Jubilismic clan: Difference between revisions

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__FORCETOC__
__FORCETOC__
The '''Jubilismic clan''' tempers out the jubilisma, [[50/49|50/49]], which means [[7/5|7/5]] and [[10/7|10/7]] are identified and the [[Octave|octave]] is divided in two. Doublewide, lemba and diminished are discussed below; others in the clan are pajara, decimal, injera, octokaidecal, hedgehog, bipelog and hexe, which are discussed elsewhere.
The '''jubilismic clan''' tempers out the jubilisma, [[50/49]], which means [[7/5]] and [[10/7]] are identified and the [[octave]] is divided in two. Doublewide, lemba and diminished are discussed below; others in the clan are [[Diaschismic family #Pajara|pajara]], [[Dicot family #Decimal|decimal]], [[Meantone family #Injera|injera]], [[Trienstonic clan #Octokaidecal|octokaidecal]], [[Porcupine family #Hedgehog|hedgehog]], [[Pelogic family #Bipelog|bipelog]] and [[Augmented family #Hexe|hexe]], which are discussed elsewhere.


No-threes [[POTE_tuning|POTE generator]]: 380.840
No-threes [[POTE_tuning|POTE generator]]: 380.840
Line 6: Line 6:
No-threes map: [<2 0 1 1|, <0 0 1 1|]
No-threes map: [<2 0 1 1|, <0 0 1 1|]


EDOs: [[10edo|10]], [[12edo|12]], [[16edo|16]], [[22edo|22]], [[104edo|104]]
EDOs: {{EDOs|10, 12, 16, 22, 104}}


=Diminished=
=Diminished=
<span style="display: block; text-align: right;">[[:de:Verminderte_Temperaturen|Deutsch]]</span>
<span style="display: block; text-align: right;">[[:de:Verminderte_Temperaturen|Deutsch]]</span>
{{see also|Dimipent family}}


Commas: 36/35, 50/49
Commas: 36/35, 50/49
Line 17: Line 18:
Map: [&lt;4 0 3 5|, &lt;0 1 1 1|]
Map: [&lt;4 0 3 5|, &lt;0 1 1 1|]


EDOs: [[4edo|4]], [[12edo|12]]
EDOs: {{EDOs|4, 12}}


Badness: 0.0224
Badness: 0.0224
Line 28: Line 29:
Map: [&lt;4 0 3 5 14|, &lt;0 1 1 1 0|]
Map: [&lt;4 0 3 5 14|, &lt;0 1 1 1 0|]


EDOs: [[4edo|4]], [[8edo|8]], [[12edo|12]], [[44edo|44]]
EDOs: {{EDOs|4, 8, 12, 44}}


Badness: 0.0221
Badness: 0.0221
Line 39: Line 40:
Map: [&lt;4 0 3 5 14 15|, &lt;0 1 1 1 0 0|]
Map: [&lt;4 0 3 5 14 15|, &lt;0 1 1 1 0 0|]


EDOs: 4, 8d, 12f, 20cdef
EDOs: {{EDOs|4, 8d, 12f, 20cdef}}


Badness: 0.0195
Badness: 0.0195
Line 50: Line 51:
Map: [&lt;4 0 3 5 -5|, &lt;0 1 1 1 3|]
Map: [&lt;4 0 3 5 -5|, &lt;0 1 1 1 3|]


EDOs: 12, 28, 40de
EDOs: {{EDOs|12, 28, 40de}}


Badness: 0.0266
Badness: 0.0266
Line 61: Line 62:
Map: [&lt;4 1 4 6 6|, &lt;0 2 2 2 3|]
Map: [&lt;4 1 4 6 6|, &lt;0 2 2 2 3|]


EDOs: 12, 20b
EDOs: {{EDOs|12, 20b}}


Badness: 0.0550
Badness: 0.0550
Line 72: Line 73:
Map: [&lt;2 1 3 4|, &lt;0 4 3 3|]
Map: [&lt;2 1 3 4|, &lt;0 4 3 3|]


EDOs: [[18edo|18]], [[22edo|22]], [[26edo|26edo]], [[48edo|48]], [[70edo|70c]]
EDOs: {{EDOs|18, 22, 26, 48, 70c}}


Badness: 0.0435
Badness: 0.0435
Line 83: Line 84:
Map: [&lt;2 1 3 4 8|, &lt;0 4 3 3 -2|]
Map: [&lt;2 1 3 4 8|, &lt;0 4 3 3 -2|]


EDOs: [[18edo|18]], [[22edo|22]], [[48edo|48]], [[70edo|70c]], [[118edo|118cd]]
EDOs: {{EDOs|18, 22, 48, 70], 118cd}}


