Jubilismic clan: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Xenllium (talk | contribs)
autopatrolled
4,516 edits
Add a new temperament
Xenllium (talk | contribs)
autopatrolled
4,516 edits
No edit summary
Line 42: Line 42:
POTE generator: ~8/7 = 230.974
POTE generator: ~8/7 = 230.974


Vals: {{Val list| 10, 16, 26 }}
Optimal GPV sequence: {{Val list| 10, 16, 26 }}


Badness: 0.041563
Badness: 0.041563
Line 55: Line 55:
POTE generator: ~8/7 = 230.966
POTE generator: ~8/7 = 230.966


Vals: {{Val list| 10, 16, 26 }}
Optimal GPV sequence: {{Val list| 10, 16, 26 }}


Badness: 0.025477
Badness: 0.025477
Line 90: Line 90:
POTE generator: ~3/2 = 709.109
POTE generator: ~3/2 = 709.109


Vals: {{Val list| 4, 8d, 12, 32cddee, 44cddeee }}
Optimal GPV sequence: {{Val list| 4, 8d, 12, 32cddee, 44cddeee }}


Badness: 0.022132
Badness: 0.022132
Line 107: Line 107:
POTE generator: ~3/2 = 713.773
POTE generator: ~3/2 = 713.773


Vals: {{Val list| 4, 8d, 12f, 20cdef }}
Optimal GPV sequence: {{Val list| 4, 8d, 12f, 20cdef }}


Badness: 0.019509
Badness: 0.019509
Line 124: Line 124:
POTE generator: ~3/2 = 689.881
POTE generator: ~3/2 = 689.881


Vals: {{Val list| 12, 28, 40de }}
Optimal GPV sequence: {{Val list| 12, 28, 40de }}


Badness: 0.026574
Badness: 0.026574
Line 139: Line 139:
POTE generator: ~12/11 = 101.679
POTE generator: ~12/11 = 101.679


Vals: {{Val list| 8bce, 12 }}
Optimal GPV sequence: {{Val list| 8bce, 12 }}


Badness: 0.054965
Badness: 0.054965
Line 165: Line 165:
POTE generator: ~6/5 = 325.545
POTE generator: ~6/5 = 325.545


Vals: {{Val list| 4, 14bd, 18, 22, 48, 70c, 118cd }}
Optimal GPV sequence: {{Val list| 4, 14bd, 18, 22, 48, 70c, 118cd }}


Badness: 0.032058
Badness: 0.032058
Line 178: Line 178:
POTE generator: ~6/5 = 327.038
POTE generator: ~6/5 = 327.038


Vals: {{Val list| 4e, 18e, 22 }}
Optimal GPV sequence: {{Val list| 4e, 18e, 22 }}


Badness: 0.035202
Badness: 0.035202
Line 191: Line 191:
POTE generator: ~6/5 = 327.841
POTE generator: ~6/5 = 327.841


Vals: {{Val list| 4ef, 18e, 22, 84bddf }}
Optimal GPV sequence: {{Val list| 4ef, 18e, 22, 84bddf }}


Badness: 0.031835
Badness: 0.031835
Line 204: Line 204:
POTE generator: ~6/5 = 323.427
POTE generator: ~6/5 = 323.427


Vals: {{Val list| 22e, 26 }}
Optimal GPV sequence: {{Val list| 22e, 26 }}


Badness: 0.052899
Badness: 0.052899
Line 217: Line 217:
POTE generator: ~6/5 = 323.396
POTE generator: ~6/5 = 323.396


Vals: {{Val list| 22ef, 26 }}
Optimal GPV sequence: {{Val list| 22ef, 26 }}


Badness: 0.035040
Badness: 0.035040


== Elvis ==
== Elvis ==
Subgroup: 2.3.5
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Elvis]].''


