Mint temperaments

These are low complexity, high error temperaments tempering out the septimal quarter-tone, 36/35. 36 is both a square and a triangular number, and this helps make 36/35 a septimal interval of considerable significance. Temperaments tempering it out include beep, dicot, dominant, father, diminished, august, hystrix, penta, hexadecimal, ripple and gorgo.

Progression

5-limit

Comma list: 3456/3125

Mapping: [⟨1 1 2], ⟨0 5 3]]

POTE generator: ~25/24 = 140.995

Badness: 0.2005

7-limit

Comma list: 36/35, 392/375

Mapping: [⟨1 1 2 2], ⟨0 5 3 7]]

Wedgie: ⟨⟨ 5 3 7 -7 -3 8 ]]

POTE generator: ~15/14 = 140.927

Badness: 0.0484

11-limit

Comma list: 36/35, 56/55, 77/75

Mapping: [⟨1 1 2 2 3], ⟨0 5 3 7 4]]

POTE generators: ~12/11 = 140.747

Badness: 0.0261

13-limit

Comma list: 26/25, 36/35, 56/55, 66/65

Mapping: [⟨1 1 2 2 3 3], ⟨0 5 3 7 4 6]]

POTE generators: ~13/12 = 140.751

Badness: 0.0182

17-limit

Comma list: 26/25, 36/35, 51/50, 56/55, 66/65

Mapping: [⟨1 1 2 2 3 3 4], ⟨0 5 3 7 4 6 1]]

POTE generators: ~13/12 = 141.404

Badness: 0.0167

19-limit

Comma list: 26/25, 36/35, 51/50, 56/55, 57/55, 66/65

Mapping: [⟨1 1 2 2 3 3 4 4], ⟨0 5 3 7 4 6 1 2]]

POTE generators: ~13/12 = 140.479

Badness: 0.0168

Ripple

See also: Ripple family § Ripple

Comma list: 36/35, 2560/2401

Mapping: [⟨1 2 3 3], ⟨0 -5 -8 -2]]

Wedgie: ⟨⟨ 5 8 2 1 -11 -18 ]]

POTE generator: ~21/20 = 99.483

Badness: 0.0597

11-limit

Comma list: 36/35, 80/77, 126/121

Mapping: [⟨1 2 3 3 4], ⟨0 -5 -8 -2 -6]]

POTE generator: ~21/20 = 99.385

Badness: 0.0388

13-limit

Comma list: 36/35, 40/39, 66/65, 147/143

Mapping: [⟨1 2 3 3 4 4], ⟨0 -5 -8 -2 -6 -3]]

POTE generator: ~21/20 = 98.572

Badness: 0.0316

Smate

See also: Smate family § Smate

Comma list: 36/35, 2048/1875

Mapping: [⟨1 3 2 6], ⟨0 -4 1 -9]]

Wedgie: ⟨⟨ 4 -1 9 -11 3 24 ]]

POTE generator: ~5/4 = 422.275

Badness: 0.0779

11-limit

Comma list: 36/35, 56/55, 243/242

Mapping: [⟨1 3 2 6 7], ⟨0 -4 1 -9 -10]]

POTE generator: ~5/4 = 422.217

Badness: 0.0425

13-limit

Comma list: 26/25, 36/35, 56/55, 243/242

Mapping: [⟨1 3 2 6 7 3], ⟨0 -4 1 -9 -10 2]]

POTE generator: ~5/4 = 423.020

Badness: 0.0368

Subklei

5-limit

Comma list: 17496/15625

Mapping: [⟨1 3 4], ⟨0 -6 -7]]

POTE generator: ~6/5 = 284.293

Badness: 0.3559

7-limit

Comma list: 36/35, 1029/1000

Mapping: [⟨1 3 4 4], ⟨0 -6 -7 -5]]

Wedgie: ⟨⟨ 6 7 5 -3 -9 -8 ]]

POTE generator: ~6/5 = 284.219

Badness: 0.0611

11-limit

Comma list: 36/35, 77/75, 352/343

Mapping: [⟨1 3 4 4 7], ⟨0 -6 -7 -5 -15]]

POTE generator: ~6/5 = 283.253

Badness: 0.0447

13-limit

Comma list: 26/25, 36/35, 66/65, 352/343

POTE generator: ~6/5 = 282.856

Mapping: [⟨1 3 4 4 7 7], ⟨0 -6 -7 -5 -15 -14]]

POTE generator: ~6/5 = 282.856

Badness: 0.0323

Subkla

Comma list: 36/35, 56/55, 1029/1000

Mapping: [⟨1 3 4 4 3], ⟨0 -6 -7 -5 2]]

POTE generator: ~6/5 = 283.822

Badness: 0.0472

13-limit

Comma list: 36/35, 56/55, 66/65, 640/637

Mapping: [⟨1 3 4 4 3 3], ⟨0 -6 -7 -5 2 3]]

POTE generator: ~6/5 = 283.882

Badness: 0.0367

Slurpee

5-limit

Comma list: 177147/156250

Mapping: [⟨1 2 3], ⟨0 -7 -11]]

POTE generator: ~27/25 = 72.742

Badness: 0.6893

7-limit

Comma list: 36/35, 51200/50421

Mapping: [⟨1 2 3 3], ⟨0 -7 -11 -3]]

Wedgie: ⟨⟨ 7 11 3 1 -15 -24 ]]

POTE generator: ~21/20 = 72.303

Badness: 0.1149

11-limit

Comma list: 36/35, 121/120, 352/343

Mapping: [⟨1 2 3 3 4], ⟨0 -7 -11 -3 -9]]

POTE generator: ~21/20 = 72.297

Badness: 0.0505

13-limit

Comma list: 36/35. 66/65, 143/140, 352/343

Mapping: [⟨1 2 3 3 4 4], ⟨0 -7 -11 -3 -9 -5]]

POTE generator: ~21/20 = 72.409

Badness: 0.0331