Canopic clan: Difference between revisions

Revision as of 10:16, 15 January 2022

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:

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

Canopus

Main article: Canopus

Subgroup: 3.5.7

Comma list: 16875/16807

Sval mapping: [⟨1 3 3], ⟨0 -5 -4]]

Sval mapping generators: ~3, ~7/5

POTE generator: ~7/5 = 583.9584

Optimal GPV sequence: b13, b62, b75, b88, b101, b114, b355, b469, b583, b697

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

Optimal GPV sequence: 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

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

POTE generator: ~5/4 = 386.826

Optimal GPV sequence: 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

Optimal GPV sequence: 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]]

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: Template:Val list

Badness: 0.040182

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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: Template:Val list

Badness: 0.011775

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

Optimal GPV sequence: 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

Optimal GPV sequence: Template:Val list

Badness: 0.025137

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

Optimal GPV sequence: 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

Optimal GPV sequence: Template:Val list

Badness: 0.028387

Septendesemi

The name septendesemi means a septendecimal semitone (17/16). The septendesemi temperament (80&103) tempers out the mirkwai comma and 1959552/1953125 (parkleiness comma, zotritrigu) in the 7-limit. 183EDO provides an excellent tuning for 7, 11, 13, and 17-limit septendesemi.

Subgroup: 2.3.5.7

Comma list: 16875/16807, 1959552/1953125

Mapping: [⟨1 -2 -1 -2], ⟨0 41 38 55]]

Wedgie: ⟨⟨ 41 38 55 -35 -28 21 ]]

POTE generator: ~343/324 = 104.916

Template:Val list

Badness: 0.146795

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 1375/1372, 43923/43750

Mapping: [⟨1 -2 -1 -2 -1], ⟨0 41 38 55 51]]

POTE generator: ~35/33 = 104.916

Optimal GPV sequence: Template:Val list

Badness: 0.041554

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 540/539, 1375/1372, 4225/4224

Mapping: [⟨1 -2 -1 -2 -1 3], ⟨0 41 38 55 51 8]]

POTE generator: ~35/33 = 104.908

Optimal GPV sequence: Template:Val list

Badness: 0.027908

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 351/350, 540/539, 561/560, 715/714, 4225/4224

Mapping: [⟨1 -2 -1 -2 -1 3 4], ⟨0 41 38 55 51 8 1]]

POTE generator: ~17/16 = 104.909

Optimal GPV sequence: Template:Val list

Badness: 0.020128

Gaster

Subgroup: 2.3.5.7

Comma list: 16875/16807, 14348907/14336000

Mapping: [⟨1 11 38 37], ⟨0 -19 -72 -69]]

POTE generator: ~800/567 = 594.64130

Optimal ET sequence: 111, 224

Badness: 0.154521

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 1375/1372, 14348907/14336000

Mapping: [⟨1 11 38 37 -1], ⟨0 -19 -72 -69 9]]

POTE generator: ~512/363 = 594.63909

Optimal GPV sequence: Template:Val list

Badness: 0.054060

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 540/539, 729/728, 1375/1372, 2200/2197

Mapping: [⟨1 11 38 37 -1 26], ⟨0 -19 -72 -69 9 -45]]

POTE generator: ~55/39 = 594.63899

Optimal GPV sequence: Template:Val list

Badness: 0.024882

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 540/539, 715/714, 729/728, 936/935, 2200/2197

Mapping: [⟨1 11 38 37 -1 26 14], ⟨0 -19 -72 -69 9 -45 -20]]

POTE generator: ~24/17 = 594.63553

Optimal GPV sequence: Template:Val list

Badness: 0.021436

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 324/323, 400/399, 495/494, 540/539, 715/714, 1445/1444

Mapping: [⟨1 11 38 37 -1 26 14 32], ⟨0 -19 -72 -69 9 -45 -20 -56]]

POTE generator: ~24/17 = 594.63620

Optimal GPV sequence: Template:Val list

Badness: 0.018370

23-limit

Subgroup: 2.3.5.7.11.13.17.19.23

Comma list: 324/323, 400/399, 460/459, 495/494, 529/528, 540/539, 715/714

Mapping: [⟨1 11 38 37 -1 26 14 32 7], ⟨0 -19 -72 -69 9 -45 -20 -56 -5]]

POTE generator: ~24/17 = 594.64147

Optimal GPV sequence: Template:Val list

Badness: 0.017619

29-limit

Subgroup: 2.3.5.7.11.13.17.19.23.29

Comma list: 290/289, 324/323, 400/399, 460/459, 495/494, 529/528, 540/539, 715/714

