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

See also: Trienstonic clan § 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

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

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

Badness: 0.0242

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

Badness: 0.0530

Walid

Subgroup: 2.3.5.7

Comma list: 16/15, 50/49

Mapping: [⟨2 0 8 9], ⟨0 1 -1 -1]]

Wedgie: ⟨⟨ 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

Wedgie: ⟨⟨ 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]]

Wedgie: ⟨⟨ 0 0 5 0 8 12 ]]

POTE generator: ~8/7 = 182.097

Badness: 0.0483