Jubilismic clan: Difference between revisions

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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]], [[Augmented family #Hexe|hexe]] and [[Magic family #Astrology|astrology]], which are discussed elsewhere.
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]], [[Augmented family #Hexe|hexe]] and [[Magic family #Astrology|astrology]], which are discussed elsewhere.


== No-3 jubilismic ==
== No-3 jubilismic ==


Subgroup: 2.5.7
Subgroup: 2.5.7
Line 15: Line 15:
{{Val list|legend=1| 2, 4, 6, 16, 22, 60d, 82d, 104dd }}
{{Val list|legend=1| 2, 4, 6, 16, 22, 60d, 82d, 104dd }}


== Diminished ==
== Lemba ==
{{main| Lemba }}
{{see also| Gamelismic clan #Lemba }}
 
Subgroup: 2.3.5.7
 
[[Comma list]]: 50/49, 525/512
 
[[Mapping]]: [{{val| 2 2 5 6 }}, {{val| 0 3 -1 -1 }}]
 
[[POTE generator]]: ~8/7 = 232.089
 
{{Val list|legend=1| 10, 16, 26, 62 }}
 
[[Badness]]: 0.0622
 
=== 11-limit ===
 
Subgroup: 2.3.5.7.11
 
Comma list: 45/44, 50/49, 385/384
 
Mapping: [{{val| 2 2 5 6 5 }}, {{val| 0 3 -1 -1 5 }}]
 
POTE generator: ~8/7 = 230.974
 
{{Val list|legend=1| 10, 16, 26 }}
 
Badness: 0.0416
 
=== 13-limit ===
 
Subgroup: 2.3.5.7.11.13
 
Comma list: 45/44, 50/49, 65/64, 78/77
 
Mapping: [{{val| 2 2 5 6 5 7 }}, {{val| 0 3 -1 -1 5 1 }}]
 
POTE generator: ~8/7 = 230.966
 
{{Val list|legend=1| 10, 16, 26 }}
 
Badness: 0.0255
 
== Diminished ==
<div style="float: right">[[:de:Verminderte Temperaturen|Deutsch]]</div>
<div style="float: right">[[:de:Verminderte Temperaturen|Deutsch]]</div>
{{see also|Dimipent family #Diminished}}
{{see also|Dimipent family #Diminished}}
Line 35: Line 79:
Scales: [[diminished12]]
Scales: [[diminished12]]


=== 11-limit ===
=== 11-limit ===


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 53: Line 97:
Scales: [[diminished12]]
Scales: [[diminished12]]


==== 13-limit ====
==== 13-limit ====


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
Line 71: Line 115:
Scales: [[diminished12]]
Scales: [[diminished12]]


=== Demolished ===
=== Demolished ===


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 87: Line 131:
Badness: 0.0266
Badness: 0.0266


=== Hemidim ===
=== Hemidim ===


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 103: Line 147:
Badness: 0.0550
Badness: 0.0550


== Doublewide ==
== Doublewide ==


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 117: Line 161:
[[Badness]]: 0.0435
[[Badness]]: 0.0435


=== 11-limit ===
=== 11-limit ===


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 131: Line 175:
Badness: 0.0321
Badness: 0.0321


=== Fleetwood ===
=== Fleetwood ===


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 145: Line 189:
Badness: 0.0352
Badness: 0.0352


==== 13-limit ====
==== 13-limit ====


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
Line 159: Line 203:
Badness: 0.0318
Badness: 0.0318


=== Cavalier ===
=== Cavalier ===


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 173: Line 217:
Badness: 0.0529
Badness: 0.0529


==== 13-limit ====
==== 13-limit ====


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
Line 187: Line 231:
Badness: 0.0350
Badness: 0.0350


== Lemba  ==
== Elvis ==
{{main| Lemba }}
=== 5-limit ===
{{see also| Gamelismic clan #Lemba }}
 
Subgroup: 2.3.5
 
[[Comma list]]: 36905625/33554432
 
[[Mapping]]: [{{val| 2 1 10 }}, {{val| 0 2 -5 }}]
 
[[POTE generator]]: ~45/32 = 554.546
 
{{Val list|legend=1| 26, 80bc, 106bc, 132bc }}
 
[[Badness]]: 0.8840
 
=== 7-limit ===


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


[[Comma list]]: 50/49, 525/512
[[Comma list]]: 50/49, 8505/8192
 
[[Mapping]]: [{{val| 2 1 10 11 }}, {{val| 0 2 -5 -5 }}]


[[Mapping]]: [{{val| 2 2 5 6 }}, {{val| 0 3 -1 -1 }}]
{{Multival|legend=1| 4 -10 -10 -25 -27 5 }}