Mapping: [⟨1 11 38 37 -1 26 14 32 7 -11], ⟨0 -19 -72 -69 9 -45 -20 -56 -5 32]]

POTE generator: ~24/17 = 594.64556

Optimal GPV sequence: Template:Val list

Badness: 0.016815

31-limit

Subgroup: 2.3.5.7.11.13.17.19.23.29.31

Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 540/539, 715/714

Mapping: [⟨1 11 38 37 -1 26 14 32 7 -11 0], ⟨0 -19 -72 -69 9 -45 -20 -56 -5 32 10]]

POTE generator: ~24/17 = 594.64392

Optimal GPV sequence: Template:Val list

Badness: 0.014790

37-limit

Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37

Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 540/539, 667/666, 715/714

Mapping: [⟨1 11 38 37 -1 26 14 32 7 -11 0 -27], ⟨0 -19 -72 -69 9 -45 -20 -56 -5 32 10 65]]

POTE generator: ~24/17 = 594.64383

Optimal GPV sequence: Template:Val list

Badness: 0.014377

41-limit

Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37.41

Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 533/532, 540/539, 575/574, 667/666

Mapping: [⟨1 11 38 37 -1 26 14 32 7 -11 0 -27 45], ⟨0 -19 -72 -69 9 -45 -20 -56 -5 32 10 65 -80]]

POTE generator: ~24/17 = 594.64299

Optimal GPV sequence: Template:Val list

Badness: 0.012858

Subsedia

The generator for subsedia (10&111) is 0.5 cents flat of 15/14-wide semitone and tempers out the mirkwai comma and 65536/64827 (buzzardisma, saquadru comma). In this temperament, three generators makes ~16/13, five of them equals ~24/17, twelve of them equals ~16/7, sixteen of them equals ~3/1, and 45 of them equals ~22/1.

Subgroup: 2.3.5.7

Comma list: 16875/16807, 65536/64827

Mapping: [⟨1 0 5 4], ⟨0 16 -27 -12]]

Wedgie: ⟨⟨ 16 -27 -12 -80 -64 48 ]]

POTE generator: ~15/14 = 118.965

Template:Val list

Badness: 0.157658

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 1375/1372, 65536/64827

Mapping: [⟨1 0 5 4 -1], ⟨0 16 -27 -12 45]]

POTE generator: ~15/14 = 118.968

Optimal GPV sequence: Template:Val list

Badness: 0.066838

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 540/539, 676/675, 1375/1372

Mapping: [⟨1 0 5 4 -1 4], ⟨0 16 -27 -12 45 -3]]

POTE generator: ~15/14 = 118.968

Optimal GPV sequence: Template:Val list

Badness: 0.031635

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 256/255, 352/351, 442/441, 540/539, 715/714

Mapping: [⟨1 0 5 4 -1 4 3], ⟨0 16 -27 -12 45 -3 11]]

POTE generator: ~15/14 = 118.968

Optimal GPV sequence: Template:Val list

Badness: 0.019707

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 256/255, 352/351, 400/399, 442/441, 456/455, 715/714

Mapping: [⟨1 0 5 4 -1 4 3 10], ⟨0 16 -27 -12 45 -3 11 -58]]

POTE generator: ~15/14 = 118.964

Optimal GPV sequence: Template:Val list

Badness: 0.017935

Hemiseptisix

The name hemiseptisix means a half of septimal major sixth (12/7). The hemiseptisix temperament (103&121) tempers out the mirkwai comma and 95703125/95551488 (pontiqak comma, lazozotritriyo) in the 7-limit. 224EDO provides an excellent tuning for 7, 11, and 13-limit hemiseptisix.

