Jubilismic clan: Difference between revisions
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{{Val list|legend=1| 26, 80bc, 106bc, 132bc }} | {{Val list|legend=1| 26, 80bc, 106bc, 132bc }} | ||
[[Badness]]: 0. | [[Badness]]: 0.884000 | ||
=== 7-limit === | === 7-limit === | ||
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[[POTE generator]]: ~45/32 = 553.721 | [[POTE generator]]: ~45/32 = 553.721 | ||
{{Val list|legend=1| 24c, 26 }} | {{Val list|legend=1| 2, 24c, 26 }} | ||
[[Badness]]: 0. | [[Badness]]: 0.141473 | ||
=== 11-limit === | === 11-limit === | ||
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POTE generator: ~11/8 = 553.882 | POTE generator: ~11/8 = 553.882 | ||
Vals: {{Val list| 26 }} | Vals: {{Val list| 2, 24c, 26 }} | ||
Badness: 0. | Badness: 0.063212 | ||
=== 13-limit === | === 13-limit === | ||
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POTE generator: ~11/8 = 553.892 | POTE generator: ~11/8 = 553.892 | ||
Vals: {{Val list| 26 }} | Vals: {{Val list| 2f, 24cf, 26 }} | ||
Badness: 0. | Badness: 0.043997 | ||
== Crepuscular == | == Crepuscular == | ||
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{{Val list|legend=1| 20c, 22, 86b, 108b, 130b }} | {{Val list|legend=1| 20c, 22, 86b, 108b, 130b }} | ||
Badness: 0. | [[Badness]]: 0.491181 | ||
=== 7-limit === | === 7-limit === | ||
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{{Val list|legend=1| 20cd, 22 }} | {{Val list|legend=1| 20cd, 22 }} | ||
[[Badness]]: 0. | [[Badness]]: 0.084395 | ||
=== 11-limit === | === 11-limit === | ||
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Vals: {{Val list| 20cde, 22 }} | Vals: {{Val list| 20cde, 22 }} | ||
Badness: 0. | Badness: 0.045052 | ||
=== 13-limit === | === 13-limit === | ||
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Vals: {{Val list| 22 }} | Vals: {{Val list| 22 }} | ||
Badness: 0. | Badness: 0.041470 | ||
== Bipyth == | == Bipyth == | ||
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{{Val list|legend=1| 10cd, 12cd, 22 }} | {{Val list|legend=1| 10cd, 12cd, 22 }} | ||
[[Badness]]: 0. | [[Badness]]: 0.165033 | ||
=== 11-limit === | === 11-limit === | ||
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Vals: {{Val list| 10cd, 12cde, 22 }} | Vals: {{Val list| 10cd, 12cde, 22 }} | ||
Badness: 0. | Badness: 0.070910 | ||
== Duodecim == | == Duodecim == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
Comma list: 36/35, 50/49, 64/63 | [[Comma list]]: 36/35, 50/49, 64/63 | ||
[[Mapping]]: [{{val| 12 19 28 34 0 }}, {{val| 0 0 0 0 1 }}] | |||
[[POTE generator]]: ~11/8 = 565.023 | |||
POTE generator: ~11/8 = 565.023 | |||
{{Val list|legend=1| 12, 24d, 36d }} | {{Val list|legend=1| 12, 24d, 36d }} | ||
Badness: 0.030536 | [[Badness]]: 0.030536 | ||
== Vigintiduo == | == Vigintiduo == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
Comma list: 50/49, 64/63, 245/243 | [[Comma list]]: 50/49, 64/63, 245/243 | ||
Mapping: [{{val| 22 35 51 62 0 }}, {{val| 0 0 0 0 1 }}] | [[Mapping]]: [{{val| 22 35 51 62 0 }}, {{val| 0 0 0 0 1 }}] | ||
POTE generator: ~11/8 = 557.563 | [[POTE generator]]: ~11/8 = 557.563 | ||
{{Val list|legend=1| 22, 66de, 88bde, 110bd, 198bcdde }} | {{Val list|legend=1| 22, 66de, 88bde, 110bd, 198bcdde }} | ||
Badness: 0. | [[Badness]]: 0.048372 | ||
== Vigin == | == Vigin == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
Comma list: 50/49, 55/54, 64/63, 99/98 | [[Comma list]]: 50/49, 55/54, 64/63, 99/98 | ||
Mapping: [{{val| 22 35 51 62 76 0 }}, {{val| 0 0 0 0 0 1 }}] | [[Mapping]]: [{{val| 22 35 51 62 76 0 }}, {{val| 0 0 0 0 0 1 }}] | ||
POTE generator: ~13/8 = 844.624 | [[POTE generator]]: ~13/8 = 844.624 | ||
{{Val list|legend=1| 22, 44 }} | {{Val list|legend=1| 22, 44 }} | ||
Badness: 0.029849 | [[Badness]]: 0.029849 | ||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||
Revision as of 12:33, 6 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
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
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
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
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
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
Badness: 0.884000
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
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
Vals: 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
Vals: Template:Val list
Badness: 0.043997
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
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
Badness: 0.491181
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
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
Vals: 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
Vals: 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
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
Vals: Template:Val list
Badness: 0.070910
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
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
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
Badness: 0.029849