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Keemic family: Difference between revisions

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"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
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== Supermagic  ==
== Supermagic  ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 875/864
[[Comma list]]: 875/864


[[Mapping]]: [{{val| 1 0 0 5 }}, {{val| 0 1 0 3 }}, {{val| 0 0 1 -3 }}]
{{Mapping|legend=1| 1 0 0 5 | 0 1 0 3 | 0 0 1 -3 }}


Mapping generators: ~2, ~3, ~5
: mapping generators: ~2, ~3, ~5


[[Mapping to lattice]]: [{{val| 0 0 -1 3 }}, {{val| 0 1 1 0 }}]
[[Mapping to lattice]]: [{{val| 0 0 -1 3 }}, {{val| 0 1 1 0 }}]
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: Angle (6/5, 3/2) = 77.834
: Angle (6/5, 3/2) = 77.834


[[POTE generator]]s: ~3/2 = 701.8733, ~5/4 = 380.4684
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 701.8733, ~5/4 = 380.4684


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* 7- and [[9-odd-limit]]
* [[7-odd-limit|7-]] and [[9-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 0 1 0 0 }}, {{monzo| 5/4 3/4 1/4 -1/4 }}, {{monzo| 5/4 3/4 -3/4 3/4 }}]
: {{monzo list| 1 0 0 0 | 0 1 0 0 | 5/4 3/4 1/4 -1/4 | 5/4 3/4 -3/4 3/4 }}
: Eigenmonzos: 2, 4/3, 7/5
: [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.3.7/5


{{Optimal ET sequence|legend=1| 7, 15, 19, 41 }}
{{Optimal ET sequence|legend=1| 7, 15, 19, 41 }}
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== Undecimal supermagic ==
== Undecimal supermagic ==
Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 100/99, 385/384
[[Comma list]]: 100/99, 385/384


[[Mapping]]: [{{val| 1 0 0 5 2 }}, {{val| 0 1 0 3 -2 }}, {{val| 0 0 1 -3 2 }}]
{{Mapping|legend=1| 1 0 0 5 2 | 0 1 0 3 -2 | 0 0 1 -3 2 }}


[[POTE generator]]s: ~3/2 = 704.1985, ~5/4 = 381.5394
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 704.1985, ~5/4 = 381.5394


{{Optimal ET sequence|legend=1| 7, 15, 19, 22, 37, 41, 104, 145c, 201ce, 264bce, 305bcce }}
{{Optimal ET sequence|legend=1| 7, 15, 19, 22, 37, 41, 104, 145c, 201ce, 264bce, 305bcce }}
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== Supernatural ==
== Supernatural ==
Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 225/224, 245/243
[[Comma list]]: 225/224, 245/243


[[Mapping]]: [{{val| 1 0 2 -1 0 }}, {{val| 0 5 1 12 0 }}, {{val| 0 0 0 0 1 }}]
{{Mapping|legend=1| 1 0 2 -1 0 | 0 5 1 12 0 | 0 0 0 0 1 }}


[[POTE generator]]s: ~5/4 = 380.3520, ~11/8 = 547.5758
: mapping generators: ~2, ~5, ~11
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~5/4 = 380.3520, ~11/8 = 547.5758


{{Optimal ET sequence|legend=1| 19, 22, 41, 82e, 101cd, 224ccde, 265ccde * }}
{{Optimal ET sequence|legend=1| 19, 22, 41, 82e, 101cd, 224ccde, 265ccde * }}
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Comma list: 105/104, 196/195, 245/243
Comma list: 105/104, 196/195, 245/243


Mapping: [{{val| 1 0 2 -1 0 -2 }}, {{val| 0 5 1 12 0 18 }}, {{val| 0 0 0 0 1 0 }}]
Mapping: {{mapping| 1 0 2 -1 0 -2 | 0 5 1 12 0 18 | 0 0 0 0 1 0 }}


[[POTE generator]]s: ~5/4 = 380.0401, ~11/8 = 546.6672
Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 380.0401, ~11/8 = 546.6672


{{Optimal ET sequence|legend=1| 19, 22f, 41, 60e, 101cd }}
{{Optimal ET sequence|legend=1| 19, 22f, 41, 60e, 101cd }}
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