Keemic temperaments
These temper out the keema, [-5 -3 3 1⟩ = 875/864. Keemic temperaments include doublewide, flattone, porcupine, superkleismic, magic, keemun, and sycamore. Discussed below are quasitemp and barbad.
Quasitemp
- For the 5-limit version of this temperament, see High badness temperaments #Quasitemp.
Subgroup: 2.3.5.7
Comma list: 875/864, 2401/2400
Mapping: [⟨1 5 5 5], ⟨0 -14 -11 -9]]
Wedgie: ⟨⟨ 14 11 9 -15 -25 -10 ]]
POTE generator: ~25/21 = 292.710
Badness: 0.060269
11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 385/384, 1375/1372
Mapping: [⟨1 5 5 5 2], ⟨0 -14 -11 -9 6]]
POTE generator: ~25/21 = 292.547
Vals: Template:Val list
Badness: 0.043209
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 196/195, 275/273, 385/384
POTE generator: ~13/11 = 292.457
Mapping: [⟨1 5 5 5 2 2], ⟨0 -14 -11 -9 6 7]]
POTE generator: ~13/11 = 292.457
Vals: Template:Val list
Badness: 0.032913
Quato
Subgroup: 2.3.5.7.11
Comma list: 243/242, 441/440, 625/616
Mapping: [⟨1 5 5 5 12], ⟨0 -14 -11 -9 -35]]
POTE generator: ~25/21 = 292.851
Vals: Template:Val list
Badness: 0.041170
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 243/242, 275/273, 325/324
Mapping: [⟨1 5 5 5 12 12], ⟨0 -14 -11 -9 -35 -34]]
POTE generator: ~13/11 = 292.928
Vals: Template:Val list
Badness: 0.030081
Chromo
- For the 5-limit version of this temperament, see High badness temperaments #Chromo.
Subgroup: 2.3.5.7
Comma list: 875/864, 2430/2401
Mapping: [⟨1 1 2 2], ⟨0 13 7 18]]
POTE generator: ~25/24 = 53.816
Badness: 0.090769
Undeka
- For the 5-limit version of this temperament, see High badness temperaments #Undeka.
Subgroup: 2.3.5.7
Comma list: 875/864, 3200/3087
Mapping: [⟨11 0 8 31], ⟨0 1 1 0]]
Wedgie: ⟨⟨ 11 11 0 -8 -31 -31 ]]
POTE generator: ~3/2 = 708.792
Badness: 0.141782
11-limit
Sugbroup: 2.3.5.7.11
Comma list: 100/99, 352/343, 385/384
Mapping: [⟨11 0 8 31 38], ⟨0 1 1 0 0]]
POTE generator: ~3/2 = 706.768
Vals: Template:Val list
Badness: 0.068672
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 65/63, 100/99, 169/165, 352/343
Mapping: [⟨11 0 8 31 38 23], ⟨0 1 1 0 0 1]]
POTE generator: ~3/2 = 707.764
Vals: Template:Val list
Badness: 0.056528
Barbad
Subgroup: 2.3.5.7
Comma list: 875/864, 16875/16807
Mapping: [⟨1 9 7 11], ⟨0 -19 -12 -21]]
Wedgie: ⟨⟨ 19 12 21 -25 -20 15 ]]
POTE generator: ~98/75 = 468.331
Badness: 0.110448
11-limit
Subgroup: 2.3.5.7.11
Comma list: 245/242, 540/539, 625/616
Mapping: [⟨1 9 7 11 14], ⟨0 -19 -12 -21 -27]]
POTE generator: ~98/75 = 468.367
Vals: Template:Val list
Badness: 0.050105
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 196/195, 245/242, 275/273
Mapping: [⟨1 9 7 11 14 8], ⟨0 -19 -12 -21 -27 -11]]
POTE generator: ~13/10 = 468.270
Vals: Template:Val list
Badness: 0.039183