Trienstonic clan

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The trienstonic clan of temperaments tempers out 28/27, the septimal third-tone or trienstonic comma.

Adding 16/15 to 28/27 leads to father temperament, adding 256/245 gives uncle, adding 50/49 gives octokaidecal and adding 126/125 gives opossum. Other members of the clan discussed elsewhere are sharp, blacksmith, and sharptone.

No-fives trienstonic

Subgroup: 2.3.7

Comma list: 28/27

Sval mapping: [1 0 -2], 0 1 3]]

Gencom mapping: [1 0 0 -2], 0 1 0 3]]

POTE generator: ~3/2 = 721.5586

Vals2d, 3d, 5, 78bb

Father

See also: Father family #Father

Subgroup: 2.3.5.7

Comma list: 16/15, 28/27

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

Wedgie⟨⟨1 -1 3 -4 2 10]]

POTE generator: ~3/2 = 742.002

Minimax tuning:

Eigenmonzos (unchanged intervals): 2, 7/5
Eigenmonzos (unchanged intervals): 2, 9/7

Vals2d, 3d, 5, 8d, 13cd, 21bccdd

Badness: 0.021312

Uncle

Subgroup: 2.3.5.7

Comma list: 28/27, 256/245

Mapping: [1 0 12 -2], 0 1 -6 3]]

Wedgie⟨⟨1 -6 3 -12 2 24]]

POTE generator: ~3/2 = 731.177

Minimax tuning:

Vals5, 13d, 18, 23bc, 41bcd

Badness: 0.072653

Wallaby

See also: Pelogic family

Subgroup: 2.3.5.7

Comma list: 28/27, 35/32

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

Wedgie⟨⟨1 -3 3 -7 2 15]]

POTE generator: ~3/2 = 691.351

Vals2d, 5c, 19ccdd

Badness: 0.058468

Octokaidecal

5-limit (supersharp)

Subgroup: 2.3.5

Comma list: 800/729

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

POTE generator: ~3/2 = 729.0966

Vals8, 10, 18, 28b

Badness: 0.123

7-limit

Subgroup: 2.3.5.7

Comma list: 28/27, 50/49

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

Wedgie⟨⟨2 6 6 5 4 -2]]

POTE generator: ~3/2 = 728.874

Minimax tuning:

Vals8d, 10, 18, 28b

Badness: 0.036747

11-limit

Subgroup: 2.3.5.7.11

Comma list: 28/27, 50/49, 55/54

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

POTE generator: ~3/2 = 732.330

Vals: 8d, 10, 18e

Badness: 0.030235

Opossum

See also: Porcupine family

Subgroup: 2.3.5.7

Comma list: 28/27, 126/125

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

Wedgie⟨⟨3 5 9 1 6 7]]

POTE generator: ~10/9 = 159.691

Minimax tuning:

Vals7d, 8d, 15

Badness: 0.040650

11-limit

Subgroup: 2.3.5.7.11

Comma list: 28/27, 55/54, 77/75

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

POTE generator: ~10/9 = 159.807

Minimax tuning:

  • 11-odd-limit eigenmonzo subgroup: 2.7

Vals: 7d, 8d, 15

Badness: 0.022325

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 28/27, 40/39, 55/54, 66/65

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

POTE generator: ~10/9 = 159.805

Minimax tuning:

  • 13-odd-limit eigenmonzo subgroup: 2.7
  • 15-odd-limit eigenmonzo subgroup: 2.7

Vals: 7d, 8d, 15, 38bcef

Badness: 0.019389

Kangaroo

Subgroup: 2.3.5

Comma list: 64000/59049

Mapping: [1 0 -3], 0 3 10]]

POTE generator: ~27/20 = 561.195

Vals15, 47b, 62b

Badness: 0.295767

7-limit

Subgroup: 2.3.5.7

Comma list: 28/27, 1029/1000

Mapping: [1 0 -3 -2], 0 3 10 9]]

Wedgie⟨⟨3 10 9 9 6 -7]]

POTE generator: ~7/5 = 560.328

Vals15

Badness: 0.077857

11-limit

Subgroup: 2.3.5.7.11

Comma list: 28/27, 77/75, 245/242

Mapping: [1 0 -3 -2 -4], 0 3 10 9 14]]

POTE generator: ~7/5 = 560.155

Vals: 15

Badness: 0.043195

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 28/27, 40/39, 77/75, 147/143

Mapping: [1 0 -3 -2 -4 0], 0 3 10 9 14 7]]

POTE generator: ~7/5 = 559.770

Vals: 15

Badness: 0.032653

Quindecic

Subgroup: 2.3.5.7.11.13

Comma list: 28/27, 49/48, 55/54, 77/75

Mapping: [15 24 35 42 52 0], 0 0 0 0 0 1]]

POTE generator: ~13/8 = 852.924

Vals: 15, 30, 45bc

Badness: 0.028944