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.  
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]], [[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]], [[Wesley family #Dubbla|dubbla]], [[Augmented family #Hexe|hexe]] and [[Magic family #Astrology|astrology]], which are discussed elsewhere.
 
== No-3 jubilismic ==


== No-three jubilismic ==
Subgroup: 2.5.7
Subgroup: 2.5.7


Line 28: Line 27:
{{Val list|legend=1| 10, 16, 26, 62c }}
{{Val list|legend=1| 10, 16, 26, 62c }}


[[Badness]]: 0.0622
[[Badness]]: 0.062208


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 40: Line 38:
POTE generator: ~8/7 = 230.974
POTE generator: ~8/7 = 230.974


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


Badness: 0.0416
Badness: 0.041563


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 54: Line 51:
POTE generator: ~8/7 = 230.966
POTE generator: ~8/7 = 230.966


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


Badness: 0.0255
Badness: 0.025477


== Diminished ==
== Diminished ==
Line 74: Line 71:
{{Val list|legend=1| 4, 8d, 12 }}
{{Val list|legend=1| 4, 8d, 12 }}


[[Badness]]: 0.0224
[[Badness]]: 0.022401


Scales: [[diminished12]]
Scales: [[diminished12]]


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 90: Line 86:
POTE generator: ~3/2 = 709.109
POTE generator: ~3/2 = 709.109


{{Val list|legend=1| 4, 8d, 12, 32cddee, 44cddeee }}
Vals: {{Val list| 4, 8d, 12, 32cddee, 44cddeee }}


Badness: 0.0221
Badness: 0.022132


Scales: [[diminished12]]
Scales: [[diminished12]]


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 108: Line 103:
POTE generator: ~3/2 = 713.773
POTE generator: ~3/2 = 713.773


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


Badness: 0.0195
Badness: 0.019509


Scales: [[diminished12]]
Scales: [[diminished12]]


=== Demolished ===
=== Demolished ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 126: Line 120:
POTE generator: ~3/2 = 689.881
POTE generator: ~3/2 = 689.881


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


Badness: 0.0266
Badness: 0.026574


=== Hemidim ===
=== Hemidim ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 142: Line 135:
POTE generator: ~12/11 = 101.679
POTE generator: ~12/11 = 101.679


{{Val list|legend=1| 12 }}
Vals: {{Val list| 8bce, 12 }}


Badness: 0.0550
Badness: 0.054965


== Doublewide ==
== Doublewide ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 158: Line 150:
{{Val list|legend=1| 4, 14bd, 18, 22, 48, 70c }}
{{Val list|legend=1| 4, 14bd, 18, 22, 48, 70c }}


[[Badness]]: 0.0435
[[Badness]]: 0.043462


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 168: Line 159:
Mapping: [{{val| 2 1 3 4 8 }}, {{val| 0 4 3 3 -2 }}]
Mapping: [{{val| 2 1 3 4 8 }}, {{val| 0 4 3 3 -2 }}]


POTE generator: ~6/5 = 325.548
POTE generator: ~6/5 = 325.545


{{Val list|legend=1| 4, 14bd, 18, 22, 48, 70c, 118cd }}
Vals: {{Val list| 4, 14bd, 18, 22, 48, 70c, 118cd }}


Badness: 0.0321
Badness: 0.032058


=== Fleetwood ===
=== Fleetwood ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 184: Line 174:
POTE generator: ~6/5 = 327.038
POTE generator: ~6/5 = 327.038


{{Val list|legend=1| 22 }}
Vals: {{Val list| 4e, 18e, 22 }}


Badness: 0.0352
Badness: 0.035202


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 198: Line 187:
POTE generator: ~6/5 = 327.841
POTE generator: ~6/5 = 327.841


{{Val list|legend=1| 18e, 22, 84bddf }}
Vals: {{Val list| 4ef, 18e, 22, 84bddf }}


Badness: 0.0318
Badness: 0.031835


=== Cavalier ===
=== Cavalier ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 212: Line 200:
POTE generator: ~6/5 = 323.427
POTE generator: ~6/5 = 323.427


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


Badness: 0.0529
Badness: 0.052899


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 226: Line 213:
POTE generator: ~6/5 = 323.396
POTE generator: ~6/5 = 323.396


{{Val list|legend=1| 22ef, 26 }}
Vals: {{Val list| 22ef, 26 }}


Badness: 0.0350
Badness: 0.035040


== Elvis ==
== Elvis ==
=== 5-limit ===
Subgroup: 2.3.5
Subgroup: 2.3.5


Line 246: Line 231:


