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]]

POTE generator: ~3/2 = 743.986

Minimax tuning:

• 5-odd-limit: ~3/2 = [1 1/2 -1/2⟩

Eigenmonzos: 2, 6/5

Badness: 0.014884

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]]

⟨⟨1 -1 3 -4 2 10]]

POTE generator: ~3/2 = 742.002

Minimax tuning:

• 7-odd-limit: ~3/2 = [1/2 0 -1/4 1/4⟩

Eigenmonzos: 2, 7/5

• 9-odd-limit: ~3/2 = [1 -2 0 1⟩ = 14/9

Eigenmonzos: 2, 9/7

Badness: 0.021312

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: 0.024152

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: 0.053001

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: 0.048978

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: 0.044321

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: 0.048312

Ternary

Subgroup: 2.3.5.7

Comma list: 10/9, 16/15

Mapping: [⟨3 5 7 0], ⟨0 0 0 1]]

⟨⟨0 0 3 0 5 7]]

POTE generator: ~8/7 = 165.987

Badness: 0.028673