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]]

⟨⟨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]]

⟨⟨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]]

⟨⟨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

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

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: Template:Val list

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: Template:Val list

Badness: 0.041238