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⁻. | [[Subgroup]]: 2.3⁻.3⁺.5 | ||
Comma | [[Comma]]s: [[81/80|{{monzo| -4 2 2 -1 }}]], {{monzo| -8 1 4 0 }} | ||
Mapping: [{{val| 1 0 2 0 }}, {{val| 0 4 | 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⁻. | [[Subgroup]]: 2.3⁻.3⁺.5 | ||
Comma | [[Comma]]s: [[81/80|{{monzo| -4 2 2 -1 }}]], {{monzo| 2 -3 0 1 }} | ||
Mapping: [{{val| 1 2 | 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⁻. | [[Subgroup]]: 2.3⁻.3⁺.5 | ||
2.9.5 [[POTE]] generator: 730.0679 | 2.9.5 [[POTE]] generator: 730.0679 | ||
| Line 31: | Line 31: | ||
== Megapyth == | == Megapyth == | ||
Subgroup: 2. | [[Subgroup]]: 2.3⁻.3⁺.5.7 | ||
[[Comma]]s: {{monzo| -4 3 1 -1 0 }}, {{monzo| 6 0 -2 0 -1 }}, {{monzo| -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. | [[Subgroup]]: 2.3⁻.3⁺.5.7 | ||
Generators: 2, | 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: | [[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 | [[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}} | ||
Revision as of 20:33, 16 January 2024
Todo: explicitly write out commas and vals for Dual-3 Octokaidecal
Dual-3 A-Team
Subgroup: 2.3⁻.3⁺.5
Commas: [-4 2 2 -1⟩, [-8 1 4 0⟩
Mapping: [⟨1 0 2 0], ⟨0 4 -1 6]]
2.9.5 POTE generator: 464.1591
Optimal ET sequence: 13, 18, 31
Dual-3 Sixix
Subgroup: 2.3⁻.3⁺.5
Commas: [-4 2 2 -1⟩, [2 -3 0 1⟩
Mapping: [⟨1 0 1 -2], ⟨0 2 1 6]]
2.9.5 POTE generator: 335.8409
Optimal ET sequence: 18, 25, 43
Dual-3 Octokaidecal
Subgroup: 2.3⁻.3⁺.5
2.9.5 POTE generator: 730.0679
Megapyth
Subgroup: 2.3⁻.3⁺.5.7
Commas: [-4 3 1 -1 0⟩, [6 0 -2 0 -1⟩, [-5 -1 6 0 0⟩
Mapping: [⟨1 1 1 0 4], ⟨0 6 1 19 -2]]
2.9.5.7 POTE generator: ~3⁺/2 = 715.319
Duofamity (Rank-3)
Subgroup: 2.3⁻.3⁺.5.7
Generators: 2, 3⁻, 3⁺
Least-squares for 5/4, 9/8, and 8/7: 690.155, 715.325
Commas: [-4 3 1 -1 0⟩, [6 0 -2 0 -1⟩
Mapping: [⟨1 0 0 -4 6], ⟨0 1 0 3 0], ⟨0 0 1 1 -2]]
Optimal ET sequence: 30c, 47b, 52b
Travesty
Subgroup: 2.3.5.97
Commas: 177147/163840, 2619/2560
Subgroup-val mapping: [⟨1 1 -4 2], ⟨0 1 11 8]]
CTE generator: ~3/2 = 689.886
Supporting ETs: 7, 40, 33, 26[+5], 47, 19[+5, +97], 54[-3], 61[-3, -5, -97], 68[-3, -5, -97]