Jubilismic clan: Difference between revisions

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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.
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


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


EDOs: {{EDOs|10, 12, 16, 22, 104}}
{{Val list|legend=1| 10, 12, 16, 22, 104}}


= Diminished =
= Diminished =
Line 12: Line 11:
{{see also|Dimipent family}}
{{see also|Dimipent family}}


Commas: 36/35, 50/49
Comma list: 36/35, 50/49


[[POTE_tuning|POTE generator]]: ~3/2 = 699.523
[[POTE generator]]: ~3/2 = 699.523


Map: [<4 0 3 5|, <0 1 1 1|]
Mapping: [{{val| 4 0 3 5 }}, {{val| 0 1 1 1 }}]


EDOs: {{EDOs|4, 12}}
{{Val list|legend=1| 4, 12 }}


Badness: 0.0224
Badness: 0.0224


== 11-limit ==
== 11-limit ==
Commas: 36/35, 50/49, 56/55
Comma list: 36/35, 50/49, 56/55


[[POTE_tuning|POTE generator]]: ~3/2 = 709.109
[[POTE generator]]: ~3/2 = 709.109


Map: [<4 0 3 5 14|, <0 1 1 1 0|]
Mapping: [{{val| 4 0 3 5 14 }}, {{val| 0 1 1 1 0 }}]


EDOs: {{EDOs|4, 8, 12, 44}}
{{Val list|legend=1| 4, 8, 12, 44 }}


Badness: 0.0221
Badness: 0.0221


=== 13-limit ===
=== 13-limit ===
Commas: 36/35, 40/39, 50/49, 66/65
Comma list: 36/35, 40/39, 50/49, 66/65


POTE generator: ~3/2 = 713.773
POTE generator: ~3/2 = 713.773


Map: [<4 0 3 5 14 15|, <0 1 1 1 0 0|]
Mapping: [{{val| 4 0 3 5 14 15 }}, {{val| 0 1 1 1 0 0 }}]


EDOs: {{EDOs|4, 8d, 12f, 20cdef}}
{{Val list|legend=1| 4, 8d, 12f, 20cdef }}


Badness: 0.0195
Badness: 0.0195


== Demolished ==
== Demolished ==
Commas: 36/35, 45/44, 50/49
Comma list: 36/35, 45/44, 50/49


POTE generator: ~3/2 = 689.881
POTE generator: ~3/2 = 689.881


Map: [<4 0 3 5 -5|, <0 1 1 1 3|]
Mapping: [{{val| 4 0 3 5 -5 }}, {{val| 0 1 1 1 3 }}]


EDOs: {{EDOs|12, 28, 40de}}
{{Val list|legend=1| 12, 28, 40de }}


Badness: 0.0266
Badness: 0.0266


== Hemidim ==
== Hemidim ==
Commas: 36/35, 50/49, 125/121
Comma list: 36/35, 50/49, 125/121


POTE generator: ~12/11 = 101.679
POTE generator: ~12/11 = 101.679


Map: [<4 1 4 6 6|, <0 2 2 2 3|]
Mapping: [{{val| 4 1 4 6 6 }}, {{val| 0 2 2 2 3 }}]


EDOs: {{EDOs|12, 20b}}
{{Val list|legend=1| 12, 20b }}


Badness: 0.0550
Badness: 0.0550


= Doublewide =
= Doublewide =
Commas: 50/49, 875/864
Comma list: 50/49, 875/864


[[POTE_tuning|POTE generator]]: ~6/5 = 325.719
[[POTE generator]]: ~6/5 = 325.719


Map: [<2 1 3 4|, <0 4 3 3|]
Mapping: [{{val| 2 1 3 4 }}, {{val| 0 4 3 3 }}]


EDOs: {{EDOs|18, 22, 26, 48, 70c}}
{{Val list|legend=1| 18, 22, 26, 48, 70c }}


Badness: 0.0435
Badness: 0.0435


== 11-limit ==
== 11-limit ==
Commas: 50/49, 99/98, 875/864
Comma list: 50/49, 99/98, 875/864


[[POTE_tuning|POTE generator]]: ~6/5 = 325.548
[[POTE generator]]: ~6/5 = 325.548


Map: [<2 1 3 4 8|, <0 4 3 3 -2|]
Mapping: [{{val| 2 1 3 4 8 }}, {{val| 0 4 3 3 -2 }}]


EDOs: {{EDOs|18, 22, 48, 70, 118cd}}
{{Val list|legend=1| 18, 22, 48, 70, 118cd }}


