Father family: Difference between revisions
→Father: Fixed typo Tags: Mobile edit Mobile web edit |
Cmloegcmluin (talk | contribs) adding parenthetical "(unchanged intervals)" to eigenmonzo lists |
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| Line 13: | Line 13: | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* [[5-odd-limit]]: ~3/2 = {{monzo| 1 1/2 -1/2 }} | * [[5-odd-limit]]: ~3/2 = {{monzo| 1 1/2 -1/2 }} | ||
: [[Eigenmonzo]]s: 2, 6/5 | : [[Eigenmonzo]]s (unchanged intervals): 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 34: | Line 34: | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* [[7-odd-limit]]: ~3/2 = {{monzo| 1/2 0 -1/4 1/4 }} | * [[7-odd-limit]]: ~3/2 = {{monzo| 1/2 0 -1/4 1/4 }} | ||
: [[Eigenmonzo]]s: 2, 7/5 | : [[Eigenmonzo]]s (unchanged intervals): 2, 7/5 | ||
* [[9-odd-limit]]: ~3/2 = {{monzo| 1 -2 0 1 }} = 14/9 | * [[9-odd-limit]]: ~3/2 = {{monzo| 1 -2 0 1 }} = 14/9 | ||
: Eigenmonzos: 2, 9/7 | : Eigenmonzos (unchanged intervals): 2, 9/7 | ||
{{Val list|legend=1| 2d, 3d, 5, 8d, 13cd, 21bccdd }} | {{Val list|legend=1| 2d, 3d, 5, 8d, 13cd, 21bccdd }} | ||
Revision as of 18:42, 23 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 (unchanged intervals): 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 (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
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