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 sharptone, sharp, and blacksmith.
Father
Comma list: 16/15, 28/27
POTE generator: ~3/2 = 742.002
Mapping: [⟨1 0 4 -2], ⟨0 1 -1 3]]
Wedgie: ⟨⟨1 -1 3 -4 2 10]]
Minimax tuning:
- 7-odd-limit
- [[1 0 0 0⟩, [3/2 0 -1/4 1/4⟩, [5/2 0 1/4 -1/4⟩, [5/2 0 -3/4 3/4⟩]
- Eigenmonzo subgroup: 2.7/5
- 9-odd-limit
- Eigenmonzo subgroup: 2.9/5
Badness: 0.0213
Uncle
Comma list: 28/27, 256/245
Mapping: [⟨1 0 12 -2], ⟨0 1 -6 3]]
Wedgie: ⟨⟨1 -6 3 -12 2 24]]
Minimax tuning:
- 7-odd-limit eigenmonzo subgroup: 2.5/3
- 9-odd-limit eigenmonzo subgroup: 2.9/5
Badness: 0.0727
Octokaidecal
Comma list: 28/27, 50/49
POTE generator: ~3/2 = 728.874
Mapping: [⟨2 0 -5 -4], ⟨0 1 3 3]]
Wedgie: ⟨⟨2 6 6 5 4 -2]]
Minimax tuning:
- 7-odd-limit eigenmonzo subgroup: 2.5
- 9-odd-limit eigenmonzo subgroup: 2.5
Badness: 0.0367
11-limit
Comma list: 28/27, 50/49, 55/54
POTE generator: ~3/2 = 732.330
Mapping: [⟨2 0 -5 -4 7], ⟨0 1 3 3 0]]
Badness: 0.0302
Opossum
Comma list: 28/27, 126/125
POTE generator: ~10/9 = 159.691
Mapping: [⟨1 2 3 4], ⟨0 -3 -5 -9]]
Wedgie: ⟨⟨3 5 9 1 6 7]]
Minimax tuning:
- 7-odd-limit eigenmonzo subgroup: 2.7
- 9-odd-limit eigenmonzo subgroup: 2.7
Badness: 0.0407
11-limit
Comma list: 28/27, 55/54, 77/75
POTE generator: ~10/9 = 159.807
Mapping: [⟨1 2 3 4 4], ⟨0 -3 -5 -9 -4]]
Minimax tuning: 11-odd-limit eigenmonzo subgroup: 2.7
Badness: 0.0223
13-limit
Comma list: 28/27, 40/39, 55/54, 66/65
POTE generator: ~10/9 = 158.805
Mapping: [⟨1 2 3 4 4 4], ⟨0 -3 -5 -9 -4 -2]]
Minimax tuning:
- 13-odd-limit eigenmonzo subgroup: 2.7
- 15-odd-limit eigenmonzo subgroup: 2.7
Badness: 0.0194
Wallaby
Comma list: 28/27, 35/32
POTE generator: ~3/2 = 691.351
Mapping: [⟨1 0 7 -2], ⟨0 1 -3 3]]
Wedgie: ⟨⟨1 -3 3 -7 2 15]]
Badness: 0.0585
Kangaroo
5-limit
Comma list: 64000/59049
POTE generator: ~27/20 = 561.195
Mapping: [⟨1 0 -3], ⟨0 3 10]]
Badness: 0.2958
7-limit
Comma list: 28/27, 1029/1000
POTE generator: ~7/5 = 560.328
Mapping: [⟨1 0 -3 -2], ⟨0 3 10 9]]
Wedgie: ⟨⟨3 10 9 9 6 -7]]
Badness: 0.0779
11-limit
Comma list: 28/27, 77/75, 245/242
POTE generator: ~7/5 = 560.155
Mapping: [⟨1 0 -3 -2 -4], ⟨0 3 10 9 14]]
Badness: 0.0432
13-limit
Comma list: 28/27, 40/39, 77/75, 147/143
POTE generator: ~7/5 = 559.770
Mapping: [⟨1 0 -3 -2 -4 0], ⟨0 3 10 9 14 7]]
Badness: 0.0327
Quindecic
Comma list: 28/27, 49/48, 55/54, 77/75
POTE generator: ~13/8 = 852.924
Mapping: [⟨15 24 35 42 52 0], ⟨0 0 0 0 0 1]]
Badness: 0.0289