Subgroup: 2.3.5.7

Comma list: 16875/16807, 95703125/95551488

Mapping: [⟨1 -19 -7 -17], ⟨0 53 24 51]]

Wedgie: ⟨⟨ 53 24 51 -85 -68 51 ]]

POTE generator: ~98/75 = 466.071

Template:Val list

Badness: 0.162826

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 1375/1372, 2734375/2725888

Mapping: [⟨1 -19 -7 -17 -28], ⟨0 53 24 51 81]]

POTE generator: ~55/42 = 466.070

Optimal GPV sequence: Template:Val list

Badness: 0.043381

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 540/539, 625/624, 1375/1372, 2200/2197

Mapping: [⟨1 -19 -7 -17 -28 -13], ⟨0 53 24 51 81 43]]

POTE generator: ~55/42 = 466.071

Optimal GPV sequence: Template:Val list

Badness: 0.021127

@@ Line 265: / Line 265: @@
 Badness: 0.040182
-== Eris ==
-Subgroup: 2.3.5.7
-[[Comma list]]: 16875/16807, 65625/65536
-[[Mapping]]: [{{val|1 10 0 6}}, {{val|0 -29 8 -11}}]
-{{Multival|legend=1|29 -8 11 -80 -64 48}}
-[[POTE generator]]: ~60/49 = 348.216
-{{Val list|legend=1| 31, 131, 162, 193, 224, 1823cd, 2271cd }}
-[[Badness]]: 0.074719
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-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
-Optimal GPV sequence: {{Val list| 31, 193, 224, 703, 927d, 1151cd }}
-Badness: 0.027621
-=== 13-limit ===
-Subgroup: 2.3.5.7.11.13
-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
-Optimal GPV sequence: {{Val list| 31, 193, 224 }}
-Badness: 0.025137
 == Mirkat ==
@@ Line 361: / Line 320: @@
 Badness: 0.011775
-== Subsemifourth ==
+== Eris ==
 Subgroup: 2.3.5.7
-[[Comma list]]: 16875/16807, 26873856/26796875
+[[Comma list]]: 16875/16807, 65625/65536
-[[Mapping]]: [{{val|1 -8 -4 -8}}, {{val|0 47 31 53}}]
+[[Mapping]]: [{{val|1 10 0 6}}, {{val|0 -29 8 -11}}]
-{{Multival|legend=1|47 31 53 -60 -48 36}}
+{{Multival|legend=1|29 -8 11 -80 -64 48}}
-[[POTE generator]]: ~144/125 = 244.719
+[[POTE generator]]: ~60/49 = 348.216
-{{Val list|legend=1| 49, 103, 152, 255, 407 }}
+{{Val list|legend=1| 31, 131, 162, 193, 224, 1823cd, 2271cd }}
-[[Badness]]: 0.135173
+[[Badness]]: 0.074719
 === 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 540/539, 1375/1372, 234375/234256
+Comma list: 540/539, 1375/1372, 65625/65536
-Mapping: [{{val|1 -8 -4 -8 -10}}, {{val|0 47 31 53 66}}]
+Mapping: [{{val|1 10 0 6 20}}, {{val|0 -29 8 -11 -57}}]
-POTE generator: ~121/105 = 244.719
+POTE generator: ~11/9 = 348.219
-Optimal GPV sequence: {{Val list| 49, 103, 152, 255, 407, 966d }}
+Optimal GPV sequence: {{Val list| 31, 193, 224, 703, 927d, 1151cd }}
-Badness: 0.034276
+Badness: 0.027621
 === 13-limit ===
 Subgroup: 2.3.5.7.11.13
-Comma list: 540/539, 847/845, 1375/1372, 1575/1573
+Comma list: 540/539, 625/624, 1375/1372, 4096/4095
-Mapping: [{{val|1 -8 -4 -8 -10 -12}}, {{val|0 47 31 53 66 77}}]
+Mapping: [{{val|1 10 0 6 20 -14}}, {{val|0 -29 8 -11 -57 61}}]
-POTE generator: ~15/13 = 244.714
+POTE generator: ~11/9 = 348.213
-Optimal GPV sequence: {{Val list| 49f, 103, 152f, 255, 407f, 662df }}
+Optimal GPV sequence: {{Val list| 31, 193, 224 }}
-Badness: 0.028387
+Badness: 0.025137
-== Hemiseptisix ==
-The name ''hemiseptisix'' means a half of septimal major sixth ([[12/7]]). The hemiseptisix temperament (103&amp;121) tempers out the mirkwai comma and 95703125/95551488 (''pontiqak'' comma, lazozotritriyo) in the 7-limit. [[224edo|224EDO]] provides an excellent tuning for 7, 11, and 13-limit hemiseptisix.
