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
5-limit
Period: 1\1
Optimal (POTE) generator: ~3125/2592 = 292.702
EDO generator: 9\37, 10\41, 11\45
Scales (Scala files):
Subgroup: 2.3.5
Comma list: 6103515625/5804752896
Mapping: [⟨1 5 5], ⟨0 -14 -11]]
Badness: 0.7678
7-limit
Period: 1\1
Optimal (POTE) generator: ~25/21 = 292.710
EDO generator: 9\37, 10\41, 11\45
Scales (Scala files):
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 ]]
Badness: 0.0603
11-limit
Period: 1\1
Optimal (POTE) generator: ~25/21 = 292.547
EDO generator: 9\37, 10\41, 19\78
Scales (Scala files):
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]]
Badness: 0.0432
13-limit
Period: 1\1
Optimal (POTE) generator: ~25/21 = 292.457
EDO generator: 9\37, 10\41, 19\78
Scales (Scala files):
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]]
Badness: 0.0329
Quato
Period: 1\1
Optimal (POTE) generator: ~25/21 = 292.851
EDO generator: 10\41, 11\45, 21\86
Scales (Scala files):
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]]
Badness: 0.0412
13-limit
Period: 1\1
Optimal (POTE) generator: ~13/11 = 292.928
EDO generator: 10\41, 11\45, 21\86
Scales (Scala files):
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]]
Badness: 0.0301
Barbad
Period: 1\1
Optimal (POTE) generator: ~98/75 = 468.331
EDO generator: 7\18, 9\23, 16\41
Scales (Scala files):
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 ]]
Badness: 0.1104
11-limit
Period: 1\1
Optimal (POTE) generator: ~98/75 = 468.367
EDO generator: 7\18, 9\23, 16\41
Scales (Scala files):
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]]
Badness: 0.0501
13-limit
Period: 1\1
Optimal (POTE) generator: ~13/10 = 468.270
EDO generator: 7\18, 9\23, 16\41
Scales (Scala files):
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]]
Badness: 0.0392