[[POTE generator]]: ~8/7 = 232.089
[[POTE generator]]: ~45/32 = 553.721


{{Val list|legend=1| 10, 16, 26, 62 }}
{{Val list|legend=1| 24c, 26 }}


[[Badness]]: 0.0622
[[Badness]]: 0.1415


=== 11-limit ===
=== 11-limit ===


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 45/44, 50/49, 385/384
Comma list: 45/44, 50/49, 1344/1331


Mapping: [{{val| 2 2 5 6 5 }}, {{val| 0 3 -1 -1 5 }}]
Mapping: [{{val| 2 1 10 11 8 }}, {{val| 0 2 -5 -5 -1 }}]


POTE generator: ~8/7 = 230.974
POTE generator: ~11/8 = 553.882


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


Badness: 0.0416
Badness: 0.0632


=== 13-limit ===
=== 13-limit ===


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 45/44, 50/49, 65/64, 78/77
Comma list: 45/44, 50/49, 78/77, 1053/1024


Mapping: [{{val| 2 2 5 6 5 7 }}, {{val| 0 3 -1 -1 5 1 }}]
Mapping: [{{val| 2 1 10 11 8 16 }}, {{val| 0 2 -5 -5 -1 -8 }}]


POTE generator: ~8/7 = 230.966
POTE generator: ~11/8 = 553.892


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


Badness: 0.0255
Badness: 0.0440


== Crepuscular ==
== Crepuscular ==
{{see also| Fifive family #Crepuscular }}
{{see also| Fifive family #Crepuscular }}


Line 248: Line 307:
[[Badness]]: 0.0867
[[Badness]]: 0.0867


=== 11-limit ===
=== 11-limit ===


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 262: Line 321:
Badness: 0.0408
Badness: 0.0408


=== 13-limit ===
=== 13-limit ===


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
Line 276: Line 335:
Badness: 0.0244
Badness: 0.0244


== Bipyth  ==
== Comic ==
 
=== 5-limit ===
Subgroup: 2.3.5.7
 
[[Comma list]]: 50/49, 20480/19683
 
[[Mapping]]: [{{val| 2 0 -24 -23 }}, {{val| 0 1 9 9 }}]
 
{{Multival|legend=1| 2 18 18 24 23 -9 }}
 
[[POTE generator]]: ~3/2 = 709.437
 
{{Val list|legend=1| 10cd, 12cd, 22 }}
 
[[Badness]]: 0.1650
 
=== 11-limit  ===
 
Subgroup: 2.3.5.7.11
 
Comma list: 50/49, 121/120, 896/891
 
Mapping: [{{val| 2 0 -24 -23 -9 }}, {{val| 0 1 9 9 5 }}]
 
POTE generator: ~3/2 = 709.310
 
{{Val list|legend=1| 10cd, 12cde, 22 }}
 
Badness: 0.0709
 
== Elvis  ==
=== 5-limit  ===
 
Subgroup: 2.3.5
 
[[Comma list]]: 36905625/33554432
 
[[Mapping]]: [{{val| 2 1 10 }}, {{val| 0 2 -5 }}]
 
[[POTE generator]]: ~45/32 = 554.546
 
{{Val list|legend=1| 26, 80bc, 106bc, 132bc }}
 
[[Badness]]: 0.8840
 
=== 7-limit  ===
 
Subgroup: 2.3.5.7
 
[[Comma list]]: 50/49, 8505/8192
 
[[Mapping]]: [{{val| 2 1 10 11 }}, {{val| 0 2 -5 -5 }}]
 
{{Multival|legend=1| 4 -10 -10 -25 -27 5 }}
 
[[POTE generator]]: ~45/32 = 553.721
 
{{Val list|legend=1| 24c, 26 }}
 
[[Badness]]: 0.1415
 
=== 11-limit  ===
 
Subgroup: 2.3.5.7.11
 
Comma list: 45/44, 50/49, 1344/1331
 
Mapping: [{{val| 2 1 10 11 8 }}, {{val| 0 2 -5 -5 -1 }}]
 
POTE generator: ~11/8 = 553.882
 
{{Val list|legend=1| 26 }}
 
Badness: 0.0632
 
=== 13-limit  ===
 
Subgroup: 2.3.5.7.11.13
 
Comma list: 45/44, 50/49, 78/77, 1053/1024
 
Mapping: [{{val| 2 1 10 11 8 16 }}, {{val| 0 2 -5 -5 -1 -8 }}]
 
POTE generator: ~11/8 = 553.892
 
{{Val list|legend=1| 26 }}
 
Badness: 0.0440
 
== Comic ==
=== 5-limit ===


Subgroup: 2.3.5
Subgroup: 2.3.5
Line 380: Line 350:
Badness: 0.4912
Badness: 0.4912


=== 7-limit ===
=== 7-limit ===


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 396: Line 366:
[[Badness]]: 0.0844
[[Badness]]: 0.0844