=== 7-limit ===
=== 7-limit ===
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 262: Line 246:


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 271: Line 254:
POTE generator: ~11/8 = 553.882
POTE generator: ~11/8 = 553.882


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


Badness: 0.0632
Badness: 0.0632


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 285: Line 267:
POTE generator: ~11/8 = 553.892
POTE generator: ~11/8 = 553.892


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


Badness: 0.0440
Badness: 0.0440
Line 296: Line 278:
[[Comma list]]: 50/49, 4375/4374
[[Comma list]]: 50/49, 4375/4374


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


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


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


{{Val list|legend=1| 26, 34d, 60d, 94d }}
{{Val list|legend=1| 8d, 26, 34d, 60d }}


[[Badness]]: 0.0867
[[Badness]]: 0.086669


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 50/49, 99/98, 1944/1925
Comma list: 50/49, 99/98, 864/847


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


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


{{Val list|legend=1| 26, 34d, 60d, 94de }}
Vals: {{Val list| 8d, 26, 34d, 60d }}


Badness: 0.0408
Badness: 0.040758


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


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


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


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


{{Val list|legend=1| 26, 34d, 60d, 94de }}
Vals: {{Val list| 8d, 26, 34d, 60d }}


Badness: 0.0244
Badness: 0.024368


== Comic ==
== Comic ==
=== 5-limit ===
Subgroup: 2.3.5
Subgroup: 2.3.5


Line 350: Line 328:


=== 7-limit ===
=== 7-limit ===
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 366: Line 343:


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 375: Line 351:
POTE generator: ~81/80 = 55.184
POTE generator: ~81/80 = 55.184


{{Val list|legend=1| 20cde, 22 }}
Vals: {{Val list| 20cde, 22 }}


Badness: 0.0451
Badness: 0.0451


=== 13-limit ===
=== 13-limit ===
 
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11


Comma list: 50/49, 65/63, 99/98, 968/945
Comma list: 50/49, 65/63, 99/98, 968/945
Line 389: Line 364:
POTE generator: ~81/80 = 54.435
POTE generator: ~81/80 = 54.435


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


Badness: 0.0415
Badness: 0.0415


== Bipyth ==
== Bipyth ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 410: Line 384:


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 419: Line 392:
POTE generator: ~3/2 = 709.310
POTE generator: ~3/2 = 709.310


{{Val list|legend=1| 10cd, 12cde, 22 }}
Vals: {{Val list| 10cd, 12cde, 22 }}


Badness: 0.0709
Badness: 0.0709


== Duodecim ==
== Duodecim ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 440: Line 412:


== Vigintiduo ==
== Vigintiduo ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 456: Line 427:


== Vigin ==
== Vigin ==
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 467: Line 437:
{{Val list|legend=1| 22, 44 }}
{{Val list|legend=1| 22, 44 }}


Badness: 0.0298
Badness: 0.029849


[[Category:Regular temperament theory]]
[[Category:Regular temperament theory]]

Revision as of 02:10, 2 August 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, dubbla, hexe and astrology, which are discussed elsewhere.

No-three 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

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: 0.062208

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

Vals: Template:Val list

Badness: 0.041563

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

Vals: Template:Val list

Badness: 0.025477

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: 0.022401

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

Vals: Template:Val list

Badness: 0.022132

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

Vals: Template:Val list

Badness: 0.019509

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

Vals: Template:Val list

Badness: 0.026574

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

Vals: Template:Val list

Badness: 0.054965

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: 0.043462

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 = 325.545

Vals: Template:Val list

Badness: 0.032058

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

Vals: Template:Val list

Badness: 0.035202

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

Vals: Template:Val list

Badness: 0.031835

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

Vals: Template:Val list

Badness: 0.052899

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

Vals: Template:Val list

Badness: 0.035040

Elvis

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

Vals: 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

Vals: 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: 0.086669

11-limit

Subgroup: 2.3.5.7.11

Comma list: 50/49, 99/98, 864/847

Mapping: [⟨2 2 3 4 6], ⟨0 5 7 7 4]]

POTE generator: ~12/11 = 140.587

Vals: Template:Val list

Badness: 0.040758

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

Vals: Template:Val list

Badness: 0.024368

Comic

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

Vals: Template:Val list

Badness: 0.0451

13-limit

Subgroup: 2.3.5.7.11.13

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

Vals: 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

Vals: 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: 0.029849

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