[[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]]: 0.884000
=== 7-limit ===
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 258: Line 247:
POTE generator: ~11/8 = 553.882
POTE generator: ~11/8 = 553.882


Vals: {{Val list| 2, 24c, 26 }}
Optimal GPV sequence: {{Val list| 2, 24c, 26 }}


Badness: 0.063212
Badness: 0.063212
Line 271: Line 260:
POTE generator: ~11/8 = 553.892
POTE generator: ~11/8 = 553.892


Vals: {{Val list| 2f, 24cf, 26 }}
Optimal GPV sequence: {{Val list| 2f, 24cf, 26 }}


Badness: 0.043997
Badness: 0.043997
Line 301: Line 290:
POTE generator: ~12/11 = 140.587
POTE generator: ~12/11 = 140.587


Vals: {{Val list| 8d, 26, 34d, 60d }}
Optimal GPV sequence: {{Val list| 8d, 26, 34d, 60d }}


Badness: 0.040758
Badness: 0.040758
Line 314: Line 303:
POTE generator: ~12/11 = 140.554
POTE generator: ~12/11 = 140.554


Vals: {{Val list| 8d, 26, 34d, 60d }}
Optimal GPV sequence: {{Val list| 8d, 26, 34d, 60d }}


Badness: 0.024368
Badness: 0.024368


== Comic ==
== Comic ==
Subgroup: 2.3.5
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Comic]].''
 
[[Comma list]]: 5120000/4782969
 
[[Mapping]]: [{{val| 2 1 -3 }}, {{val| 0 2 7 }}]
 
[[POTE generator]]: ~81/80 = 55.382
 
{{Val list|legend=1| 20c, 22, 86b, 108b, 130b }}
 
[[Badness]]: 0.491181


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


Line 355: Line 333:
POTE generator: ~81/80 = 55.184
POTE generator: ~81/80 = 55.184


Vals: {{Val list| 20cde, 22 }}
Optimal GPV sequence: {{Val list| 20cde, 22 }}


Badness: 0.045052
Badness: 0.045052
Line 368: Line 346:
POTE generator: ~81/80 = 54.435
POTE generator: ~81/80 = 54.435


Vals: {{Val list| 22 }}
Optimal GPV sequence: {{Val list| 22 }}


Badness: 0.041470
Badness: 0.041470
Line 396: Line 374:
POTE generator: ~3/2 = 709.310
POTE generator: ~3/2 = 709.310


Vals: {{Val list| 10cd, 12cde, 22 }}
Optimal GPV sequence: {{Val list| 10cd, 12cde, 22 }}


Badness: 0.070910
Badness: 0.070910
Line 424: Line 402:
POTE generator: ~3/2 = 700.331
POTE generator: ~3/2 = 700.331


Vals: {{Val list| 16, 32, 48 }}
Optimal GPV sequence: {{Val list| 16, 32, 48 }}


Badness: 0.092774
Badness: 0.092774

Revision as of 00:57, 8 January 2022

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 0 1], ⟨0 1 1]]

Sval mapping generators: ~7/5, ~5

Gencom mapping: [⟨2 0 0 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]]

Mapping generators: ~7/5, ~8/7

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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: Template:Val list

Badness: 0.035040

Elvis

For the 5-limit version of this temperament, see High badness temperaments #Elvis.

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: 0.141473

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

Optimal GPV sequence: Template:Val list

Badness: 0.063212

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

Optimal GPV sequence: Template:Val list

Badness: 0.043997

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

Optimal GPV sequence: 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

Optimal GPV sequence: Template:Val list

Badness: 0.024368

Comic

For the 5-limit version of this temperament, see High badness temperaments #Comic.

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: 0.084395

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

Optimal GPV sequence: Template:Val list

Badness: 0.045052

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

Optimal GPV sequence: Template:Val list

Badness: 0.041470

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: 0.165033

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

Optimal GPV sequence: Template:Val list

Badness: 0.070910

Sedecic

Subgroup: 2.3.5.7

Comma list: 50/49, 546875/524288

Mapping: [⟨16 0 37 45], ⟨0 1 0 0]]

Wedgie: ⟨⟨ 16 0 0 -37 -45 0 ]]

POTE generator: ~3/2 = 700.554

Template:Val list

Badness: 0.265972

11-limit

Subgroup: 2.3.5.7.11

Comma list: 50/49, 385/384, 1331/1323

Mapping: [⟨16 0 37 45 30], ⟨0 1 0 0 1]]

POTE generator: ~3/2 = 700.331

Optimal GPV sequence: Template:Val list

Badness: 0.092774

Duodecim

See also: Compton family § Duodecim

Subgroup: 2.3.5.7.11

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

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

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

POTE generator: ~11/8 = 557.563

Template:Val list

Badness: 0.048372

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

Retrieved from "https://en.xen.wiki/index.php?title=Jubilismic_clan&oldid=83385"