=== 11-limit ===
=== 11-limit ===


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 410: Line 380:
Badness: 0.0451
Badness: 0.0451


=== 13-limit ===
=== 13-limit ===


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 424: Line 394:
Badness: 0.0415
Badness: 0.0415


</div></div>
== Bipyth ==
 
Subgroup: 2.3.5.7
 
[[Comma list]]: 50/49, 20480/19683
 
[[Mapping]]: [{{val| 2 0 -24 -23 }}, {{val| 0 1 9 9 }}]
 
{{Multival|legend=1| 2 18 18 24 23 -9 }}
 
[[POTE generator]]: ~3/2 = 709.437
 
{{Val list|legend=1| 10cd, 12cd, 22 }}
 
[[Badness]]: 0.1650
 
=== 11-limit ===
 
Subgroup: 2.3.5.7.11
 
Comma list: 50/49, 121/120, 896/891
 
Mapping: [{{val| 2 0 -24 -23 -9 }}, {{val| 0 1 9 9 5 }}]
 
POTE generator: ~3/2 = 709.310
 
{{Val list|legend=1| 10cd, 12cde, 22 }}
 
Badness: 0.0709


== Duodecim ==
== Duodecim ==


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 442: Line 440:
Badness: 0.030536
Badness: 0.030536


== Vigintiduo ==
== Vigintiduo ==


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 458: Line 456:
Badness: 0.0484
Badness: 0.0484


== Vigin ==
== Vigin ==


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
Line 475: Line 473:
[[Category:Temperament clan]]
[[Category:Temperament clan]]
[[Category:Jubilismic clan| ]] <!-- main article -->
[[Category:Jubilismic clan| ]] <!-- main article -->
[[Category:Jubilismic]]
[[Category:Rank 2]]
[[Category:Rank 2]]

Revision as of 11:07, 7 July 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, hexe and astrology, which are discussed elsewhere.

No-3 jubilismic

Subgroup: 2.5.7

Sval mapping: [⟨2 1 1], ⟨0 1 1]]

Gencom mapping: [⟨2 0 1 1], ⟨0 0 1 1]]

POTE generator: ~5/4 = 380.840

Template:Val list

Lemba

Main article: Lemba
See also: Gamelismic clan § Lemba

Subgroup: 2.3.5.7

Comma list: 50/49, 525/512

Mapping: [⟨2 2 5 6], ⟨0 3 -1 -1]]

POTE generator: ~8/7 = 232.089

Template:Val list

Badness: 0.0622

11-limit

Subgroup: 2.3.5.7.11

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

Mapping: [⟨2 2 5 6 5], ⟨0 3 -1 -1 5]]

POTE generator: ~8/7 = 230.974

Template:Val list

Badness: 0.0416

13-limit

Subgroup: 2.3.5.7.11.13

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

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

POTE generator: ~8/7 = 230.966

Template:Val list

Badness: 0.0255

Diminished

Deutsch
See also: Dimipent family § Diminished

Subgroup: 2.3.5.7

Comma list: 36/35, 50/49

Mapping: [⟨4 0 3 5], ⟨0 1 1 1]]

Mapping generators: ~6/5, ~3

POTE generator: ~3/2 = 699.523

Template:Val list

Badness: 0.0224

Scales: diminished12

11-limit

Subgroup: 2.3.5.7.11

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

Mapping: [⟨4 0 3 5 14], ⟨0 1 1 1 0]]

Mapping generators: ~6/5, ~3

POTE generator: ~3/2 = 709.109

Template:Val list

Badness: 0.0221

Scales: diminished12

13-limit

Subgroup: 2.3.5.7.11.13

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

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

Mapping generators: ~6/5, ~3

POTE generator: ~3/2 = 713.773

Template:Val list

Badness: 0.0195

Scales: diminished12

Demolished

Subgroup: 2.3.5.7.11

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

Mapping: [⟨4 0 3 5 -5], ⟨0 1 1 1 3]]

Mapping generators: ~6/5, ~3

POTE generator: ~3/2 = 689.881

Template:Val list

Badness: 0.0266

Hemidim

Subgroup: 2.3.5.7.11

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

Mapping: [⟨4 1 4 6 6], ⟨0 2 2 2 3]]

Mapping generators: ~6/5, ~11/7

POTE generator: ~12/11 = 101.679

Template:Val list

Badness: 0.0550

Doublewide

Subgroup: 2.3.5.7

Comma list: 50/49, 875/864

Mapping: [⟨2 1 3 4], ⟨0 4 3 3]]

POTE generator: ~6/5 = 325.719

Template:Val list

Badness: 0.0435

11-limit

Subgroup: 2.3.5.7.11

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

Mapping: [⟨2 1 3 4 8], ⟨0 4 3 3 -2]]

