Mint temperaments

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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

Subgroup: 2.3.5

Comma list: 3456/3125

Mapping: [1 1 2], 0 5 3]]

POTE generator: ~25/24 = 140.995

Vals8, 9, 17c

Badness: 0.200483

7-limit

Subgroup: 2.3.5.7

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

Vals8d, 9, 17c

Badness: 0.048356

11-limit

Subgroup: 2.3.5.7.11

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

Vals8d, 9, 17c

Badness: 0.026050

13-limit

Subgroup: 2.3.5.7.11.13

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

Vals8d, 9, 17c

Badness: 0.018158

17-limit

Subgroup: 2.3.5.7.11.13.17

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

Vals8d, 9, 17cg

Badness: 0.016743

19-limit

Subgroup: 2.3.5.7.11.13.17.19

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

Vals8d, 9, 17cg

Badness: 0.016841

Ripple

See also: Ripple family #Ripple

Subgroup: 2.3.5.7

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

Vals12

Badness: 0.059735

11-limit

Subgroup: 2.3.5.7.11

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

Vals12

Badness: 0.038811

13-limit

Subgroup: 2.3.5.7.11.13

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

Vals12f

Badness: 0.031639

Smate

See also: Smate family #Smate

Subgroup: 2.3.5.7

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

Vals3d, 11d, 14, 17c, 37cd

Badness: 0.077871

11-limit

Subgroup: 2.3.5.7.11

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

Vals14, 17c, 37cde

Badness: 0.042518

13-limit

Subgroup: 2.3.5.7.11.13

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

Vals14, 17c

Badness: 0.036836

Subklei

5-limit

Subgroup: 2.3.5

Comma list: 17496/15625

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

POTE generator: ~6/5 = 284.293

Vals4, 17c, 21, 38c

Badness: 0.355937

7-limit

Subgroup: 2.3.5.7

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

Vals4, 17c, 21, 38c

Badness: 0.061101

11-limit

Subgroup: 2.3.5.7.11

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

Vals17c, 55cd

Badness: 0.044651

13-limit

Subgroup: 2.3.5.7.11.13

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

Vals17c

Badness: 0.032324

Subkla

Subgroup: 2.3.5.7.11

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

Vals4, 17c, 21, 38ce, 55cde

Badness: 0.047247

13-limit

Subgroup: 2.3.5.7.11.13

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

Vals4, 17c, 21, 38ce, 55cde

Badness: 0.036701

Slurpee

5-limit

Subgroup: 2.3.5

Comma list: 177147/156250

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

POTE generator: ~27/25 = 72.742

Vals16, 17c, 33

Badness: 0.689274

7-limit

Subgroup: 2.3.5.7

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

Vals16, 17c, 33, 50cd, 83bcd

Badness: 0.114869

11-limit

Subgroup: 2.3.5.7.11

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

Vals16, 17c, 33, 50cd, 83bcd

Badness: 0.050514

13-limit

Subgroup: 2.3.5.7.11.13

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

Vals16, 17c, 33, 83bcd

Badness: 0.033102

Penta

See also: Gamelismic clan #Gidorah

Subgroup: 2.3.5.7

Comma list: 28/25, 36/35

Mapping: [1 1 2 2], 0 3 2 4]]

Wedgie⟨⟨3 2 4 -4 -2 4]]

POTE generator: ~6/5 = 239.977

Vals1bd, 5

Badness: 0.046882