Badness: 0.0321
Badness: 0.0321


== Fleetwood ==
== Fleetwood ==
Commas: 50/49, 55/54, 176/175
Comma list: 50/49, 55/54, 176/175


POTE generator: ~6/5 = 327.038
POTE generator: ~6/5 = 327.038


Map: [<2 1 3 4 2|, <0 4 3 3 9|]
Mapping: [{{val| 2 1 3 4 2 }}, {{val| 0 4 3 3 9 }}]


EDOs: {{EDOs|22, 26e}}
{{Val list|legend=1| 22, 26e }}


Badness: 0.0352
Badness: 0.0352


=== 13-limit ===
=== 13-limit ===
Commas: 50/49, 55/54, 65/63, 176/175
Comma list: 50/49, 55/54, 65/63, 176/175


POTE generator: ~6/5 = 327.841
POTE generator: ~6/5 = 327.841


Map: [<2 1 3 4 2 3|, <0 4 3 3 9 8|]
Mapping: [{{val| 2 1 3 4 2 3 }}, {{val| 0 4 3 3 9 8 }}]


EDOs: {{EDOs|22, 84bdf}}
{{Val list|legend=1| 22, 84bdf }}


Badness: 0.0318
Badness: 0.0318


== Cavalier ==
== Cavalier ==
Commas: 45/44, 50/49, 875/864
Comma list: 45/44, 50/49, 875/864


POTE generator: ~6/5 = 323.427
POTE generator: ~6/5 = 323.427


Map: [<2 1 3 4 1|, <0 4 3 3 11|]
Mapping: [{{val| 2 1 3 4 1 }}, {{val| 0 4 3 3 11 }}]


EDOs: {{EDOs|26}}
{{Val list|legend=1| 26 }}


Badness: 0.0529
Badness: 0.0529


=== 13-limit ===
=== 13-limit ===
Commas: 45/44, 50/49, 78/77, 325/324
Comma list: 45/44, 50/49, 78/77, 325/324


POTE generator: ~6/5 = 323.396
POTE generator: ~6/5 = 323.396


Map: [<2 1 3 4 1 2|, <0 4 3 3 11 10|]
Mapping: [{{val| 2 1 3 4 1 2 }}, {{val| 0 4 3 3 11 10 }}]


EDOs: {{EDOs|26}}
{{Val list|legend=1| 26 }}


Badness: 0.0350
Badness: 0.0350
Line 136: Line 135:
{{see also|Lemba}}
{{see also|Lemba}}


Commas: 50/49, 525/512
Comma list: 50/49, 525/512


[[POTE_tuning|POTE generator]]: ~8/7 = 232.089
[[POTE generator]]: ~8/7 = 232.089


Map: [<2 2 5 6|, <0 3 -1 -1|]
Mapping: [{{val| 2 2 5 6 }}, {{val| 0 3 -1 -1 }}]


EDOs: {{EDOs|10, 16, 26, 62}}
{{Val list|legend=1| 10, 16, 26, 62 }}


Badness: 0.0622
Badness: 0.0622


== 11-limit ==
== 11-limit ==
Commas: 45/44, 50/49, 385/384
Comma list: 45/44, 50/49, 385/384


POTE generator: ~8/7 = 230.974
POTE generator: ~8/7 = 230.974


Map: [<2 2 5 6 5|, <0 3 -1 -1 5|]
Mapping: [{{val| 2 2 5 6 5 }}, {{val| 0 3 -1 -1 5 }}]


EDOs: {{EDOs|10, 16, 26}}
{{Val list|legend=1| 10, 16, 26 }}


Badness: 0.0416
Badness: 0.0416


== 13-limit ==
== 13-limit ==
Commas: 45/44, 50/49, 65/64, 78/77
Comma list: 45/44, 50/49, 65/64, 78/77


POTE generator: ~8/7 = 230.966
POTE generator: ~8/7 = 230.966


Map: [<2 2 5 6 5 7|, <0 3 -1 -1 5 1|]
Mapping: [{{val| 2 2 5 6 5 7 }}, {{val| 0 3 -1 -1 5 1 }}]


EDOs: {{EDOs|10, 16, 26}}
{{Val list|legend=1| 10, 16, 26 }}


Badness: 0.0255
Badness: 0.0255


= Vigintiduo =
= Vigintiduo =
Commas: 50/49, 64/63, 245/243
Comma list: 50/49, 64/63, 245/243


POTE generator: ~11/8 = 557.563
POTE generator: ~11/8 = 557.563


Map: [<22 35 51 62 0|, <0 0 0 0 1|]
Mapping: [{{val| 22 35 51 62 0 }}, {{val| 0 0 0 0 1 }}]


