Father family: Difference between revisions
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In a sense, what father is all about is using [[semisixth]]s or [[subfourth]]s 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]]. | In a sense, what father is all about is using [[semisixth]]s or [[subfourth]]s 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 | == Father == | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
| Line 10: | Line 10: | ||
[[POTE generator]]: ~3/2 = 743.986 | [[POTE generator]]: ~3/2 = 743.986 | ||
[[Minimax tuning]]: | |||
* [[5-odd-limit]]: ~3/2 = {{monzo| 1 1/2 -1/2 }} | |||
: [[Eigenmonzo]]s: 2, 6/5 | |||
{{Val list|legend=1| 1, 2, 3, 5, 8, 13c, 21bcc }} | {{Val list|legend=1| 1, 2, 3, 5, 8, 13c, 21bcc }} | ||
| Line 15: | Line 19: | ||
[[Badness]]: 0.014884 | [[Badness]]: 0.014884 | ||
=== 7-limit | === 7-limit === | ||
{{see also| Trienstonic clan #Father }} | {{see also| Trienstonic clan #Father }} | ||
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[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* [[7-odd-limit]] | * [[7-odd-limit]]: ~3/2 = {{monzo| 1/2 0 -1/4 1/4 }} | ||
: | : [[Eigenmonzo]]s: 2, 7/5 | ||
: [[Eigenmonzo | * [[9-odd-limit]]: ~3/2 = {{monzo| 1 -2 0 1 }} = 14/9 | ||
* [[9-odd-limit]] | : Eigenmonzos: 2, 9/5 | ||
: | |||
{{Val list|legend=1| 2d, 3d, 5, 8d, 13cd, 21bccdd }} | {{Val list|legend=1| 2d, 3d, 5, 8d, 13cd, 21bccdd }} | ||
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[[Badness]]: 0.021312 | [[Badness]]: 0.021312 | ||
== Mother | == Mother == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 54: | Line 57: | ||
[[Badness]]: 0.024152 | [[Badness]]: 0.024152 | ||
== Pater | == Pater == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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[[POTE generator]]: ~3/2 = 753.113 | [[POTE generator]]: ~3/2 = 753.113 | ||
{{Val list|legend=1| 3, 5d, 8d | {{Val list|legend=1| 3, 5d, 8d }} | ||
[[Badness]]: 0.053001 | [[Badness]]: 0.053001 | ||
== Walid | == Walid == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 84: | Line 87: | ||
[[Badness]]: 0.048978 | [[Badness]]: 0.048978 | ||
== Baba | == Baba == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 99: | Line 102: | ||
[[Badness]]: 0.044321 | [[Badness]]: 0.044321 | ||
== Quint | == Quint == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 114: | Line 117: | ||
[[Badness]]: 0.048312 | [[Badness]]: 0.048312 | ||
== Ternary | == Ternary == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
Revision as of 07:36, 6 June 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. 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
- 5-odd-limit: ~3/2 = [1 1/2 -1/2⟩
- Eigenmonzos: 2, 6/5
Badness: 0.014884
7-limit
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
- 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, 9/5
Badness: 0.021312
Mother
Subgroup: 2.3.5.7
Comma list: 16/15, 21/20
Mapping: [⟨1 0 4 6], ⟨0 1 -1 -2]]
Wedgie: ⟨⟨ 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]]
Wedgie: ⟨⟨ 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]]
Wedgie: ⟨⟨ 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
Wedgie: ⟨⟨ 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]]
Wedgie: ⟨⟨ 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]]
Wedgie: ⟨⟨ 0 0 3 0 5 7 ]]
POTE generator: ~8/7 = 165.987
Badness: 0.028673