Badness: 0.0321
Badness: 0.0321
Line 94: Line 95:
Map: [&lt;2 1 3 4 2|, &lt;0 4 3 3 9|]
Map: [&lt;2 1 3 4 2|, &lt;0 4 3 3 9|]


EDOs: 22, 26e
EDOs: {{EDOs|22, 26e}}


Badness: 0.0352
Badness: 0.0352
Line 105: Line 106:
Map: [&lt;2 1 3 4 2 3|, &lt;0 4 3 3 9 8|]
Map: [&lt;2 1 3 4 2 3|, &lt;0 4 3 3 9 8|]


EDOs: 22, 84bdf
EDOs: {{EDOs|22, 84bdf}}


Badness: 0.0318
Badness: 0.0318
Line 116: Line 117:
Map: [&lt;2 1 3 4 1|, &lt;0 4 3 3 11|]
Map: [&lt;2 1 3 4 1|, &lt;0 4 3 3 11|]


EDOs: 26
EDOs: {{EDOs|26}}


Badness: 0.0529
Badness: 0.0529
Line 127: Line 128:
Map: [&lt;2 1 3 4 1 2|, &lt;0 4 3 3 11 10|]
Map: [&lt;2 1 3 4 1 2|, &lt;0 4 3 3 11 10|]


EDOs: 26
EDOs: {{EDOs|26}}


Badness: 0.0350
Badness: 0.0350


=Lemba=
=Lemba=
{{see also|Gamelismic clan #Lemba}}
Commas: 50/49, 525/512
Commas: 50/49, 525/512


Line 138: Line 141:
Map: [&lt;2 2 5 6|, &lt;0 3 -1 -1|]
Map: [&lt;2 2 5 6|, &lt;0 3 -1 -1|]


EDOs: [[10edo|10]], [[16edo|16]], [[26edo|26]], [[62edo|62]]
EDOs: {{EDOs|10, 16, 26, 62}}


Badness: 0.0622
Badness: 0.0622
Line 149: Line 152:
Map: [&lt;2 2 5 6 5|, &lt;0 3 -1 -1 5|]
Map: [&lt;2 2 5 6 5|, &lt;0 3 -1 -1 5|]


EDOs: 10, 16, 26
EDOs: {{EDOs|10, 16, 26}}


Badness: 0.0416
Badness: 0.0416
Line 160: Line 163:
Map: [&lt;2 2 5 6 5 7|, &lt;0 3 -1 -1 5 1|]
Map: [&lt;2 2 5 6 5 7|, &lt;0 3 -1 -1 5 1|]


EDOs: 10, 16, 26
EDOs: {{EDOs|10, 16, 26}}


Badness: 0.0255
Badness: 0.0255
Line 171: Line 174:
Map: [&lt;22 35 51 62 0|, &lt;0 0 0 0 1|]
Map: [&lt;22 35 51 62 0|, &lt;0 0 0 0 1|]


EDOs: 22, 66de, 88bde, 110bd, 198bcdde
EDOs: {{EDOs|22, 66de, 88bde, 110bd, 198bcdde}}


Badness: 0.0484
Badness: 0.0484
Line 182: Line 185:
Map: [&lt;22 35 51 62 76 0|, &lt;0 0 0 0 0 1|]
Map: [&lt;22 35 51 62 76 0|, &lt;0 0 0 0 0 1|]


EDOs: 22, 44
EDOs: {{EDOs|22, 44}}


Badness: 0.0298
Badness: 0.0298
Line 193: Line 196:
Map: [&lt;12 19 28 34 0|, &lt;0 0 0 0 1|]
Map: [&lt;12 19 28 34 0|, &lt;0 0 0 0 1|]


EDOs: 12, 24d, 36d
EDOs: {{EDOs|12, 24d, 36d}}


Badness: 0.030536
Badness: 0.030536
Line 206: Line 209:
Wedgie: &lt;&lt;10 14 14 -1 -6 -7||
Wedgie: &lt;&lt;10 14 14 -1 -6 -7||


EDOs: 26, 34d, 60d, 94d
EDOs: {{EDOs|26, 34d, 60d, 94d}}


Badness: 0.0867
Badness: 0.0867
Line 217: Line 220:
Map: [&lt;2 2 3 4 6|, &lt;0 5 7 7 4|]
Map: [&lt;2 2 3 4 6|, &lt;0 5 7 7 4|]


EDOs: 26, 34d, 60d, 94de
EDOs: {{EDOs|26, 34d, 60d, 94de}}


Badness: 0.0408
Badness: 0.0408
Line 228: Line 231:
Map: [&lt;2 2 3 4 6 6|, &lt;0 5 7 7 4 6|]
Map: [&lt;2 2 3 4 6 6|, &lt;0 5 7 7 4 6|]


