Canopic clan: Difference between revisions

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Line 4: Line 4:
Commas: 6144/6125, 16875/16807
Commas: 6144/6125, 16875/16807


[[POTE_tuning|POTE generator]]: 386.863
[[POTE_tuning|POTE generator]]: ~5/4 = 386.863


Map: [<1 9 2 7|, <0 -23 1 -13|]
Map: [<1 9 2 7|, <0 -23 1 -13|]
Line 10: Line 10:
Wedgie: <<23 -1 13 -55 -44 33||
Wedgie: <<23 -1 13 -55 -44 33||


EDOs: 31, 90, 121, 152, 335
EDOs: 31, 90, 121, 152, 335d
 
Badness: 0.051834


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


[[POTE_tuning|POTE generator]]: 386.856
[[POTE_tuning|POTE generator]]: ~5/4 = 386.856


Map: [<1 9 2 7 17|, <0 -23 1 -13 -42|]
Map: [<1 9 2 7 17|, <0 -23 1 -13 -42|]


EDOs: 31, 90, 121, 152, 335, 487
EDOs: 31, 90e, 121, 152, 335d, 487d
 
Badness: 0.019845


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


[[POTE_tuning|POTE generator]]: 386.826
[[POTE_tuning|POTE generator]]: ~5/4 = 386.826


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


EDOs: 31, 121, 152, 425
EDOs: 31, 121, 152f, 425deff
 
Badness: 0.024839


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


[[POTE_tuning|POTE generator]]: 386.812
[[POTE_tuning|POTE generator]]: ~5/4 = 386.812


Map: [<1 9 2 7 17 -5 -3|, <0 -23 1 -13 -42 27 22|]
Map: [<1 9 2 7 17 -5 -3|, <0 -23 1 -13 -42 27 22|]


EDOs: 31, 121, 273
EDOs: 31, 121, 273defgg
 
Badness: 0.021400


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


[[POTE_tuning|POTE generator]]: 386.819
[[POTE_tuning|POTE generator]]: ~5/4 = 386.819
 
Map: [<1 9 2 7 17 -5 -3 -8|, <0 -23 1 -13 -42 27 22 38|]


Map: [<1 9 2 7 17 -5 -3|, <0 -23 1 -13 -42 27 22|]
EDOs: 31, 121, 152fg, 273defgg


EDOs: 31, 121, 152, 273
Badness: 0.018413


=Kwai=
=Kwai=
Commas: 5120/5103, 16875/16807
Commas: 5120/5103, 16875/16807


[[POTE_tuning|POTE generator]]: 702.616
[[POTE_tuning|POTE generator]]: ~3/2 = 702.616


Map: [<1 0 -50 -40|, <0 1 33 27|]
Map: [<1 0 -50 -40|, <0 1 33 27|]
Line 57: Line 67:
Wedgie: <<1 33 27 50 40 -30||
Wedgie: <<1 33 27 50 40 -30||


EDOs: 41, 111, 152, 345, 497
EDOs: 41, 111, 152, 345, 497d
 
Badness: 0.054476


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


[[POTE_tuning|POTE generator]]: 702.623
[[POTE_tuning|POTE generator]]: ~3/2 = 702.623


Map: [<1 0 -50 -40 32|, <0 1 33 27 -18|]
Map: [<1 0 -50 -40 32|, <0 1 33 27 -18|]


EDOs: 29, 41, 111, 152
EDOs: 29cd, 41, 111, 152
 
Badness: 0.026219


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


[[POTE_tuning|POTE generator]]: 702.644
[[POTE_tuning|POTE generator]]: ~3/2 = 702.644


Map: [<1 0 -50 -40 32 27|, <0 1 33 27 -18 -21|]
Map: [<1 0 -50 -40 32 27|, <0 1 33 27 -18 -21|]


EDOs: 29, 41, 111, 152
EDOs: 29cd, 41, 111, 152f
 
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]]: 702.660
[[POTE_tuning|POTE generator]]: ~3/2 = 702.660


Map: [<1 0 -50 -40 32 27 58|, <0 1 33 27 -18 -21 -34|]
Map: [<1 0 -50 -40 32 27 58|, <0 1 33 27 -18 -21 -34|]


EDOs: 29, 41, 111, 152, 263
EDOs: 29cdg, 41, 111, 152fg, 263dfg
 
Badness: 0.021950


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


[[POTE_tuning|POTE generator]]: 702.657
[[POTE_tuning|POTE generator]]: ~3/2 = 702.657


Map: [<1 0 -50 -40 32 27 58 -56|, <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|]


EDOs: 29, 41, 111, 152, 263
EDOs: 29cdgh, 41, 111, 152fg, 263dfgh
 
Badness: 0.016957


=Pluto=
=Pluto=
Commas: 4000/3969, 10976/10935
Commas: 4000/3969, 10976/10935


[[POTE_tuning|POTE generator]]: 585.147
[[POTE_tuning|POTE generator]]: ~7/5 = 585.147


Map: [<1 5 15 15|, <0 -7 -26 -25|]
Map: [<1 5 15 15|, <0 -7 -26 -25|]
Line 104: Line 124:
Wedgie: <<7 26 25 25 20 -15||
Wedgie: <<7 26 25 25 20 -15||


EDOs: 39, 41, 80, 121, 404
EDOs: 39d, 41, 80, 121, 404bd
 
Badness: 0.057514


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


[[POTE_tuning|POTE generator]]: 585.114
[[POTE_tuning|POTE generator]]: ~7/5 = 585.114


