Keenanismic family: Difference between revisions
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[[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 }}] | [[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] | Generators: ~2, ~3, ~5, ~7 | ||
[[Transpose]]: [2 3 5 7 385/35] | |||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* [[11-odd-limit]] | |||
: [{{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 }}] | : [{{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 | ||
| Line 25: | Line 28: | ||
[[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 }}] | [[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] | Generators: ~2, ~3, ~5, ~7 | ||
[[Transpose]]: [2 3 5 7 385/35 324/25] | |||
[[Minimax tuning]]: | [[Minimax tuning]]: {{confirm}} <!-- contradiction with the data in Rank-4 temperament --> | ||
: [{{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 }}] | : [{{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 | ||
| Line 42: | Line 47: | ||
[[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 }}] | [[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] | Generators: ~2, ~3, ~5, ~7 | ||
[[Transpose]]: [2 3 5 7 385/35 625/48] | |||
{{Val list|legend=1| 6, 15, 19, 22, 31, 50, 53, 72, 87, 103, 140, 159, 190 }} | {{Val list|legend=1| 6, 15, 19, 22, 31, 50, 53, 72, 87, 103, 140, 159, 190 }} | ||
Revision as of 07:57, 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]]
Generators: ~2, ~3, ~5, ~7
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]]
Generators: ~2, ~3, ~5, ~7
Transpose: [2 3 5 7 385/35 324/25]
Minimax tuning: [to be confirmed]
- [[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]]
Generators: ~2, ~3, ~5, ~7
Transpose: [2 3 5 7 385/35 625/48]
Badness: 2.573 × 10-6