EDOs: 26, 34d, 60d, 94de
EDOs: {{EDOs|26, 34d, 60d, 94de}}


Badness: 0.0244
Badness: 0.0244
Line 250: Line 253:
Map: [&lt;2 0 -24 -23 -9|, &lt;0 1 9 9 5|]
Map: [&lt;2 0 -24 -23 -9|, &lt;0 1 9 9 5|]


EDOs: 22
EDOs: {{EDOs|22}}


Badness: 0.0709
Badness: 0.0709
Line 261: Line 264:
Map: [&lt;2 1 10|, &lt;0 2 -5|]
Map: [&lt;2 1 10|, &lt;0 2 -5|]


EDOs: 24c, 26, 80bc, 106bc, 132bc
EDOs: {{EDOs|24c, 26, 80bc, 106bc, 132bc}}


Badness: 0.8840
Badness: 0.8840
Line 274: Line 277:
Wedgie: &lt;&lt;4 -10 -10 -25 -27 5||
Wedgie: &lt;&lt;4 -10 -10 -25 -27 5||


EDOs: 24c, 26
EDOs: {{EDOs|24c, 26}}


Badness: 0.1415
Badness: 0.1415
Line 285: Line 288:
Map: [&lt;2 1 10 11 8|, &lt;0 2 -5 -5 -1|]
Map: [&lt;2 1 10 11 8|, &lt;0 2 -5 -5 -1|]


EDOs: 24c, 26
EDOs: {{EDOs|24c, 26}}


Badness: 0.0632
Badness: 0.0632
Line 296: Line 299:
Map: [&lt;2 1 10 11 8 16|, &lt;0 2 -5 -5 -1 -8|]
Map: [&lt;2 1 10 11 8 16|, &lt;0 2 -5 -5 -1 -8|]


EDOs: 26
EDOs: {{EDOs|26}}


Badness: 0.0440
Badness: 0.0440
Line 303: Line 306:
[[Category:Jubilismic]]
[[Category:Jubilismic]]
[[Category:Clan]]
[[Category:Clan]]
[[Category:Rank 2]]
[[Category:Todo:review]]

Revision as of 17:07, 8 November 2020

The jubilismic clan tempers out the jubilisma, 50/49, which means 7/5 and 10/7 are identified and the octave is divided in two. Doublewide, lemba and diminished are discussed below; others in the clan are pajara, decimal, injera, octokaidecal, hedgehog, bipelog and hexe, which are discussed elsewhere.

No-threes POTE generator: 380.840

No-threes map: [<2 0 1 1|, <0 0 1 1|]

EDOs: 10, 12, 16, 22, 104

Diminished

Deutsch

See also: Dimipent family

Commas: 36/35, 50/49

POTE generator: ~3/2 = 699.523

Map: [<4 0 3 5|, <0 1 1 1|]

EDOs: 4, 12

Badness: 0.0224

11-limit

Commas: 36/35, 50/49, 56/55

POTE generator: ~3/2 = 709.109

Map: [<4 0 3 5 14|, <0 1 1 1 0|]

EDOs: 4, 8, 12, 44

Badness: 0.0221

13-limit

Commas: 36/35, 40/39, 50/49, 66/65

POTE generator: ~3/2 = 713.773

Map: [<4 0 3 5 14 15|, <0 1 1 1 0 0|]

EDOs: 4, 8d, 12f, 20cdef

Badness: 0.0195

Demolished

Commas: 36/35, 45/44, 50/49

POTE generator: ~3/2 = 689.881

Map: [<4 0 3 5 -5|, <0 1 1 1 3|]

EDOs: 12, 28, 40de

Badness: 0.0266

Hemidim

Commas: 36/35, 50/49, 125/121

POTE generator: ~12/11 = 101.679

Map: [<4 1 4 6 6|, <0 2 2 2 3|]

EDOs: 12, 20b

Badness: 0.0550

Doublewide

Commas: 50/49, 875/864

POTE generator: ~6/5 = 325.719

Map: [<2 1 3 4|, <0 4 3 3|]

EDOs: 18, 22, 26, 48, 70c

Badness: 0.0435

11-limit

Commas: 50/49, 99/98, 875/864

POTE generator: ~6/5 = 325.548

Map: [<2 1 3 4 8|, <0 4 3 3 -2|]

EDOs: 18, 22, 48, 70], 118cd

Badness: 0.0321

Fleetwood

Commas: 50/49, 55/54, 176/175

POTE generator: ~6/5 = 327.038

Map: [<2 1 3 4 2|, <0 4 3 3 9|]