EDOs: {{EDOs|22, 66de, 88bde, 110bd, 198bcdde}}
{{Val list|legend=1| 22, 66de, 88bde, 110bd, 198bcdde }}


Badness: 0.0484
Badness: 0.0484


= Vigin =
= Vigin =
Commas: 50/49, 55/54, 64/63, 99/98
Comma list: 50/49, 55/54, 64/63, 99/98


POTE generator: ~13/8 = 844.624
POTE generator: ~13/8 = 844.624


Map: [<22 35 51 62 76 0|, <0 0 0 0 0 1|]
Mapping: [{{val| 22 35 51 62 76 0 }}, {{val| 0 0 0 0 0 1 }}]


EDOs: {{EDOs|22, 44}}
{{Val list|legend=1| 22, 44 }}


Badness: 0.0298
Badness: 0.0298


= Duodecim =
= Duodecim =
Commas: 36/35, 50/49, 64/63
Comma list: 36/35, 50/49, 64/63


POTE generator: ~11/8 = 565.023
POTE generator: ~11/8 = 565.023


Map: [<12 19 28 34 0|, <0 0 0 0 1|]
Mapping: [{{val| 12 19 28 34 0 }}, {{val| 0 0 0 0 1 }}]


EDOs: {{EDOs|12, 24d, 36d}}
{{Val list|legend=1| 12, 24d, 36d }}


Badness: 0.030536
Badness: 0.030536
Line 204: Line 203:
{{see also|Fifive family #Crepuscular}}
{{see also|Fifive family #Crepuscular}}


Commas: 50/49, 4375/4374
Comma list: 50/49, 4375/4374


POTE generator: ~27/25 = 140.349
POTE generator: ~27/25 = 140.349


Map: [<2 2 3 4|, <0 5 7 7|]
Mapping: [{{val| 2 2 3 4 }}, {{val| 0 5 7 7 }}]


Wedgie: <<10 14 14 -1 -6 -7||
{{Multival|legend=1| 10 14 14 -1 -6 -7 }}


EDOs: {{EDOs|26, 34d, 60d, 94d}}
{{Val list|legend=1| 26, 34d, 60d, 94d }}


Badness: 0.0867
Badness: 0.0867


== 11-limit ==
== 11-limit ==
Commas: 50/49, 99/98, 1944/1925
Comma list: 50/49, 99/98, 1944/1925


POTE generator: ~12/11 = 140.587
POTE generator: ~12/11 = 140.587


Map: [<2 2 3 4 6|, <0 5 7 7 4|]
Mapping: [{{val| 2 2 3 4 6 }}, {{val| 0 5 7 7 4 }}]


EDOs: {{EDOs|26, 34d, 60d, 94de}}
{{Val list|legend=1| 26, 34d, 60d, 94de }}


Badness: 0.0408
Badness: 0.0408


== 13-limit ==
== 13-limit ==
Commas: 50/49, 78/77, 99/98, 144/143
Comma list: 50/49, 78/77, 99/98, 144/143


POTE generator: ~12/11 = 140.554
POTE generator: ~12/11 = 140.554


Map: [<2 2 3 4 6 6|, <0 5 7 7 4 6|]
Mapping: [{{val| 2 2 3 4 6 6 }}, {{val| 0 5 7 7 4 6 }}]


EDOs: {{EDOs|26, 34d, 60d, 94de}}
{{Val list|legend=1| 26, 34d, 60d, 94de }}


Badness: 0.0244
Badness: 0.0244


= Bipyth =
= Bipyth =
Commas: 50/49, 20480/19683
Comma list: 50/49, 20480/19683


POTE generator: ~3/2 = 709.437
POTE generator: ~3/2 = 709.437


Map: [<2 0 -24 -23|, <0 1 9 9|]
Mapping: [{{val| 2 0 -24 -23 }}, {{val| 0 1 9 9 }}]


Wedgie: <<2 18 18 24 23 -9||
{{Multival|legend=1| 2 18 18 24 23 -9 }}


Badness: 0.1650
Badness: 0.1650


== 11-limit ==
== 11-limit ==
Commas: 50/49, 121/120, 896/891
Comma list: 50/49, 121/120, 896/891


POTE generator: ~3/2 = 709.310
POTE generator: ~3/2 = 709.310


Map: [<2 0 -24 -23 -9|, <0 1 9 9 5|]
Mapping: [{{val| 2 0 -24 -23 -9 }}, {{val| 0 1 9 9 5 }}]


