Jubilismic clan
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 and hexe, which are discussed elsewhere.
No-threes POTE generator: ~5/4 = 380.840
No-threes mapping: [⟨2 0 1 1], ⟨0 0 1 1]]
Diminished
Period: 1\4
Optimal (POTE) generator: ~3/2 = 699.523
EDO generators: 5\8, 7\12, 9\16
Scales (Scala files): diminished12
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
Badness: 0.0224
11-limit
Period: 1\4
Optimal (POTE) generator: ~3/2 = 709.109
Scales (Scala files): diminished12
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
Badness: 0.0221
13-limit
Period: 1\4
Optimal (POTE) generator: ~3/2 = 713.773
Scales (Scala files): diminished12
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
Badness: 0.0195
Demolished
Period: 1\4
Optimal (POTE) generator: ~3/2 = 689.881
EDO generators: 7\12, 9\16, 14\28
Scales (Scala files):
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
Badness: 0.0266
Hemidim
Period: 1\4
Optimal (POTE) generator: ~12/11 = 101.679
EDO generators: 7\12
Scales (Scala files):
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
Badness: 0.0550
Doublewide
Period: 1\2
Optimal (POTE) generator: ~6/5 = 325.719
EDO generators: 6\22, 7\26, 13\48
Scales (Scala files):
Subgroup: 2.3.5.7
Comma list: 50/49, 875/864
Mapping: [⟨2 1 3 4], ⟨0 4 3 3]]
Badness: 0.0435
11-limit
Period: 1\2
Optimal (POTE) generator: ~6/5 = 325.548
EDO generators: 6\22, 7\26, 13\48
Scales (Scala files):
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]]
Badness: 0.0321
Fleetwood
Period: 1\2
Optimal (POTE) generator: ~6/5 = 327.038
Scales (Scala files):
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]]
Badness: 0.0352
13-limit
Period: 1\2
Optimal (POTE) generator: ~6/5 = 327.841
Scales (Scala files):
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]]
Badness: 0.0318
Cavalier
Period: 1\2
Optimal (POTE) generator: ~6/5 = 323.427
Scales (Scala files):
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]]
Badness: 0.0529
13-limit
Period: 1\2
Optimal (POTE) generator: ~6/5 = 323.396
Scales (Scala files):
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]]
Badness: 0.0350
Lemba
Period: 1\2
Optimal (POTE) generator: ~8/7 = 232.089
EDO generator: 2\10, 3\16, 5\26
Scales (Scala files):
Subgroup: 2.3.5.7
Comma list: 50/49, 525/512
Mapping: [⟨2 2 5 6], ⟨0 3 -1 -1]]
Badness: 0.0622
11-limit
Period: 1\2
Optimal (POTE) generator: ~8/7 = 230.974
EDO generators: 2\10, 3\16, 5\26
Scales (Scala files):
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]]
Badness: 0.0416
13-limit
Period: 1\2
Optimal (POTE) generator: ~8/7 = 230.966
EDO generators: 2\10, 3\16, 5\26
Scales (Scala files):
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]]
Badness: 0.0255
Crepuscular
Comma list: 50/49, 4375/4374
POTE generator: ~27/25 = 140.349
Mapping: [⟨2 2 3 4], ⟨0 5 7 7]]
Wedgie: ⟨⟨ 10 14 14 -1 -6 -7 ]]
Badness: 0.0867
11-limit
Comma list: 50/49, 99/98, 1944/1925
POTE generator: ~12/11 = 140.587
Mapping: [⟨2 2 3 4 6], ⟨0 5 7 7 4]]
Badness: 0.0408
13-limit
Comma list: 50/49, 78/77, 99/98, 144/143
POTE generator: ~12/11 = 140.554
Mapping: [⟨2 2 3 4 6 6], ⟨0 5 7 7 4 6]]
Badness: 0.0244
Bipyth
Comma list: 50/49, 20480/19683
POTE generator: ~3/2 = 709.437
Mapping: [⟨2 0 -24 -23], ⟨0 1 9 9]]
Wedgie: ⟨⟨ 2 18 18 24 23 -9 ]]
Badness: 0.1650
11-limit
Comma list: 50/49, 121/120, 896/891
POTE generator: ~3/2 = 709.310
Mapping: [⟨2 0 -24 -23 -9], ⟨0 1 9 9 5]]
Badness: 0.0709
Elvis
5-limit
Comma list: 36905625/33554432
POTE generator: ~45/32 = 554.546
Mapping: [⟨2 1 10], ⟨0 2 -5]]
Badness: 0.8840
7-limit
Comma list: 50/49, 8505/8192
POTE generator: ~45/32 = 553.721
Mapping: [⟨2 1 10 11], ⟨0 2 -5 -5]]
Wedgie: ⟨⟨ 4 -10 -10 -25 -27 5 ]]
Badness: 0.1415
11-limit
Comma list: 45/44, 50/49, 1344/1331
POTE generator: ~11/8 = 553.882
Mapping: [⟨2 1 10 11 8], ⟨0 2 -5 -5 -1]]
Badness: 0.0632
13-limit
Comma list: 45/44, 50/49, 78/77, 1053/1024
POTE generator: ~11/8 = 553.892
Mapping: [⟨2 1 10 11 8 16], ⟨0 2 -5 -5 -1 -8]]
Badness: 0.0440
Comic
5-limit
Comma list: 5120000/4782969
POTE generator: ~81/80 = 55.382
Mapping: [⟨2 1 -3], ⟨0 2 7]]
Badness: 0.4912
7-limit
Comma list: 50/49, 2240/2187
POTE generator: ~81/80 = 54.699
Mapping: [⟨2 1 -3 -2], ⟨0 2 7 7]]
Wedgie: <<4 14 14 13 11 -7||
Badness: 0.0844
11-limit
Comma list: 50/49, 99/98, 2662/2625
POTE generator: ~81/80 = 55.184
Mapping: [⟨2 1 -3 -2 -4], ⟨0 2 7 7 10]]
Badness: 0.0451
13-limit
Comma list: 50/49, 65/63, 99/98, 968/945
POTE generator: ~81/80 = 54.435
Mapping: [⟨2 1 -3 -2 -4 3], ⟨0 2 7 7 10 4]]
Badness: 0.0415
Duodecim
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]]
Badness: 0.030536
Vigintiduo
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]]
Badness: 0.0484
Vigin
Comma list: 50/49, 55/54, 64/63, 99/98
POTE generator: ~13/8 = 844.624
Mapping: [⟨22 35 51 62 76 0], ⟨0 0 0 0 0 1]]
Badness: 0.0298