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| Line 479: |
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| Badness (Sintel): 1.08 | | Badness (Sintel): 1.08 |
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| == Involution ==
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| Involution tempers out the [[45/32|ptolemaic augmented fourth (45/32)]]. Its ploidacot is monocot. It was named by [[User:CompactStar|CompactStar]] in 2023.
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| [[Subgroup]]: 2.3.5
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| [[Comma list]]: [[45/32]]
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| {{Mapping|legend=1| 1 0 5 | 0 1 -2 }}
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| : mapping generators: ~2, ~3
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| [[Optimal tuning]]s:
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| * [[WE]]: ~2 = 1265.406{{c}}, ~3/2 = 552.346{{c}}
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| : [[error map]]: {{val| +65.405 -84.203 -94.789 }}
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| * [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 520.626{{c}}
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| : error map: {{val| 0.000 -181.329 -227.565 }}
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| {{Optimal ET sequence|legend=1| 2c, 5bc, 7bbcc }}
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| [[Badness]] (Sintel): 3.12
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| === 7-limit ===
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| Subgroup: 2.3.5.7
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| Comma list: 8/7, 45/28
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| Mapping: {{mapping| 1 0 5 3 | 0 1 -2 0 }}
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| Optimal tunings:
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| * WE: ~2 = 1205.230{{c}}, ~3/2 = 517.557{{c}}
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| * CWE: ~2 = 1200.000{{c}}, ~3/2 = 515.099{{c}}
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| Optimal ET sequence: none
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| Badness (Sintel): 3.01
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| == Devolution ==
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| Devolution was named by [[User:Akselai|Akselai]] in 2024.
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| [[Subgroup]]: 3.5.7
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| [[Comma list]]: [[35/27]]
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| {{Mapping|legend=1| 1 0 3 | 0 1 -1 }}
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| : mapping generators: ~3, ~5
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| [[Optimal tuning]]s:
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| * [[WE]]: ~3 = 1988.549{{c}}, ~5/3 = 719.679{{c}}
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| : [[error map]]: {{val| +86.594 -78.085 -111.407 }}
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| * [[CWE]]: ~3 = 1901.955{{c}}, ~5/3 = 691.468{{c}}
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| : error map: {{val| 0.000 -192.891 -256.384 }}
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| [[Optimal ET sequence]]: [[1edt|b1]], [[2edt|b2d]], [[3edt|b3]], [[8edt|b8cdd]]
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| [[Badness]] (Sintel): 0.751
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| == Codex == | | == Codex == |
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| {{Optimal ET sequence|legend=1| 1c, …, 6bcd, 7d }}* | | {{Optimal ET sequence|legend=1| 1c, …, 6bcd, 7d }}* |
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| <nowiki/>*[[Optimal patent val]]: [[8edo|8]] | | <nowiki/>* [[Optimal patent val]]: [[8edo|8]] |
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| [[Badness]] (Sintel): 1.52 | | [[Badness]] (Sintel): 1.52 |