Trienstonic clan
Adding 16/15 to the trienstonic comma of 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[edit]
Commas: 16/15, 28/27
7-limit minimax
[<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-limit eigenmonzo subgroup: 2.9/5
POTE generator: 742.002
Map: [<1 0 4 -2|, <0 1 -1 3|]
Wedgie: <<1 -1 3 -4 2 10||
EDOs: 5, 8d, 13cd, 21bcd
Badness: 0.0213
Uncle[edit]
Commas: 28/27, 256/245
7-limit eigenmonzo subgroup: 2.5/3
9-limit eigenmonzo subgroup: 2.9/5
Map: [<1 0 12 -2|, <0 1 -6 3|]
Wedgie: <<1 -6 3 -12 2 24||
EDOs: 13d, 18, 23bc, 41bcd
Badness: 0.0727
Octokaidecal[edit]
Commas: 28/27, 50/49
7-limit eigenmonzo subgroup: 2.5
9-limit eigenmonzo subgroup: 2.5
POTE generator: 728.874
Map: [<2 0 -5 -4|, <0 1 3 3|]
Wedgie: <<2 6 6 5 4 -2||
EDOs: 10, 18, 28b
Badness: 0.0367
11-limit[edit]
Commas: 28/27, 50/49, 55/54
POTE generator: ~3/2 = 732.330
Map: [<2 0 -5 -4 7|, <0 1 3 3 0|]
EDOs: 10, 18e
Badness: 0.0302
Opossum[edit]
Commas: 28/27, 126/125
7-limit eigenmonzo subgroup: 2.7
9-limit eigenmonzo subgroup: 2.7
POTE generator: ~10/9 = 159.691
Map: [<1 2 3 4|, <0 -3 -5 -9|]
Wedgie: <<3 5 9 1 6 7||
EDOs: 7d, 8d, 15
Badness: 0.0407
11-limit[edit]
Commas: 28/27, 55/54, 77/75
11-limit eigenmonzo subgroup: 2.7
POTE generator: ~10/9 = 159.807
Map: [<1 2 3 4 4|, <0 -3 -5 -9 -4|]
EDOs: 7d, 8d, 15
Badness: 0.0223
13-limit[edit]
Commas: 28/27, 40/39, 55/54, 66/65
13-limit eigenmonzo subgroup: 2.7
15-limit eigenmonzo subgroup: 2.7
POTE generator: ~10/9 = 158.805
Map: [<1 2 3 4 4 4|, <0 -3 -5 -9 -4 -2|]
EDOs: 7d, 8d, 15, 38bcef
Badness: 0.0194
Wallaby[edit]
Commas: 28/27, 35/32
POTE generator: ~3/2 = 691.351
Map: [<1 0 7 -2|, <0 1 -3 3|]
Wedgie: <<1 -3 3 -7 2 15||
EDOs: 2d, 5c, 19ccdd
Badness: 0.0585
Kangaroo[edit]
Comma: 64000/59049
POTE generator: ~27/20 = 561.195
Map: [<1 0 -3|, <0 3 10|]
EDOs: 15, 47b, 62b
Badness: 0.2958
7-limit[edit]
Commas: 28/27, 1029/1000
POTE generator: ~7/5 = 560.328
Map: [<1 0 -3 -2|, <0 3 10 9|]
Wedgie: <<3 10 9 9 6 -7||
EDOs: 15
Badness: 0.0779
11-limit[edit]
Commas: 28/27, 77/75, 245/242
POTE generator: ~7/5 = 560.155
Map: [<1 0 -3 -2 -4|, <0 3 10 9 14|]
EDOs: 15
Badness: 0.0432
13-limit[edit]
Commas: 28/27, 40/39, 77/75, 147/143
POTE generator: ~7/5 = 559.770
Map: [<1 0 -3 -2 -4 0|, <0 3 10 9 14 7|]
EDOs: 15
Badness: 0.0327
Quindecic[edit]
Commas: 28/27, 49/48, 55/54, 77/75
POTE generator: ~13/8 = 852.924
Map: [<15 24 35 42 52 0|, <0 0 0 0 0 1|]
EDOs: 15, 30, 45bc
Badness: 0.0289