EDOs: {{EDOs|22}}
{{Val list|legend=1| 22 }}


Badness: 0.0709
Badness: 0.0709


= Elvis =
= Elvis =
Comma: 36905625/33554432
Comma list: 36905625/33554432


POTE generator: ~45/32 = 554.546
POTE generator: ~45/32 = 554.546


Map: [<2 1 10|, <0 2 -5|]
Mapping: [{{val| 2 1 10 }}, {{val| 0 2 -5 }}]


EDOs: {{EDOs|24c, 26, 80bc, 106bc, 132bc}}
{{Val list|legend=1| 24c, 26, 80bc, 106bc, 132bc }}


Badness: 0.8840
Badness: 0.8840


== 7-limit ==
== 7-limit ==
Commas: 50/49, 8505/8192
Comma list: 50/49, 8505/8192


POTE generator: ~45/32 = 553.721
POTE generator: ~45/32 = 553.721


Map: [<2 1 10 11|, <0 2 -5 -5|]
Mapping: [{{val| 2 1 10 11 }}, {{val| 0 2 -5 -5 }}]


Wedgie: <<4 -10 -10 -25 -27 5||
{{Multival|legend=1| 4 -10 -10 -25 -27 5 }}


EDOs: {{EDOs|24c, 26}}
{{Val list|legend=1| 24c, 26 }}


Badness: 0.1415
Badness: 0.1415


== 11-limit ==
== 11-limit ==
Commas: 45/44, 50/49, 1344/1331
Comma list: 45/44, 50/49, 1344/1331


POTE generator: ~11/8 = 553.882
POTE generator: ~11/8 = 553.882


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


EDOs: {{EDOs|24c, 26}}
{{Val list|legend=1| 24c, 26 }}


Badness: 0.0632
Badness: 0.0632


== 13-limit ==
== 13-limit ==
Commas: 45/44, 50/49, 78/77, 1053/1024
Comma list: 45/44, 50/49, 78/77, 1053/1024


POTE generator: ~11/8 = 553.892
POTE generator: ~11/8 = 553.892


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


EDOs: {{EDOs|26}}
{{Val list|legend=1| 26 }}


Badness: 0.0440
Badness: 0.0440

Revision as of 01:38, 17 March 2021

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: [{{val| 2 0 1 1|, {{val| 0 0 1 1|]

Template:Val list

Diminished

Deutsch

See also: Dimipent family

Comma list: 36/35, 50/49

POTE generator: ~3/2 = 699.523

Mapping: [⟨4 0 3 5], ⟨0 1 1 1]]

Template:Val list

Badness: 0.0224

11-limit

Comma list: 36/35, 50/49, 56/55

POTE generator: ~3/2 = 709.109

Mapping: [⟨4 0 3 5 14], ⟨0 1 1 1 0]]

Template:Val list

Badness: 0.0221

13-limit

Comma list: 36/35, 40/39, 50/49, 66/65

POTE generator: ~3/2 = 713.773

Mapping: [⟨4 0 3 5 14 15], ⟨0 1 1 1 0 0]]

Template:Val list

Badness: 0.0195

Demolished

Comma list: 36/35, 45/44, 50/49

POTE generator: ~3/2 = 689.881

Mapping: [⟨4 0 3 5 -5], ⟨0 1 1 1 3]]

Template:Val list

Badness: 0.0266

Hemidim

Comma list: 36/35, 50/49, 125/121

POTE generator: ~12/11 = 101.679

Mapping: [⟨4 1 4 6 6], ⟨0 2 2 2 3]]

Template:Val list

Badness: 0.0550

Doublewide

Comma list: 50/49, 875/864

POTE generator: ~6/5 = 325.719

Mapping: [⟨2 1 3 4], ⟨0 4 3 3]]

Template:Val list

Badness: 0.0435

11-limit

Comma list: 50/49, 99/98, 875/864

POTE generator: ~6/5 = 325.548

Mapping: [⟨2 1 3 4 8], ⟨0 4 3 3 -2]]

Template:Val list

Badness: 0.0321

Fleetwood

Comma list: 50/49, 55/54, 176/175

POTE generator: ~6/5 = 327.038

Mapping: [⟨2 1 3 4 2], ⟨0 4 3 3 9]]

Template:Val list

Badness: 0.0352

13-limit

Comma list: 50/49, 55/54, 65/63, 176/175

POTE generator: ~6/5 = 327.841

Mapping: [⟨2 1 3 4 2 3], ⟨0 4 3 3 9 8]]

