line 251:
Badness: 0.040182
Badness: 0.040182


= Eris =
== Eris ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 266: Line 266:
[[Badness]]: 0.074719
[[Badness]]: 0.074719


== 11-limit ==
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 279: Line 279:
Badness: 0.027621
Badness: 0.027621


== 13-limit ==
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 292: Line 292:
Badness: 0.025137
Badness: 0.025137


= Mirkat =
== Mirkat ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 307: Line 307:
[[Badness]]: 0.059376
[[Badness]]: 0.059376


== 11-limit ==
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 320: Line 320:
Badness: 0.022126
Badness: 0.022126


== 13-limit ==
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 333: Line 333:
Badness: 0.018632
Badness: 0.018632


== 17-limit ==
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Line 346: Line 346:
Badness: 0.011775
Badness: 0.011775


= Subsemifourth =
== Subsemifourth ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 361: Line 361:
[[Badness]]: 0.135173
[[Badness]]: 0.135173


== 11-limit ==
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 374: Line 374:
Badness: 0.034276
Badness: 0.034276


== 13-limit ==
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13



Revision as of 15:33, 31 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