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Dual-fifth temperaments: Difference between revisions

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changed 3⁻.9 to 3⁻.3⁺ as per Fumica and frostburn's suggestion in Discord, added mappings
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Todo: explicitly write out vals
Todo: explicitly write out commas and vals for Dual-3 Octokaidecal


== Dual-3 A-Team ==
== Dual-3 A-Team ==
Subgroup: 2.3⁻.9.5
[[Subgroup]]: 2.3⁻.3⁺.5


Comma list: 81/80, {{monzo| -8 -3 4 0 }}
[[Comma]]s: [[81/80|{{monzo| -4 2 2 -1 }}]], {{monzo| -8 1 4 0 }}


Mapping: [{{val| 1 0 2 0 }}, {{val| 0 4 3 6 }}]
Mapping: [{{val| 1 0 2 0 }}, {{val| 0 4 -1 6 }}]


2.9.5 POTE generator: 464.1591
2.9.5 [[POTE]] generator: 464.1591


{{Optimal ET sequence|legend=1| 13, 18, 31 }}
{{Optimal ET sequence|legend=1| 13, 18, 31 }}


== Dual-3 Sixix ==
== Dual-3 Sixix ==
Subgroup: 2.3⁻.9.5
[[Subgroup]]: 2.3⁻.3⁺.5


Comma list: 81/80, {{monzo| 2 -3 0 1 }}
[[Comma]]s: [[81/80|{{monzo| -4 2 2 -1 }}]], {{monzo| 2 -3 0 1 }}


Mapping: [{{val| 1 2 4 4 }}, {{val| 0 -2 -3 -6 }}]
Mapping: [{{val| 1 0 1 -2 }}, {{val| 0 2 1 6 }}]


2.9.5 POTE generator: 335.8409
2.9.5 [[POTE]] generator: 335.8409


{{Optimal ET sequence|legend=1| 18, 25, 43 }}
{{Optimal ET sequence|legend=1| 18, 25, 43 }}


== Dual-3 Octokaidecal ==
== Dual-3 Octokaidecal ==
Subgroup: 2.3⁻.9.5
[[Subgroup]]: 2.3⁻.3⁺.5


2.9.5 [[POTE]] generator: 730.0679
2.9.5 [[POTE]] generator: 730.0679
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== Megapyth ==
== Megapyth ==
Subgroup: 2.3-.3+.5.7
[[Subgroup]]: 2.3⁻.3⁺.5.7


2.9.5.7 [[POTE]] generator: ~3+/2 = 715.319
[[Comma]]s: {{monzo| -4 3 1 -1 0 }}, {{monzo| 6 0 -2 0 -1 }}, {{monzo| -5 -1 6 0 0 }}


[[Comma]]s: 2.3-.3+.5.7[-4 3 1 -1 0], 2.3-.3+.5.7[6 0 -2 0 -1], 2.3-.3+.5.7[-5 -1 6 0 0]
Mapping: [{{val| 1 1 1 0 4 }}, {{val| 0 6 1 19 -2 }}]


{{Optimal ET sequence|47b, 52b}}
2.9.5.7 [[POTE]] generator: ~3⁺/2 = 715.319
 
{{Optimal ET sequence|legend=1|47b, 52b}}


== Duofamity (Rank-3) ==
== Duofamity (Rank-3) ==
Subgroup: 2.3-.3+.5.7
[[Subgroup]]: 2.3⁻.3⁺.5.7


Generators: 2, 3-, 3+
Generators: 2, 3⁻, 3⁺


Least-squares for 5/4, 9/8, and 8/7: 690.155, 715.325
Least-squares for 5/4, 9/8, and 8/7: 690.155, 715.325


[[Comma]]s: 2.3-.3+.5.7[-4 3 1 -1 0], 2.3-.3+.5.7[6 0 -2 0 -1]  
[[Comma]]s: {{monzo| -4 3 1 -1 0 }}, {{monzo| 6 0 -2 0 -1 }}
 
Mapping: [{{val| 1 0 0 -4 6 }}, {{val| 0 1 0 3 0 }}, {{val| 0 0 1 1 -2 }}]


{{Optimal ET sequence|30c, 47b, 52b}}
{{Optimal ET sequence|legend=1|30c, 47b, 52b}}


== Travesty ==
== Travesty ==
[[Subgroup]]: 2.3.5.97
[[Subgroup]]: 2.3.5.97


[[Comma list]]: [[177147/163840]], 2619/2560
[[Comma]]s: [[177147/163840]], 2619/2560


{{Mapping|legend=2|1 1 -4 2|0 1 11 8}}
{{Mapping|legend=2|1 1 -4 2|0 1 11 8}}
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