EDOs: 22, 26e

Badness: 0.0352

13-limit

Commas: 50/49, 55/54, 65/63, 176/175

POTE generator: ~6/5 = 327.841

Map: [<2 1 3 4 2 3|, <0 4 3 3 9 8|]

EDOs: 22, 84bdf

Badness: 0.0318

Cavalier

Commas: 45/44, 50/49, 875/864

POTE generator: ~6/5 = 323.427

Map: [<2 1 3 4 1|, <0 4 3 3 11|]

EDOs: 26

Badness: 0.0529

13-limit

Commas: 45/44, 50/49, 78/77, 325/324

POTE generator: ~6/5 = 323.396

Map: [<2 1 3 4 1 2|, <0 4 3 3 11 10|]

EDOs: 26

Badness: 0.0350

Lemba

See also: Gamelismic clan § Lemba

Commas: 50/49, 525/512

POTE generator: ~8/7 = 232.089

Map: [<2 2 5 6|, <0 3 -1 -1|]

EDOs: 10, 16, 26, 62

Badness: 0.0622

11-limit

Commas: 45/44, 50/49, 385/384

POTE generator: ~8/7 = 230.974

Map: [<2 2 5 6 5|, <0 3 -1 -1 5|]

EDOs: 10, 16, 26

Badness: 0.0416

13-limit

Commas: 45/44, 50/49, 65/64, 78/77

POTE generator: ~8/7 = 230.966

Map: [<2 2 5 6 5 7|, <0 3 -1 -1 5 1|]

EDOs: 10, 16, 26

Badness: 0.0255

Vigintiduo

Commas: 50/49, 64/63, 245/243

POTE generator: ~11/8 = 557.563

Map: [<22 35 51 62 0|, <0 0 0 0 1|]

EDOs: 22, 66de, 88bde, 110bd, 198bcdde

Badness: 0.0484

Vigin

Commas: 50/49, 55/54, 64/63, 99/98

POTE generator: ~13/8 = 844.624

Map: [<22 35 51 62 76 0|, <0 0 0 0 0 1|]

EDOs: 22, 44

Badness: 0.0298

Duodecim

Commas: 36/35, 50/49, 64/63

POTE generator: ~11/8 = 565.023

Map: [<12 19 28 34 0|, <0 0 0 0 1|]

EDOs: 12, 24d, 36d

Badness: 0.030536

Crepuscular

Commas: 50/49, 4375/4374

POTE generator: ~27/25 = 140.349

Map: [<2 2 3 4|, <0 5 7 7|]

Wedgie: <<10 14 14 -1 -6 -7||

EDOs: 26, 34d, 60d, 94d

Badness: 0.0867

11-limit

Commas: 50/49, 99/98, 1944/1925

POTE generator: ~12/11 = 140.587

Map: [<2 2 3 4 6|, <0 5 7 7 4|]

EDOs: 26, 34d, 60d, 94de

Badness: 0.0408

13-limit

Commas: 50/49, 78/77, 99/98, 144/143

POTE generator: ~12/11 = 140.554

Map: [<2 2 3 4 6 6|, <0 5 7 7 4 6|]

EDOs: 26, 34d, 60d, 94de

Badness: 0.0244

Bipyth

Commas: 50/49, 20480/19683

POTE generator: ~3/2 = 709.437

Map: [<2 0 -24 -23|, <0 1 9 9|]

Wedgie: <<2 18 18 24 23 -9||

Badness: 0.1650

11-limit

Commas: 50/49, 121/120, 896/891

POTE generator: ~3/2 = 709.310

Map: [<2 0 -24 -23 -9|, <0 1 9 9 5|]

EDOs: 22

Badness: 0.0709

Elvis

Comma: 36905625/33554432

POTE generator: ~45/32 = 554.546

Map: [<2 1 10|, <0 2 -5|]

EDOs: 24c, 26, 80bc, 106bc, 132bc

Badness: 0.8840

7-limit

Commas: 50/49, 8505/8192

POTE generator: ~45/32 = 553.721

Map: [<2 1 10 11|, <0 2 -5 -5|]

Wedgie: <<4 -10 -10 -25 -27 5||

EDOs: 24c, 26

Badness: 0.1415

11-limit

Commas: 45/44, 50/49, 1344/1331

POTE generator: ~11/8 = 553.882

Map: [<2 1 10 11 8|, <0 2 -5 -5 -1|]

EDOs: 24c, 26

Badness: 0.0632

13-limit

Commas: 45/44, 50/49, 78/77, 1053/1024

POTE generator: ~11/8 = 553.892

Map: [<2 1 10 11 8 16|, <0 2 -5 -5 -1 -8|]

EDOs: 26

Badness: 0.0440

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