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


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


==13-limit==
Badness: 0.029844
 
===13-limit===
Commas: 325/324, 352/351, 364/363, 540/539
Commas: 325/324, 352/351, 364/363, 540/539


[[POTE_tuning|POTE generator]]: 585.123
[[POTE_tuning|POTE generator]]: ~7/5 = 585.123


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


EDOs: 39, 41, 80, 121
EDOs: 39d, 41, 80, 121
 
Badness: 0.025717


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


[[POTE_tuning|POTE generator]]: 585.116
[[POTE_tuning|POTE generator]]: ~7/5 = 585.116


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


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


==19-limit==
Badness: 0.021463
 
===19-limit===
Commas: 190/189, 256/255, 325/324, 352/351, 361/360, 595/594
Commas: 190/189, 256/255, 325/324, 352/351, 361/360, 595/594


[[POTE_tuning|POTE generator]]: 585.109
[[POTE_tuning|POTE generator]]: ~7/5 = 585.109


Map: [<1 5 15 15 2 -8 -12 14|, <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|]


EDOs: 39, 41, 80, 121, 564, 685
EDOs: 39d, 41, 80, 121


==Orcus==
Badness: 0.017650
 
===Orcus===
Commas: 144/143, 196/195, 275/273, 896/891
Commas: 144/143, 196/195, 275/273, 896/891


Line 149: Line 179:
Map: [<1 5 15 15 2 12|, <0 -7 -26 -25 3 -17|]
Map: [<1 5 15 15 2 12|, <0 -7 -26 -25 3 -17|]


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


Badness: 0.0334
Badness: 0.033441


=Plutino=
==Plutino==
Commas: 100/99, 245/242, 16875/16807
Commas: 100/99, 245/242, 10976/10935


POTE generator: ~7/5 = 585.283
POTE generator: ~7/5 = 585.283
Line 160: Line 190:
Map: [<1 5 15 15 22|, <0 -7 -26 -25 -38|]
Map: [<1 5 15 15 22|, <0 -7 -26 -25 -38|]


EDOs: 41, 123c
EDOs: 2cde, 39dee, 41


Badness: 0.0580
Badness: 0.057966


==13-limit==
===13-limit===
Commas: 100/99, 196/195, 245/242, 729/728
Commas: 100/99, 196/195, 245/242, 729/728


Line 171: Line 201:
Map: [<1 5 15 15 22 12|, <0 -7 -26 -25 -38 -17|]
Map: [<1 5 15 15 22 12|, <0 -7 -26 -25 -38 -17|]


EDOs: 41, 121ef
EDOs: 2cde, 39deef, 41


Badness: 0.0402
Badness: 0.040182


=Eris=
=Eris=

Revision as of 06:49, 10 April 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

Commas: 6144/6125, 16875/16807

POTE generator: ~5/4 = 386.863

Map: [<1 9 2 7|, <0 -23 1 -13|]

Wedgie: <<23 -1 13 -55 -44 33||

EDOs: 31, 90, 121, 152, 335d

Badness: 0.051834

11-limit

Commas: 540/539, 1375/1372, 5632/5625

POTE generator: ~5/4 = 386.856

Map: [<1 9 2 7 17|, <0 -23 1 -13 -42|]

EDOs: 31, 90e, 121, 152, 335d, 487d

Badness: 0.019845

13-limit

Commas: 352/351, 540/539, 625/624, 1375/1372

POTE generator: ~5/4 = 386.826

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

EDOs: 31, 121, 152f, 425deff

Badness: 0.024839

17-limit

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

POTE generator: ~5/4 = 386.812

Map: [<1 9 2 7 17 -5 -3|, <0 -23 1 -13 -42 27 22|]

EDOs: 31, 121, 273defgg

Badness: 0.021400

19-limit

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

POTE generator: ~5/4 = 386.819

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

EDOs: 31, 121, 152fg, 273defgg

Badness: 0.018413

Kwai

Commas: 5120/5103, 16875/16807

POTE generator: ~3/2 = 702.616

Map: [<1 0 -50 -40|, <0 1 33 27|]

Wedgie: <<1 33 27 50 40 -30||

EDOs: 41, 111, 152, 345, 497d

Badness: 0.054476

11-limit

Commas: 540/539, 1375/1372, 16384/16335

POTE generator: ~3/2 = 702.623

Map: [<1 0 -50 -40 32|, <0 1 33 27 -18|]

EDOs: 29cd, 41, 111, 152

Badness: 0.026219

13-limit

Commas: 352/351, 540/539, 729/728, 1375/1372

POTE generator: ~3/2 = 702.644

Map: [<1 0 -50 -40 32 27|, <0 1 33 27 -18 -21|]

EDOs: 29cd, 41, 111, 152f

Badness: 0.024555

17-limit

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

POTE generator: ~3/2 = 702.660

Map: [<1 0 -50 -40 32 27 58|, <0 1 33 27 -18 -21 -34|]

EDOs: 29cdg, 41, 111, 152fg, 263dfg

Badness: 0.021950

19-limit

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

POTE generator: ~3/2 = 702.657

Map: [<1 0 -50 -40 32 27 58 -56|, <0 1 33 27 -18 -21 -34 38|]

EDOs: 29cdgh, 41, 111, 152fg, 263dfgh

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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