+== Subsemifourth ==
 Subgroup: 2.3.5.7
-[[Comma list]]: 16875/16807, 95703125/95551488
+[[Comma list]]: 16875/16807, 26873856/26796875
-[[Mapping]]: [{{val|1 -19 -7 -17}}, {{val|0 53 24 51}}]
+[[Mapping]]: [{{val|1 -8 -4 -8}}, {{val|0 47 31 53}}]
-{{Multival|legend=1|53 24 51 -85 -68 51}}
+{{Multival|legend=1|47 31 53 -60 -48 36}}
-[[POTE generator]]: ~98/75 = 466.071
+[[POTE generator]]: ~144/125 = 244.719
-{{Val list|legend=1| 18, 103, 121, 224 }}
+{{Val list|legend=1| 49, 103, 152, 255, 407 }}
-[[Badness]]: 0.162826
+[[Badness]]: 0.135173
 === 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 540/539, 1375/1372, 2734375/2725888
+Comma list: 540/539, 1375/1372, 234375/234256
-Mapping: [{{val|1 -19 -7 -17 -28}}, {{val|0 53 24 51 81}}]
+Mapping: [{{val|1 -8 -4 -8 -10}}, {{val|0 47 31 53 66}}]
-POTE generator: ~55/42 = 466.070
+POTE generator: ~121/105 = 244.719
-Optimal GPV sequence: {{Val list| 103, 121, 224 }}
+Optimal GPV sequence: {{Val list| 49, 103, 152, 255, 407, 966d }}
-Badness: 0.043381
+Badness: 0.034276
 === 13-limit ===
 Subgroup: 2.3.5.7.11.13
-Comma list: 540/539, 625/624, 1375/1372, 2200/2197
+Comma list: 540/539, 847/845, 1375/1372, 1575/1573
-Mapping: [{{val|1 -19 -7 -17 -28 -13}}, {{val|0 53 24 51 81 43}}]
+Mapping: [{{val|1 -8 -4 -8 -10 -12}}, {{val|0 47 31 53 66 77}}]
-POTE generator: ~55/42 = 466.071
+POTE generator: ~15/13 = 244.714
-Optimal GPV sequence: {{Val list| 103, 121, 224 }}
+Optimal GPV sequence: {{Val list| 49f, 103, 152f, 255, 407f, 662df }}
-Badness: 0.021127
+Badness: 0.028387
 == Septendesemi ==
@@ Line 500: / Line 457: @@
 Badness: 0.020128
+== Gaster ==
+Subgroup: 2.3.5.7
+[[Comma list]]: 16875/16807, 14348907/14336000
+[[Mapping]]: [{{val|1 11 38 37}}, {{val|0 -19 -72 -69}}]
+[[POTE generator]]: ~800/567 = 594.64130
+{{Optimal GPV sequence|legend=1| 111, 224 }}
+[[Badness]]: 0.154521
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 540/539, 1375/1372, 14348907/14336000
+Mapping: [{{val|1 11 38 37 -1}}, {{val|0 -19 -72 -69 9}}]
+POTE generator: ~512/363 = 594.63909
+Optimal GPV sequence: {{Val list| 111, 224, 783d, 1007d, 1231dd }}
+Badness: 0.054060
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 540/539, 729/728, 1375/1372, 2200/2197
+Mapping: [{{val|1 11 38 37 -1 26}}, {{val|0 -19 -72 -69 9 -45}}]
+POTE generator: ~55/39 = 594.63899
+Optimal GPV sequence: {{Val list| 111, 224, 783df, 1007df, 1231ddf }}
+Badness: 0.024882
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 540/539, 715/714, 729/728, 936/935, 2200/2197
+Mapping: [{{val|1 11 38 37 -1 26 14}}, {{val|0 -19 -72 -69 9 -45 -20}}]
+POTE generator: ~24/17 = 594.63553
+Optimal GPV sequence: {{Val list| 111, 224, 559dgg }}
+Badness: 0.021436
+=== 19-limit ===
+Subgroup: 2.3.5.7.11.13.17.19
+Comma list: 324/323, 400/399, 495/494, 540/539, 715/714, 1445/1444
+Mapping: [{{val|1 11 38 37 -1 26 14 32}}, {{val|0 -19 -72 -69 9 -45 -20 -56}}]
+POTE generator: ~24/17 = 594.63620
+Optimal GPV sequence: {{Val list| 111, 224 }}
+Badness: 0.018370
+=== 23-limit ===
+Subgroup: 2.3.5.7.11.13.17.19.23
+Comma list: 324/323, 400/399, 460/459, 495/494, 529/528, 540/539, 715/714
+Mapping: [{{val|1 11 38 37 -1 26 14 32 7}}, {{val|0 -19 -72 -69 9 -45 -20 -56 -5}}]
+POTE generator: ~24/17 = 594.64147
