Keemic temperaments

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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

Optimal GPV sequence4, 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]]

POTE generator: ~25/21 = 292.547

Vals: 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

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: 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]]

POTE generator: ~25/21 = 292.851

Vals: 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]]

POTE generator: ~13/11 = 292.928

Vals: 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]]

POTE generator: ~25/24 = 53.816

Optimal GPV sequence22, 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]]

Wedgie⟨⟨11 11 0 -8 -31 -31]]

POTE generator: ~3/2 = 708.792

Optimal GPV sequence11c, 22

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]]

POTE generator: ~3/2 = 706.768

Vals: 11c, 22

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: 11cf, 22

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

Optimal GPV sequence18, 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]]

POTE generator: ~98/75 = 468.367

Vals: 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]]

POTE generator: ~13/10 = 468.270

Vals: 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]]

Wedgie⟨⟨17 16 3 -14 -43 -38]]

POTE generator: ~6/5 = 323.780

Optimal GPV sequence26, 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]]

POTE generator: ~6/5 = 323.796

Vals: 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]]

POTE generator: ~6/5 = 323.790

Vals: 26, 37, 63

Badness: 0.035724

Sevond

Subgroup: 2.3.5.7

Comma list: 875/864, 327680/321489

Mapping: [7 0 -6 53], 0 1 2 -3]]

POTE generator: ~3/2 = 705.613

Optimal GPV sequence7, 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]]

POTE generator: ~3/2 = 705.518

Vals: 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]]

POTE generator: ~3/2 = 705.344

Vals: 7, 56, 63, 119

Badness: 0.041238