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

Minimax tuning:

• 5-odd-limit: ~3/2 = [1 1/2 -1/2⟩

Eigenmonzos (unchanged intervals): 2, 6/5

Badness: 0.014884

Septimal father

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: ~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

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 GPV sequence: Template:Val list

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

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 GPV sequence: Template:Val list

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

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 GPV sequence: Template:Val list

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 ]]

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 GPV sequence: Template:Val list

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

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 GPV sequence: Template:Val list

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

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 GPV sequence: Template:Val list

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