Canopic clan: Difference between revisions

Revision as of 06:12, 18 July 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:

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

Vals: 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

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

Hemiseptisix

The name hemiseptisix means a half of septimal major sixth, two of which make a major sixth which approximates 12/7.

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

Vals: 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

Vals: Template:Val list

Badness: 0.021127

Canopic clan: Difference between revisions

Revision as of 06:12, 18 July 2021

Contents

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

Eris

11-limit

13-limit

Mirkat

11-limit

13-limit

17-limit

Subsemifourth

11-limit

13-limit

Hemiseptisix

11-limit

13-limit

Navigation menu

@@ Line 26: / Line 26: @@
 [[Val]]s: [[13edt|b13]], [[62edt|b62]], [[75edt|b75]], [[88edt|b88]], [[101edt|b101]], [[114edt|b114]], [[355edt|b355]], [[469edt|b469]], [[583edt|b583]], [[697edt|b697]]
-== Grendel  ==
+== Grendel ==
 Subgroup: 2.3.5.7
@@ Line 41: / Line 41: @@
 [[Badness]]: 0.051834
-=== 11-limit  ===
+=== 11-limit ===
 Subgroup: 2.3.5.7.11
@@ Line 54: / Line 54: @@
 Badness: 0.019845
-=== 13-limit  ===
+=== 13-limit ===
 Subgroup: 2.3.5.7.11.13
@@ Line 67: / Line 67: @@
 Badness: 0.024839
-=== 17-limit  ===
+=== 17-limit ===
 Subgroup: 2.3.5.7.11.13.17
@@ Line 80: / Line 80: @@
 Badness: 0.021400
-=== 19-limit  ===
+=== 19-limit ===
 Subgroup: 2.3.5.7.11.13.17.19
@@ Line 93: / Line 93: @@
 Badness: 0.018413
-== Kwai  ==
+== Kwai ==
 Subgroup: 2.3.5.7
@@ Line 108: / Line 108: @@
 [[Badness]]: 0.054476
-=== 11-limit  ===
+=== 11-limit ===
 Subgroup: 2.3.5.7.11
@@ Line 121: / Line 121: @@
 Badness: 0.026219
-=== 13-limit  ===
+=== 13-limit ===
 Subgroup: 2.3.5.7.11.13
@@ Line 134: / Line 134: @@
 Badness: 0.024555
-=== 17-limit  ===
+=== 17-limit ===
 Subgroup: 2.3.5.7.11.13.17
@@ Line 147: / Line 147: @@
 Badness: 0.021950
-=== 19-limit  ===
+=== 19-limit ===
 Subgroup: 2.3.5.7.11.13.17.19
@@ Line 160: / Line 160: @@
 Badness: 0.016957
-== Pluto  ==
+== Pluto ==
 Subgroup: 2.3.5.7
@@ Line 175: / Line 175: @@
 [[Badness]]: 0.057514
-=== 11-limit  ===
+=== 11-limit ===
 Subgroup: 2.3.5.7.11
@@ Line 188: / Line 188: @@
 Badness: 0.029844
-==== 13-limit  ====
+==== 13-limit ====
 Subgroup: 2.3.5.7.11.13
@@ Line 201: / Line 201: @@
 Badness: 0.025717
-===== 17-limit  =====
+===== 17-limit =====
 Subgroup: 2.3.5.7.11.13.17
@@ Line 214: / Line 214: @@
 Badness: 0.021463
-===== 19-limit  =====
+===== 19-limit =====
 Subgroup: 2.3.5.7.11.13.17.19
@@ Line 227: / Line 227: @@
 Badness: 0.017650
-==== Orcus  ====
+==== Orcus ====
 Subgroup: 2.3.5.7.11.13
@@ Line 240: / Line 240: @@
 Badness: 0.033441
-=== Plutino  ===
+=== Plutino ===
 Subgroup: 2.3.5.7.11
@@ Line 253: / Line 253: @@
 Badness: 0.057966
-==== 13-limit  ====
+==== 13-limit ====
 Subgroup: 2.3.5.7.11.13
@@ Line 266: / Line 266: @@
 Badness: 0.040182
-== Eris  ==
+== Eris ==
 Subgroup: 2.3.5.7
@@ Line 281: / Line 281: @@
 [[Badness]]: 0.074719
-=== 11-limit  ===
+=== 11-limit ===
 Subgroup: 2.3.5.7.11
@@ Line 294: / Line 294: @@
 Badness: 0.027621
-=== 13-limit  ===
+=== 13-limit ===
 Subgroup: 2.3.5.7.11.13
@@ Line 307: / Line 307: @@
 Badness: 0.025137
-== Mirkat  ==
+== Mirkat ==
 Subgroup: 2.3.5.7
@@ Line 322: / Line 322: @@
 [[Badness]]: 0.059376
-=== 11-limit  ===
+=== 11-limit ===
 Subgroup: 2.3.5.7.11
@@ Line 335: / Line 335: @@
 Badness: 0.022126
-=== 13-limit  ===
+=== 13-limit ===
 Subgroup: 2.3.5.7.11.13
@@ Line 348: / Line 348: @@
 Badness: 0.018632
-=== 17-limit  ===
+=== 17-limit ===
 Subgroup: 2.3.5.7.11.13.17
@@ Line 361: / Line 361: @@
 Badness: 0.011775
-== Subsemifourth  ==
+== Subsemifourth ==
 Subgroup: 2.3.5.7
@@ Line 376: / Line 376: @@
 [[Badness]]: 0.135173
-=== 11-limit  ===
+=== 11-limit ===
 Subgroup: 2.3.5.7.11
@@ Line 389: / Line 389: @@
 Badness: 0.034276
-=== 13-limit  ===
+=== 13-limit ===
 Subgroup: 2.3.5.7.11.13
@@ Line 401: / Line 401: @@
 Badness: 0.028387
+== Hemiseptisix ==
+The name ''hemiseptisix'' means a half of septimal major sixth, two of which make a major sixth which approximates [[12/7]].
+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
+Vals: {{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
+Vals: {{Val list| 103, 121, 224 }}
+Badness: 0.021127
 [[Category:Regular temperament theory]]

Canopic clan: Difference between revisions

Revision as of 06:12, 18 July 2021

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

Eris

11-limit

13-limit

Mirkat

11-limit

13-limit

17-limit

Subsemifourth

11-limit

13-limit

Hemiseptisix

11-limit

13-limit

Navigation menu

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