Trienstonic clan
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 → Dicot family
- Blacksmith → Archytas clan
- Sharptone → Meantone family
- Opossum → Porcupine family
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
Optimal ET sequence: 2d, 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
- 7-odd-limit: ~3/2 = [1/2 0 -1/4 1/4⟩
- eigenmonzos (unchanged-intervals): 2, 7/5
- 9-odd-limit: ~3/2 = [1 -2 0 1⟩ = 14/9
- eigenmonzos (unchanged-intervals): 2, 9/7
Optimal ET sequence: 2d, 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
- 7-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.5/3
- 9-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.9/5
Optimal ET sequence: 5, 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
Optimal ET sequence: 2d, 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 = 729.097
Optimal ET sequence: 8, 10, 18, 28b
Badness: 0.122848
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
- 7-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.5
- 9-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.5
Optimal ET sequence: 8d, 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
Optimal ET sequence: 8d, 10, 18e
Badness: 0.030235
Kangaroo
- For the 5-limit version of this temperament, see High badness temperaments #Kangaroo.
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
Optimal ET sequence: 2cd, 13cd, 15
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
Badness: 0.043195
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 28/27, 40/39, 66/65, 147/143
Mapping: [⟨1 0 -3 -2 -4 0], ⟨0 3 10 9 14 7]]
POTE generator: ~7/5 = 559.770
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
Optimal ET sequence: 15, 30, 45bc
Badness: 0.028944