Father family: Difference between revisions
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| Line 2: | Line 2: | ||
= Father = | = Father = | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
| Line 15: | Line 14: | ||
[[Badness]]: 0.0149 | [[Badness]]: 0.0149 | ||
= 7-limit = | == 7-limit == | ||
{{see also| Trienstonic clan #Father }} | {{see also| Trienstonic clan #Father }} | ||
| Line 37: | Line 36: | ||
{{Val list|legend=1| 2d, 3d, 5, 8d, 13cd, 21bccdd }} | {{Val list|legend=1| 2d, 3d, 5, 8d, 13cd, 21bccdd }} | ||
[[Badness]]: 0. | [[Badness]]: 0.021312 | ||
= Mother = | = Mother = | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 53: | Line 51: | ||
{{Val list|legend=1| 2, 3, 5 }} | {{Val list|legend=1| 2, 3, 5 }} | ||
[[Badness]]: 0. | [[Badness]]: 0.024152 | ||
= Pater = | = Pater = | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 69: | Line 66: | ||
{{Val list|legend=1| 3, 5d, 8d, 27bbccdd, 35bbbcccddd }} | {{Val list|legend=1| 3, 5d, 8d, 27bbccdd, 35bbbcccddd }} | ||
[[Badness]]: 0. | [[Badness]]: 0.053001 | ||
= Walid = | = Walid = | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 85: | Line 81: | ||
{{Val list|legend=1| 2, 6, 8d }} | {{Val list|legend=1| 2, 6, 8d }} | ||
[[Badness]]: 0. | [[Badness]]: 0.048978 | ||
= Baba = | = Baba = | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 101: | Line 96: | ||
{{Val list|legend=1| 5, 11b, 16bc }} | {{Val list|legend=1| 5, 11b, 16bc }} | ||
[[Badness]]: 0. | [[Badness]]: 0.044321 | ||
= Quint = | = Quint = | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
[[Comma list]]: 16/15, 27/25 | [[Comma list]]: 16/15, 27/25 | ||
[[Mapping]]: [{{val| 5 8 12 0 }}, {{val| 0 0 0 | [[Mapping]]: [{{val| 5 8 12 0 }}, {{val| 0 0 0 1 }}] | ||
{{Multival|legend=1| 0 0 5 0 8 12 }} | {{Multival|legend=1| 0 0 5 0 8 12 }} | ||
| Line 117: | Line 111: | ||
{{Val list|legend=1| 5, 15ccd }} | {{Val list|legend=1| 5, 15ccd }} | ||
[[Badness]]: 0. | [[Badness]]: 0.048312 | ||
= Ternary = | |||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 10/9, 16/15 | |||
[[Mapping]]: [{{val| 3 5 7 0 }}, {{val| 0 0 0 1 }}] | |||
{{Multival|legend=1| 0 0 3 0 5 7 }} | |||
[[POTE generator]]: ~8/7 = 165.987 | |||
{{Val list|legend=1| 3, 6, 15bb }} | |||
[[Badness]]: 0.028673 | |||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||
Revision as of 05:36, 4 April 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
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
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
- [[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
- Eigenmonzo subgroup: 2.9/5
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