Father family: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
m Some cleanup
m Cleanup +1
Line 48: Line 48:


= Pater =
= Pater =
Commas: 16/15, 126/125
Comma list: 16/15, 126/125


POTE generator: ~3/2 = 753.113
POTE generator: ~3/2 = 753.113


Map: [<1 0 4 11|, <0 1 -1 -5|]
Mapping: [{{val| 1 0 4 11 }}, {{val| 0 1 -1 -5 }}]


Wedgie: <<1 -1 -5 -4 -11 -9||
Wedgie: {{wedgie| 1 -1 -5 -4 -11 -9 }}


EDOs: 3, 11b, 16bcd, 27bcd
{{Val list|legend=1| 3, 11b, 16bcd, 27bcd }}


Badness: 0.0530
Badness: 0.0530


= Walid =
= Walid =
Commas: 16/15, 50/49
Comma list: 16/15, 50/49


POTE generator: ~3/2 = 749.415
POTE generator: ~3/2 = 749.415


Map: [<2 0 8 9|, <0 1 -1 -1|]
Mapping: [{{val| 2 0 8 9 }}, {{val| 0 1 -1 -1 }}]


Wedgie: <<2 -2 -2 -8 -9 1||
Wedgie: {{wedgie| 2 -2 -2 -8 -9 1 }}


EDOs: 2, 6, 10cd, 14bd, 16bcd
{{Val list|legend=1| 2, 6, 10cd, 14bd, 16bcd }}


Badness: 0.0490
Badness: 0.0490


= Baba =
= Baba =
Commas: 16/15, 49/45
Comma list: 16/15, 49/45


POTE generator: ~8/7 = 226.704
POTE generator: ~8/7 = 226.704


Map: [<1 0 4 2|, <0 2 -2 1|]
Mapping: [{{val| 1 0 4 2 }}, {{val| 0 2 -2 1 }}]


Wedgie: <<2 -2 1 -8 -4 8||
Wedgie: {{wedgie| 2 -2 1 -8 -4 8 }}


EDOs: 1, 5, 11b, 16bc
{{Val list|legend=1| 1, 5, 11b, 16bc }}


Badness: 0.0443
Badness: 0.0443


= Quint =
= Quint =
Commas: 16/15, 27/25
Comma list: 16/15, 27/25


POTE generator: ~8/7 = 182.097
POTE generator: ~8/7 = 182.097


Map: [<5 8 12 0|, <0 0 0 -1|]
Mapping: [{{val| 5 8 12 0 }}, {{val| 0 0 0 -1 }}]


Wedgie: <<0 0 5 0 8 12||
Wedgie: {{wedgie| 0 0 5 0 8 12 }}


EDOs: 5, 15cd
{{Val list|legend=1| 5, 15cd }}


Badness: 0.0483
Badness: 0.0483

Revision as of 15:09, 10 February 2021

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

Comma list: 16/15

POTE generator: ~3/2 = 743.986

Mapping: [1 0 4], 0 1 -1]]

Template:Val list

Badness: 0.0149

7-limit

Comma list: 16/15, 28/27

POTE generator: ~3/2 = 742.002

Mapping: [1 0 4 -2], 0 1 -1 3]]

Wedgie: ⟨⟨1 -1 3 -4 2 10]]

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

Template:Val list

Badness: 0.0213

Mother

Comma list: 16/15, 21/20

POTE generator: ~3/2 = 721.569

Mapping: [1 0 4 6], 0 1 -1 -2]]

Wedgie: ⟨⟨1 -1 -2 -4 -6 -2]]

Template:Val list

Badness: 0.0242

Pater

Comma list: 16/15, 126/125

POTE generator: ~3/2 = 753.113

Mapping: [1 0 4 11], 0 1 -1 -5]]

Wedgie: ⟨⟨1 -1 -5 -4 -11 -9]]

Template:Val list

Badness: 0.0530

Walid

Comma list: 16/15, 50/49

POTE generator: ~3/2 = 749.415

Mapping: [2 0 8 9], 0 1 -1 -1]]

Wedgie: ⟨⟨2 -2 -2 -8 -9 1]]

Template:Val list

Badness: 0.0490

Baba

Comma list: 16/15, 49/45

POTE generator: ~8/7 = 226.704

Mapping: [1 0 4 2], 0 2 -2 1]]

Wedgie: ⟨⟨2 -2 1 -8 -4 8]]

Template:Val list

Badness: 0.0443

Quint

Comma list: 16/15, 27/25

POTE generator: ~8/7 = 182.097

Mapping: [5 8 12 0], 0 0 0 -1]]

Wedgie: ⟨⟨0 0 5 0 8 12]]

Template:Val list

Badness: 0.0483