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]]
- mapping generators: ~2, ~25/21
Wedgie: ⟨⟨ 14 11 9 -15 -25 -10 ]]
Optimal tuning (POTE): ~2 = 1\1, ~25/21 = 292.710
Optimal ET sequence: 4, 37, 41
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]]
Optimal tuning (POTE): ~2 = 1\1, ~25/21 = 292.547
Optimal ET sequence: 4, 37, 41, 119
Badness: 0.043209
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 196/195, 275/273, 385/384
Mapping: [⟨1 5 5 5 2 2], ⟨0 -14 -11 -9 6 7]]
Optimal tuning (POTE): ~2 = 1\1, ~13/11 = 292.457
Optimal ET sequence: 4, 37, 41, 78, 119f
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]]
Optimal tuning (POTE): ~2 = 1\1, ~25/21 = 292.851
Optimal ET sequence: 41, 127cd, 168cd
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]]
Optimal tuning (POTE): ~2 = 1\1, ~13/11 = 292.928
Optimal ET sequence: 41, 86ce, 127cd
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]]
- mapping generators: ~2, ~25/24
Optimal tuning (POTE): ~2 = 1\1, ~25/24 = 53.816
Optimal ET sequence: 22, 45, 67c
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]]
- mapping generators: ~21/20, ~3
Wedgie: ⟨⟨ 11 11 0 -8 -31 -31 ]]
Optimal tuning (POTE): ~21/20 = 1\11, ~3/2 = 708.792
Badness: 0.141782
11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 352/343, 385/384
Mapping: [⟨11 0 8 31 38], ⟨0 1 1 0 0]]
Optimal tuning (POTE): ~21/20 = 1\11, ~3/2 = 706.768
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]]
Optimal tuning (POTE): ~13/12 = 1\11, ~3/2 = 707.764
Badness: 0.056528
Barbad
Subgroup: 2.3.5.7
Comma list: 875/864, 16875/16807
Mapping: [⟨1 9 7 11], ⟨0 -19 -12 -21]]
- mapping generators: ~2, ~98/75
Wedgie: ⟨⟨ 19 12 21 -25 -20 15 ]]
Optimal tuning (POTE): ~2 = 1\1, ~98/75 = 468.331
Optimal ET sequence: 18, 23d, 41
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]]
Optimal tuning (POTE): ~2 = 1\1, ~98/75 = 468.367
Optimal ET sequence: 18e, 23de, 41, 228ccdd
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]]
Optimal tuning (POTE): ~2 = 1\1, ~13/10 = 468.270
Optimal ET sequence: 18e, 23de, 41
Badness: 0.039183
Hyperkleismic
Subgroup: 2.3.5.7
Comma list: 875/864, 51200/50421
Mapping: [⟨1 -3 -2 2], ⟨0 17 16 3]]
- mapping generators: ~2, ~6/5
Wedgie: ⟨⟨ 17 16 3 -14 -43 -38 ]]
Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 323.780
Optimal ET sequence: 26, 37, 63
Badness: 0.157830
11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 385/384, 2420/2401
Mapping: [⟨1 -3 -2 2 4], ⟨0 17 16 3 -2]]
Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 323.796
Optimal ET sequence: 26, 37, 63
Badness: 0.065356
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 169/168, 275/273, 385/384
Mapping: [⟨1 -3 -2 2 4 1], ⟨0 17 16 3 -2 10]]
Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 323.790
Optimal ET sequence: 26, 37, 63
Badness: 0.035724
Sevond
10/9 is tempered to be exactly 1\7 of an octave. Therefore 3/2 is 1 generator sharp of a 7edo step and 5/4 is 2 generators sharp.
Subgroup: 2.3.5.7
Comma list: 875/864, 327680/321489
Mapping: [⟨7 0 -6 53], ⟨0 1 2 -3]]
- mapping generators: ~10/9, ~3
Optimal tuning (POTE): ~10/9 = 1\7, ~3/2 = 705.613
Optimal ET sequence: 7, 56, 63, 119
Badness: 0.206592
11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 385/384, 6655/6561
Mapping: [⟨7 0 -6 53 2], ⟨0 1 2 -3 2]]
Optimal tuning (POTE): ~10/9 = 1\7, ~3/2 = 705.518
Optimal ET sequence: 7, 56, 63, 119
Badness: 0.070437
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 169/168, 352/351, 385/384
Mapping: [⟨7 0 -6 53 2 37], ⟨0 1 2 -3 2 -1]]
Optimal tuning (POTE): ~10/9 = 1\7, ~3/2 = 705.344
Optimal ET sequence: 7, 56, 63, 119
Badness: 0.041238