Template:Val list

Badness: 0.0318

Cavalier

Comma list: 45/44, 50/49, 875/864

POTE generator: ~6/5 = 323.427

Mapping: [⟨2 1 3 4 1], ⟨0 4 3 3 11]]

Template:Val list

Badness: 0.0529

13-limit

Comma list: 45/44, 50/49, 78/77, 325/324

POTE generator: ~6/5 = 323.396

Mapping: [⟨2 1 3 4 1 2], ⟨0 4 3 3 11 10]]

Template:Val list

Badness: 0.0350

Lemba

See also: Gamelismic clan § Lemba
See also: Lemba

Comma list: 50/49, 525/512

POTE generator: ~8/7 = 232.089

Mapping: [⟨2 2 5 6], ⟨0 3 -1 -1]]

Template:Val list

Badness: 0.0622

11-limit

Comma list: 45/44, 50/49, 385/384

POTE generator: ~8/7 = 230.974

Mapping: [⟨2 2 5 6 5], ⟨0 3 -1 -1 5]]

Template:Val list

Badness: 0.0416

13-limit

Comma list: 45/44, 50/49, 65/64, 78/77

POTE generator: ~8/7 = 230.966

Mapping: [⟨2 2 5 6 5 7], ⟨0 3 -1 -1 5 1]]

Template:Val list

Badness: 0.0255

Vigintiduo

Comma list: 50/49, 64/63, 245/243

POTE generator: ~11/8 = 557.563

Mapping: [⟨22 35 51 62 0], ⟨0 0 0 0 1]]

Template:Val list

Badness: 0.0484

Vigin

Comma list: 50/49, 55/54, 64/63, 99/98

POTE generator: ~13/8 = 844.624

Mapping: [⟨22 35 51 62 76 0], ⟨0 0 0 0 0 1]]

Template:Val list

Badness: 0.0298

Duodecim

Comma list: 36/35, 50/49, 64/63

POTE generator: ~11/8 = 565.023

Mapping: [⟨12 19 28 34 0], ⟨0 0 0 0 1]]

Template:Val list

Badness: 0.030536

Crepuscular

See also: Fifive family § Crepuscular

Comma list: 50/49, 4375/4374

POTE generator: ~27/25 = 140.349

Mapping: [⟨2 2 3 4], ⟨0 5 7 7]]

Wedgie: ⟨⟨ 10 14 14 -1 -6 -7 ]]

Template:Val list

Badness: 0.0867

11-limit

Comma list: 50/49, 99/98, 1944/1925

POTE generator: ~12/11 = 140.587

Mapping: [⟨2 2 3 4 6], ⟨0 5 7 7 4]]

Template:Val list

Badness: 0.0408

13-limit

Comma list: 50/49, 78/77, 99/98, 144/143

POTE generator: ~12/11 = 140.554

Mapping: [⟨2 2 3 4 6 6], ⟨0 5 7 7 4 6]]

Template:Val list

Badness: 0.0244

Bipyth

Comma list: 50/49, 20480/19683

POTE generator: ~3/2 = 709.437

Mapping: [⟨2 0 -24 -23], ⟨0 1 9 9]]

Wedgie: ⟨⟨ 2 18 18 24 23 -9 ]]

Badness: 0.1650

11-limit

Comma list: 50/49, 121/120, 896/891

POTE generator: ~3/2 = 709.310

Mapping: [⟨2 0 -24 -23 -9], ⟨0 1 9 9 5]]

Template:Val list

Badness: 0.0709

Elvis

Comma list: 36905625/33554432

POTE generator: ~45/32 = 554.546

Mapping: [⟨2 1 10], ⟨0 2 -5]]

Template:Val list

Badness: 0.8840

7-limit

Comma list: 50/49, 8505/8192

POTE generator: ~45/32 = 553.721

Mapping: [⟨2 1 10 11], ⟨0 2 -5 -5]]

Wedgie: ⟨⟨ 4 -10 -10 -25 -27 5 ]]

Template:Val list

Badness: 0.1415

11-limit

Comma list: 45/44, 50/49, 1344/1331

POTE generator: ~11/8 = 553.882

Mapping: [{{val| 2 1 10 11 8|, {{val| 0 2 -5 -5 -1|]

Template:Val list

Badness: 0.0632

13-limit

Comma list: 45/44, 50/49, 78/77, 1053/1024

POTE generator: ~11/8 = 553.892

Mapping: [⟨2 1 10 11 8 16], ⟨0 2 -5 -5 -1 -8]]

Template:Val list

Badness: 0.0440

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