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. In a sense, what father is all about is using semisixths or subfourths and pretending that's 5-limit, and like any temperament which seems to involve pretending, father is at the edge of what can sensibly be called a temperament at all. In other words, it is an exotemperament.
Father
Subgroup: 2.3.5
Comma list: 16/15
Mapping: [⟨1 0 4], ⟨0 1 -1]]
Mapping generators: ~2, ~3
POTE generator: ~3/2 = 743.986
- 5-odd-limit: ~3/2 = [1 1/2 -1/2⟩
- Eigenmonzos (unchanged-intervals): 2, 6/5
Optimal ET sequence: 1, 2, 3, 5, 8, 13c, 21bcc
Badness: 0.014884
Septimal 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
11-limit
Subgroup: 2.3.5.7.11
Comma list: 16/15, 22/21, 28/27
Mapping: [⟨1 0 4 -2 -3], ⟨0 1 -1 3 4]]
POTE generator: ~3/2 = 747.156
Optimal ET sequence: 2de, 3de, 5, 8d
Badness: 0.020589
Mother
Subgroup: 2.3.5.7
Comma list: 16/15, 21/20
Mapping: [⟨1 0 4 6], ⟨0 1 -1 -2]]
Wedgie: ⟨⟨ 1 -1 -2 -4 -6 -2 ]]
POTE generator: ~3/2 = 721.569
Optimal ET sequence: 2, 3, 5
Badness: 0.024152
11-limit
Subgroup: 2.3.5.7.11
Comma list: 11/10, 16/15, 21/20
Mapping: [⟨1 0 4 6 5], ⟨0 1 -1 -2 -1]]
POTE generator: ~3/2 = 717.364
Optimal ET sequence: 2, 3, 5
Badness: 0.021957
Pater
Subgroup: 2.3.5.7
Comma list: 16/15, 126/125
Mapping: [⟨1 0 4 11], ⟨0 1 -1 -5]]
Wedgie: ⟨⟨ 1 -1 -5 -4 -11 -9 ]]
POTE generator: ~3/2 = 753.113
Optimal ET sequence: 3, 5d, 8d
Badness: 0.053001
11-limit
Subgroup: 2.3.5.7.11
Comma list: 16/15, 22/21, 100/99
Mapping: [⟨1 0 4 11 10], ⟨0 1 -1 -5 -4]]
POTE generator: ~3/2 = 751.396
Optimal ET sequence: 3, 5de, 8d
Badness: 0.035487
Baba
Subgroup: 2.3.5.7
Comma list: 16/15, 49/45
Mapping: [⟨1 0 4 2], ⟨0 2 -2 1]]
Mapping generators: ~2, ~7/4
POTE generator: ~7/4 = 973.296
Wedgie: ⟨⟨ 2 -2 1 -8 -4 8 ]]
Optimal ET sequence: 5, 11b, 16bc
Badness: 0.044321
11-limit
Subgroup: 2.3.5.7.11
Comma list: 16/15, 22/21, 49/45
Mapping: [⟨1 0 4 2 1], ⟨0 2 -2 1 3]]
POTE generator: ~7/4 = 978.164
Optimal ET sequence: 5, 11b, 16bc, 27bbcc
Badness: 0.036538
Walid
Subgroup: 2.3.5.7
Comma list: 16/15, 50/49
Mapping: [⟨2 0 8 9], ⟨0 1 -1 -1]]
Mapping generators: ~7/5, ~3
Wedgie: ⟨⟨ 2 -2 -2 -8 -9 1 ]]
POTE generator: ~3/2 = 749.415
Optimal ET sequence: 2, 6, 8d
Badness: 0.048978
11-limit
Subgroup: 2.3.5.7.11
Comma list: 16/15, 22/21, 50/49
Mapping: [⟨2 0 8 9 7], ⟨0 1 -1 -1 0]]
POTE generator: ~3/2 = 749.756
Optimal ET sequence: 2, 6, 8d
Badness: 0.029193
Ternary
Subgroup: 2.3.5.7
Comma list: 10/9, 16/15
Mapping: [⟨3 5 7 0], ⟨0 0 0 1]]
Mapping generators: ~5/4, ~7
Wedgie: ⟨⟨ 0 0 3 0 5 7 ]]
POTE generator: ~7/4 = 1034.013
Optimal ET sequence: 3d, 6, 9bd, 15bbd
Badness: 0.028673
11-limit
Subgroup: 2.3.5.7.11
Comma list: 10/9, 16/15, 22/21
Mapping: [⟨3 5 7 0 2], ⟨0 0 0 1 1]]
POTE generator: ~7/4 = 1033.153
Optimal ET sequence: 3de, 6, 15bbdee
Badness: 0.025592
Quint
Subgroup: 2.3.5.7
Comma list: 16/15, 27/25
Mapping: [⟨5 8 12 0], ⟨0 0 0 1]]
Mapping generators: ~9/8, ~7
Wedgie: ⟨⟨ 0 0 5 0 8 12 ]]
POTE generator: ~7/4 = 1017.903
Badness: 0.048312