Father family
The father family of temperaments tempers out 16/15, the just diatonic semitone. This equates 4/3 with 5/4, so these are "fourth-thirds", or father, temperaments.
Father
Subgroup: 2.3.5
Comma list: 16/15
Mapping: [⟨1 0 4], ⟨0 1 -1]]
POTE generator: ~3/2 = 743.986
Badness: 0.0149
7-limit
Subgroup: 2.3.5.7
Comma list: 16/15, 28/27
Mapping: [⟨1 0 4 -2], ⟨0 1 -1 3]]
⟨⟨1 -1 3 -4 2 10]]
POTE generator: ~3/2 = 742.002
- [[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
- Eigenmonzo subgroup: 2.9/5
Badness: 0.0213
Mother
Subgroup: 2.3.5.7
Comma list: 16/15, 21/20
Mapping: [⟨1 0 4 6], ⟨0 1 -1 -2]]
⟨⟨1 -1 -2 -4 -6 -2]]
POTE generator: ~3/2 = 721.569
Badness: 0.0242
Pater
Subgroup: 2.3.5.7
Comma list: 16/15, 126/125
Mapping: [⟨1 0 4 11], ⟨0 1 -1 -5]]
⟨⟨1 -1 -5 -4 -11 -9]]
POTE generator: ~3/2 = 753.113
Badness: 0.0530
Walid
Subgroup: 2.3.5.7
Comma list: 16/15, 50/49
Mapping: [⟨2 0 8 9], ⟨0 1 -1 -1]]
⟨⟨2 -2 -2 -8 -9 1]]
POTE generator: ~3/2 = 749.415
Badness: 0.0490
Baba
Subgroup: 2.3.5.7
Comma list: 16/15, 49/45
Mapping: [⟨1 0 4 2], ⟨0 2 -2 1]]
POTE generator: ~8/7 = 226.704
⟨⟨2 -2 1 -8 -4 8]]
Badness: 0.0443
Quint
Subgroup: 2.3.5.7
Comma list: 16/15, 27/25
Mapping: [⟨5 8 12 0], ⟨0 0 0 -1]]
⟨⟨0 0 5 0 8 12]]
POTE generator: ~8/7 = 182.097
Badness: 0.0483