+Optimal GPV sequence: {{Val list| 111, 224 }}
+Badness: 0.017619
+=== 29-limit ===
+Subgroup: 2.3.5.7.11.13.17.19.23.29
+Comma list: 290/289, 324/323, 400/399, 460/459, 495/494, 529/528, 540/539, 715/714
+Mapping: [{{val|1 11 38 37 -1 26 14 32 7 -11}}, {{val|0 -19 -72 -69 9 -45 -20 -56 -5 32}}]
+POTE generator: ~24/17 = 594.64556
+Optimal GPV sequence: {{Val list| 111, 113, 224 }}
+Badness: 0.016815
+=== 31-limit ===
+Subgroup: 2.3.5.7.11.13.17.19.23.29.31
+Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 540/539, 715/714
+Mapping: [{{val|1 11 38 37 -1 26 14 32 7 -11 0}}, {{val|0 -19 -72 -69 9 -45 -20 -56 -5 32 10}}]
+POTE generator: ~24/17 = 594.64392
+Optimal GPV sequence: {{Val list| 111, 113, 224 }}
+Badness: 0.014790
+=== 37-limit ===
+Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37
+Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 540/539, 667/666, 715/714
+Mapping: [{{val|1 11 38 37 -1 26 14 32 7 -11 0 -27}}, {{val|0 -19 -72 -69 9 -45 -20 -56 -5 32 10 65}}]
+POTE generator: ~24/17 = 594.64383
+Optimal GPV sequence: {{Val list| 111, 113, 224 }}
+Badness: 0.014377
+=== 41-limit ===
+Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37.41
+Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 533/532, 540/539, 575/574, 667/666
+Mapping: [{{val|1 11 38 37 -1 26 14 32 7 -11 0 -27 45}}, {{val|0 -19 -72 -69 9 -45 -20 -56 -5 32 10 65 -80}}]
+POTE generator: ~24/17 = 594.64299
+Optimal GPV sequence: {{Val list| 111, 113, 224 }}
+Badness: 0.012858
 == Subsedia ==
@@ Line 569: / Line 656: @@
 Badness: 0.017935
+== Hemiseptisix ==
+The name ''hemiseptisix'' means a half of septimal major sixth ([[12/7]]). The hemiseptisix temperament (103&amp;121) tempers out the mirkwai comma and 95703125/95551488 (''pontiqak'' comma, lazozotritriyo) in the 7-limit. [[224edo|224EDO]] provides an excellent tuning for 7, 11, and 13-limit hemiseptisix.
+Subgroup: 2.3.5.7
+[[Comma list]]: 16875/16807, 95703125/95551488
+[[Mapping]]: [{{val|1 -19 -7 -17}}, {{val|0 53 24 51}}]
+{{Multival|legend=1|53 24 51 -85 -68 51}}
+[[POTE generator]]: ~98/75 = 466.071
+{{Val list|legend=1| 18, 103, 121, 224 }}
+[[Badness]]: 0.162826
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 540/539, 1375/1372, 2734375/2725888
+Mapping: [{{val|1 -19 -7 -17 -28}}, {{val|0 53 24 51 81}}]
+POTE generator: ~55/42 = 466.070
+Optimal GPV sequence: {{Val list| 103, 121, 224 }}
+Badness: 0.043381
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 540/539, 625/624, 1375/1372, 2200/2197
+Mapping: [{{val|1 -19 -7 -17 -28 -13}}, {{val|0 53 24 51 81 43}}]
+POTE generator: ~55/42 = 466.071
+Optimal GPV sequence: {{Val list| 103, 121, 224 }}
+Badness: 0.021127
 [[Category:Regular temperament theory]]

Canopic clan: Difference between revisions

Revision as of 10:16, 15 January 2022

Canopus

Grendel

11-limit

13-limit

17-limit

19-limit

Kwai

11-limit

13-limit

17-limit

19-limit

Pluto

11-limit

13-limit

17-limit

19-limit

Orcus

Plutino

13-limit

Mirkat

11-limit

13-limit

17-limit

Eris

11-limit

13-limit

Subsemifourth

11-limit

13-limit

Septendesemi

11-limit

13-limit

17-limit

Gaster

11-limit

13-limit

17-limit

19-limit

23-limit

29-limit

31-limit

37-limit

41-limit

Subsedia

11-limit

13-limit

17-limit

19-limit

Hemiseptisix

11-limit

13-limit

Navigation menu

Search