Jubilismic clan
The jubilismic clan tempers out the jubilisma, 50/49, which means 7/5 and 10/7 are both equated to the 600-cent tritone and the octave is divided in two.
Jubilic
The head of this clan, jubilic, is generated by ~5/4. That and a semioctave gives ~7/4.
Subgroup: 2.5.7
Comma list: 50/49
Sval mapping: [⟨2 0 1], ⟨0 1 1]]
- sval mapping generators: ~7/5, ~5
Gencom mapping: [⟨2 0 0 1], ⟨0 0 1 1]]
Optimal tuning (POTE): ~7/5 = 1\2, ~5/4 = 380.840
Optimal ET sequence: 2, 4, 6, 16, 22, 60d, 82d, 104dd
Overview to extensions
Lemba finds the perfect fifth three steps away by tempering out 1029/1024. Astrology, five steps away by tempering out 3125/3072. Decimal, two steps away by tempering out 25/24 and 49/48. Walid merges ~5/4 and ~4/3 by tempering out 16/15.
Diminished splits the ~7/5 period into a further two. Pajara slices the ~7/4 into two, with antikythera being every other step thereof. Injera slices the ~5/1 into four. Hedgehog slices the ~7/1 into five. Crepuscular slices the ~7/4 into seven.
Lemba, astrology, and doublewide are discussed below; others in the clan are
- Diminished → Dimipent family
- Pajara → Diaschismic family
- Decimal → Dicot family
- Injera → Meantone family
- Octokaidecal → Trienstonic clan
- Hedgehog → Porcupine family
- Dubbla → Wesley family
- Bipelog → Pelogic family
- Crepuscular → Fifive family
- Hexe → Augmented family
- Byhearted → Tetracot family
which are discussed elsewhere.
Lemba
- Main article: Lemba
Lemba tempers out 1029/1024, the gamelisma, and a stack of three ~8/7 generators gives an approximate perfect fifth.
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
Optimal tuning (POTE): ~7/5 = 1\2, ~8/7 = 232.089
Optimal ET sequence: 10, 16, 26, 62c
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]]
Optimal tuning (POTE): ~7/5 = 1\2, ~8/7 = 230.974
Optimal ET sequence: 10, 16, 26
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]]
Optimal tuning (POTE): ~7/5 = 1\2, ~8/7 = 230.966
Optimal ET sequence: 10, 16, 26
Badness: 0.025477
Astrology
Astrology tempers out 3125/3072, the magic comma, and a stack of five ~5/4 generators gives an approximate harmonic 3.
Subgroup: 2.3.5.7
Comma list: 50/49, 3125/3072
Mapping: [⟨2 0 4 5], ⟨0 5 1 1]]
- mapping geenerators: ~7/5, ~5/4
Wedgie: ⟨⟨10 2 2 -20 -25 -1]]
Optimal tuning (POTE): ~7/5 = 1\2, ~5/4 = 380.578
Optimal ET sequence: 6, 16, 22, 60d, 82d
Badness: 0.082673
11-limit
Subgroup: 2.3.5.7.11
Comma list: 50/49, 121/120, 176/175
Mapping: [⟨2 0 4 5 5], ⟨0 5 1 1 3]]
Optimal tuning (POTE): ~7/5 = 1\2, ~5/4 = 380.530
Optimal ET sequence: 6, 16, 22, 60de, 82de
Badness: 0.039151
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 50/49, 65/64, 78/77, 121/120
Mapping: [⟨2 0 4 5 5 8], ⟨0 5 1 1 3 -1]]
Optimal tuning (POTE): ~7/5 = 1\2, ~5/4 = 379.787
Optimal ET sequence: 6, 16, 22, 38f
Badness: 0.034376
- Music
Horoscope
Subgroup: 2.3.5.7.11.13
Comma list: 50/49, 66/65, 105/104, 121/120
Mapping: [⟨2 0 4 5 5 3], ⟨0 5 1 1 3 7]]
Optimal tuning (POTE): ~7/5 = 1\2, ~5/4 = 379.837
Optimal ET sequence: 16, 22f, 38
Badness: 0.035284
Walid
Subgroup: 2.3.5.7
Comma list: 16/15, 50/49
Mapping: [⟨2 0 8 9], ⟨0 1 -1 -1]]
- mapping generators: ~7/5, ~3
Wedgie: ⟨⟨2 -2 -2 -8 -9 1]]
Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 749.415
Optimal ET sequence: 2, 6, 8d
Badness: 0.048978
11-limit
Subgroup: 2.3.5.7.11
Comma list: 16/15, 22/21, 50/49
Mapping: [⟨2 0 8 9 7], ⟨0 1 -1 -1 0]]
Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 749.756
Optimal ET sequence: 2, 6, 8d
Badness: 0.029193
Antikythera
Named by Gene Ward Smith in 2011[1], antikythera is every other step of pajara.
Subgroup: 2.9.5.7
Comma list: 50/49, 64/63
Sval mapping: [⟨2 0 11 12], ⟨0 1 -1 -1]]
- mapping generators: ~7/5, ~9
Gencom mapping: [⟨2 3 5 6], ⟨0 1/2 -1 -1]]
- gencom: [7/5 8/7; 50/49 64/63]
Optimal tuning (POTE): ~7/5 = 1\2, ~8/7 = 214.095
Optimal ET sequence: 4, 6, 16, 22, 28
Badness: 0.00501
Doublewide
Subgroup: 2.3.5.7
Comma list: 50/49, 875/864
Mapping: [⟨2 1 3 4], ⟨0 4 3 3]]
Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 325.719
Optimal ET sequence: 4, 14bd, 18, 22, 48, 70c
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]]
Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 325.545
Optimal ET sequence: 4, 14bd, 18, 22, 48, 70c, 118cd
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]]
Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 327.038
Optimal ET sequence: 4e, 18e, 22
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]]
Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 327.841
Optimal ET sequence: 4ef, 18e, 22, 84bddf
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]]
Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 323.427
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]]
Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 323.396
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]]
Optimal tuning (POTE): ~7/5 = 1\2, ~45/32 = 553.721
Optimal ET sequence: 2, 24c, 26
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]]
Optimal tuning (POTE): ~7/5 = 1\2, ~11/8 = 553.882
Optimal ET sequence: 2, 24c, 26
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]]
Optimal tuning (POTE): ~7/5 = 1\2, ~11/8 = 553.892
Optimal ET sequence: 2f, 24cf, 26
Badness: 0.043997
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]]
Optimal tuning (POTE): ~7/5 = 1\2, ~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]]
Optimal tuning (POTE): ~7/5 = 1\2, ~81/80 = 55.184
Optimal ET sequence: 20cde, 22
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]]
Optimal tuning (POTE): ~7/5 = 1\2, ~81/80 = 54.435
Badness: 0.041470
Bipyth
- See also: Archytas clan #Superpyth
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]]
Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 709.437
Optimal ET sequence: 10cd, 12cd, 22
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]]
Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 709.310
Optimal ET sequence: 10cd, 12cde, 22
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]]
Optimal tuning (POTE): ~128/125 = 1\16, ~3/2 = 700.554
Optimal ET sequence: 16, 32, 48
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]]
Optimal tuning (POTE): ~22/21 = 1\16, ~3/2 = 700.331
Optimal ET sequence: 16, 32, 48
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]]
Optimal tuning (POTE): ~16/15 = 1\12, ~11/8 = 565.023
Optimal ET sequence: 12, 24d, 36d
Badness: 0.030536