Keenanismic family: Difference between revisions
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m Cleanup (1/2) |
m Cleanup (2/2) |
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== Keenanismic == | == Keenanismic == | ||
Subgroup: 2.3.5.7.11 | |||
[[Comma list]]: 385/384 | [[Comma list]]: 385/384 | ||
[[Mapping]]: [ | [[Mapping]]: [{{val| 1 0 0 0 7 }}, {{val| 0 1 0 0 1 }}, {{val| 0 0 1 0 -1 }}, {{val| 0 0 0 1 -1 }}] | ||
Transpose: [2 3 5 7 385/35] | Transpose: [2 3 5 7 385/35] | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
: [|1 0 0 0 0 | : [{{monzo| 1 0 0 0 0 }}, {{monzo| 0 1 0 0 0 }}, {{monzo| 7/3 1/3 2/3 -1/3 -1/3 }}, {{monzo| 7/3 1/3 -1/3 2/3 -1/3 }}, {{monzo| 7/3 1/3 -1/3 -1/3 2/3 }}] | ||
: Eigenmonzos: 2, 3, 7/5, 11/5 | : Eigenmonzos: 2, 3, 7/5, 11/5 | ||
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== Martwin == | == Martwin == | ||
Subgroup: 2.3.5.7.11.13 | |||
[[Comma list]]: 385/384 | [[Comma list]]: 325/324, 385/384 | ||
[[Mapping]]: [ | [[Mapping]]: [{{val| 1 0 0 0 7 2 }}, {{val| 0 1 0 0 1 4 }}, {{val| 0 0 1 0 -1 -2 }}, {{val| 0 0 0 1 -1 0 }}] | ||
Transpose: [2 3 5 7 385/35 324/25] | Transpose: [2 3 5 7 385/35 324/25] | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
: | : [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 0 1 0 0 0 0 }}, {{monzo| 2/3 4/3 1/3 0 0 -1/3 }}, {{monzo| 17/3 -5/3 1/3 0 -1 2/3 }}, {{monzo| 2/3 4/3 -2/3 0 1 -1/3 }}, {{monzo| 2/3 4/3 -2/3 0 0 2/3 }}] | ||
: Eigenmonzos: 2, 3, 11/5, 13/5 | : Eigenmonzos: 2, 3, 11/5, 13/5 | ||
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== Ancient == | == Ancient == | ||
Subgroup: 2.3.5.7.11.13 | |||
[[Comma list]]: 385/384, 625/624 | [[Comma list]]: 385/384, 625/624 | ||
[[Mapping]]: [ | [[Mapping]]: [{{val| 1 0 0 0 7 -4 }}, {{val| 0 1 0 0 1 -1 }}, {{val| 0 0 1 0 -1 4 }}, {{val| 0 0 0 1 -1 0 }}] | ||
Transpose: [2 3 5 7 385/35 625/48] | Transpose: [2 3 5 7 385/35 625/48] | ||
Revision as of 07:25, 1 August 2021
The keenanismic family of rank-4 temperaments tempers out the keenanisma, the 11-limit comma 385/384 = [-7 -1 1 1 1⟩ of 4.503 cents.
Keenanismic
Subgroup: 2.3.5.7.11
Comma list: 385/384
Mapping: [⟨1 0 0 0 7], ⟨0 1 0 0 1], ⟨0 0 1 0 -1], ⟨0 0 0 1 -1]]
Transpose: [2 3 5 7 385/35]
- [[1 0 0 0 0⟩, [0 1 0 0 0⟩, [7/3 1/3 2/3 -1/3 -1/3⟩, [7/3 1/3 -1/3 2/3 -1/3⟩, [7/3 1/3 -1/3 -1/3 2/3⟩]
- Eigenmonzos: 2, 3, 7/5, 11/5
Badness: 15.159 × 10-9
Martwin
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 385/384
Mapping: [⟨1 0 0 0 7 2], ⟨0 1 0 0 1 4], ⟨0 0 1 0 -1 -2], ⟨0 0 0 1 -1 0]]
Transpose: [2 3 5 7 385/35 324/25]
- [[1 0 0 0 0 0⟩, [0 1 0 0 0 0⟩, [2/3 4/3 1/3 0 0 -1/3⟩, [17/3 -5/3 1/3 0 -1 2/3⟩, [2/3 4/3 -2/3 0 1 -1/3⟩, [2/3 4/3 -2/3 0 0 2/3⟩]
- Eigenmonzos: 2, 3, 11/5, 13/5
Badness: 2.206 × 10-6
Ancient
Subgroup: 2.3.5.7.11.13
Comma list: 385/384, 625/624
Mapping: [⟨1 0 0 0 7 -4], ⟨0 1 0 0 1 -1], ⟨0 0 1 0 -1 4], ⟨0 0 0 1 -1 0]]
Transpose: [2 3 5 7 385/35 625/48]
Badness: 2.573 × 10-6