Jubilismic clan: Difference between revisions
Ordering by strong/weak extension |
m →Lemba: -link to gamelismic clan and fix an edo error |
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== Lemba == | == Lemba == | ||
{{main| Lemba }} | {{main| Lemba }} | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 27: | Line 26: | ||
[[POTE generator]]: ~8/7 = 232.089 | [[POTE generator]]: ~8/7 = 232.089 | ||
{{Val list|legend=1| 10, 16, 26, | {{Val list|legend=1| 10, 16, 26, 62c }} | ||
[[Badness]]: 0.0622 | [[Badness]]: 0.0622 | ||
Revision as of 11:12, 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
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: 0.0622
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
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
Badness: 0.0255
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: 0.0224
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Badness: 0.0440
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: 0.0867
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
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
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
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
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
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
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
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
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
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
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
Badness: 0.0298