POTE generator: ~6/5 = 325.548

Template:Val list

Badness: 0.0321

Fleetwood

Subgroup: 2.3.5.7.11

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

Mapping: [⟨2 1 3 4 2], ⟨0 4 3 3 9]]

POTE generator: ~6/5 = 327.038

Template:Val list

Badness: 0.0352

13-limit

Subgroup: 2.3.5.7.11.13

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

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

POTE generator: ~6/5 = 327.841

Template:Val list

Badness: 0.0318

Cavalier

Subgroup: 2.3.5.7.11

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

Mapping: [⟨2 1 3 4 1], ⟨0 4 3 3 11]]

POTE generator: ~6/5 = 323.427

Template:Val list

Badness: 0.0529

13-limit

Subgroup: 2.3.5.7.11.13

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

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

POTE generator: ~6/5 = 323.396

Template:Val list

Badness: 0.0350

Elvis

5-limit

Subgroup: 2.3.5

Comma list: 36905625/33554432

Mapping: [⟨2 1 10], ⟨0 2 -5]]

POTE generator: ~45/32 = 554.546

Template:Val list

Badness: 0.8840

7-limit

Subgroup: 2.3.5.7

Comma list: 50/49, 8505/8192

Mapping: [⟨2 1 10 11], ⟨0 2 -5 -5]]

Wedgie: ⟨⟨ 4 -10 -10 -25 -27 5 ]]

POTE generator: ~45/32 = 553.721

Template:Val list

Badness: 0.1415

11-limit

Subgroup: 2.3.5.7.11

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

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

POTE generator: ~11/8 = 553.882

Template:Val list

Badness: 0.0632

13-limit

Subgroup: 2.3.5.7.11.13

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

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

POTE generator: ~11/8 = 553.892

Template:Val list

Badness: 0.0440

Crepuscular

See also: Fifive family § Crepuscular

Subgroup: 2.3.5.7

Comma list: 50/49, 4375/4374

Mapping: [⟨2 2 3 4], ⟨0 5 7 7]]

Wedgie: ⟨⟨ 10 14 14 -1 -6 -7 ]]

POTE generator: ~27/25 = 140.349

Template:Val list

Badness: 0.0867

11-limit

Subgroup: 2.3.5.7.11

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

Mapping: [⟨2 2 3 4 6], ⟨0 5 7 7 4]]

POTE generator: ~12/11 = 140.587

Template:Val list

Badness: 0.0408

13-limit

Subgroup: 2.3.5.7.11.13

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

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

POTE generator: ~12/11 = 140.554

Template:Val list

Badness: 0.0244

Comic

5-limit

Subgroup: 2.3.5

Comma list: 5120000/4782969

Mapping: [⟨2 1 -3], ⟨0 2 7]]

POTE generator: ~81/80 = 55.382

Template:Val list

Badness: 0.4912

7-limit

Subgroup: 2.3.5.7

Comma list: 50/49, 2240/2187

Mapping: [⟨2 1 -3 -2], ⟨0 2 7 7]]

Wedgie: ⟨⟨ 4 14 14 13 11 -7 ]]

POTE generator: ~81/80 = 54.699

Template:Val list

Badness: 0.0844

11-limit

Subgroup: 2.3.5.7.11

Comma list: 50/49, 99/98, 2662/2625

Mapping: [⟨2 1 -3 -2 -4], ⟨0 2 7 7 10]]

POTE generator: ~81/80 = 55.184

Template:Val list

Badness: 0.0451

13-limit

Subgroup: 2.3.5.7.11

Comma list: 50/49, 65/63, 99/98, 968/945

Mapping: [⟨2 1 -3 -2 -4 3], ⟨0 2 7 7 10 4]]

POTE generator: ~81/80 = 54.435

Template:Val list

Badness: 0.0415

Bipyth

Subgroup: 2.3.5.7

Comma list: 50/49, 20480/19683

Mapping: [⟨2 0 -24 -23], ⟨0 1 9 9]]

Wedgie: ⟨⟨ 2 18 18 24 23 -9 ]]

POTE generator: ~3/2 = 709.437

Template:Val list

Badness: 0.1650

11-limit

Subgroup: 2.3.5.7.11

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

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

POTE generator: ~3/2 = 709.310

Template:Val list

Badness: 0.0709

Duodecim

Subgroup: 2.3.5.7.11

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]]

POTE generator: ~11/8 = 565.023

Template:Val list

Badness: 0.030536

Vigintiduo

Subgroup: 2.3.5.7.11

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]]

POTE generator: ~11/8 = 557.563

Template:Val list

Badness: 0.0484

Vigin

Subgroup: 2.3.5.7.11.13

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

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

POTE generator: ~13/8 = 844.624

Template:Val list

Badness: 0.0298

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