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| [[Badness]] (Sintel): 1.22 | | [[Badness]] (Sintel): 1.22 |
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| == Sept ==
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| {{See also| Whitewood family }}
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| Sept preserves the 2.3.7-subgroup of mapping of 7edo, and harmonic 5 is mapped to an independent generator. As harmonic 5 is way more accurately approximated than 7 by 7edo, this temperament provides little improvement to 7edo's 7-limit tuning, so in what way this temperament is useful remains unexplained. It would make much more sense to, for example, preserve the 5-limit structure of 7edo and give prime 7 an independent generator instead, which is exactly what [[jamesbond]] does.
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| This temperament used to be known as ''mujannab''.
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| [[Subgroup]]: 2.3.5.7
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| [[Comma list]]: 54/49, 64/63
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| {{Mapping|legend=1| 7 11 0 20 | 0 0 1 0 }}
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| [[Optimal tuning]]s:
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| * [[WE]]: ~9/8 = 170.823{{c}}, ~5/4 = 393.792{{c}} (~15/14 = 52.145{{c}})
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| : [[error map]]: {{val| -4.236 -22.898 -0.994 +47.642 }}
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| * [[CWE]]: ~9/8 = 171.429{{c}}, ~5/4 = 392.719{{c}} (~15/14 = 49.862{{c}})
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| : error map: {{val| 0.000 -16.241 +6.406 +59.746 }}
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| {{Optimal ET sequence|legend=1| 7, 14d }}
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| [[Badness]] (Sintel): 2.68
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 45/44, 54/49, 64/63
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| Mapping: {{mapping| 7 11 0 20 8 | 0 0 1 0 1 }}
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| Optimal tunings:
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| * WE: ~11/10 = 170.817{{c}}, ~5/4 = 393.252{{c}} (~33/32 = 51.619{{c}})
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| * CWE: ~11/10 = 171.429{{c}}, ~5/4 = 391.840{{c}} (~33/32 = 48.983{{c}})
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| {{Optimal ET sequence|legend=0| 7, 14de }}
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| Badness (Sintel): 2.02
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| === 13-limit ===
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 27/26, 45/44, 52/49, 64/63
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| Mapping: {{mapping| 7 11 0 20 8 26 | 0 0 1 0 1 0 }}
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| Optimal tunings:
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| * WE: ~11/10 = 170.795{{c}}, ~5/4 = 393.611{{c}} (~33/32 = 52.021{{c}})
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| * CWE: ~11/10 = 171.429{{c}}, ~5/4 = 392.725{{c}} (~33/32 = 49.868{{c}})
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| {{Optimal ET sequence|legend=0| 7, 14de }}
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| Badness (Sintel): 1.77
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| == Geryon == | | == Geryon == |
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Line 578: |
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| [[Badness]] (Sintel): 1.52 | | [[Badness]] (Sintel): 1.52 |
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| == Bixby ==
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| {{Main| Bixby }}
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| [[Subgroup]]: 2.3.5
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| [[Comma list]]: [[4/3]]
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| {{Mapping|legend=1| 1 2 0 | 0 0 1 }}
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| [[Optimal tuning]]s:
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| * [[WE]]: ~2 = 1020.058{{c}}, ~5/4 = 674.394{{c}}
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| : [[error map]]: {{val| -179.942 +138.161 -71.803 }}
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| * [[CWE]]: ~2 = 1200.000{{c}}, ~5/4 = 629.521{{c}}
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| : error map: {{val| 0.000 +498.045 +243.208 }}
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| {{Optimal ET sequence|legend=1| 1c, 2b, 3bbcc }}
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| [[Badness]] (Sintel): 0.424
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| == Archon ==
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| {{Main| Archon }}
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| [[Subgroup]]: 2.3.5
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| [[Comma list]]: [[5/4]]
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| {{Mapping|legend=1| 1 0 2 | 0 1 0 }}
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| [[Optimal tuning]]s:
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| * [[WE]]: ~2 = 1268.274{{c}}, ~3/2 = 612.921{{c}}
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| : [[error map]]: {{val| +68.274 -20.760 -249.765 }}
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| * [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 614.055{{c}}
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| : error map: {{val| 0.000 -87.900 -386.314 }}
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| {{Optimal ET sequence|legend=1| 2c }}
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| [[Badness]] (Sintel): 0.474
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| == Seesaw ==
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| {{Main| Seesaw }}
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| Seesaw tempers out the [[6/5|classic minor third (6/5)]], equating the [[5/1|fifth]] and [[6/1|sixth harmonic]]s. It was named by [[User:Xenllium|Xenllium]] in 2026.
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| [[Subgroup]]: 2.3.5
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| [[Comma list]]: 6/5
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| {{Mapping|legend=1| 1 0 1 | 0 1 1 }}
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| [[Optimal tuning]]s:
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| * [[WE]]: ~2 = 1155.569{{c}}, ~3/2 = 643.349{{c}}
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| : [[error map]]: {{val| -44.431 -103.037 +168.173 }}
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| * [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 627.511{{c}}
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| : error map: {{val| 0.000 -74.444 +241.197 }}
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| {{Optimal ET sequence|legend=1| 2 }}
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| [[Badness]] (Sintel): 0.367
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| === 2.3.5.11 subgroup ===
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| This temperament is extended to the 2.3.5.11 subgroup naturally, tempering out both [[11/10]] and [[12/11]], undecimal neutral seconds.
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| Subgroup: 2.3.5.11
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| Comma list: 6/5, 11/10
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| Mapping: {{mapping| 1 0 1 2 | 0 1 1 1 }}
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| Optimal tunings:
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| * WE: ~2 = 1156.418{{c}}, ~3/2 = 643.202{{c}}
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| * CWE: ~2 = 1200.000{{c}}, ~3/2 = 627.023{{c}}
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| {{Optimal ET sequence|legend=0| 2 }}
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| Badness (Sintel): 0.499
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| === Heavy windmill ===
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| Heavy windmill tempers out [[9/7]] and [[15/14]] in the 7-limit.
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| Subgroup: 2.3.5.7
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| Comma list: 6/5, 9/7
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| Mapping: {{mapping| 1 0 1 0 | 0 1 1 2 }}
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| Optimal tunings:
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| * WE: ~2 = 1161.600{{c}}, ~3/2 = 571.169{{c}}
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| * CWE: ~2 = 1200.000{{c}}, ~3/2 = 559.563{{c}}
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| {{Optimal ET sequence|legend=0| 2 }}
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| Badness (Sintel): 0.676
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| ==== 11-limit ====
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| Subgroup: 2.3.5.7.11
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| Comma list: 6/5, 9/7, 11/10
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| Mapping: {{mapping| 1 0 1 0 2 | 0 1 1 2 1 }}
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| Optimal tunings:
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| * WE: ~2 = 1166.584{{c}}, ~3/2 = 568.073{{c}}
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| * CWE: ~2 = 1200.000{{c}}, ~3/2 = 558.941{{c}}
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| {{Optimal ET sequence|legend=0| 2 }}
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| Badness (Sintel): 0.774
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| === Light windmill ===
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| Light windmill tempers out [[8/7]] and [[21/20]] in the 7-limit.
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| Subgroup: 2.3.5.7
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| Comma list: 6/5, 8/7
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| Mapping: {{mapping| 1 0 1 3 | 0 1 1 0 }}
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| Optimal tunings:
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| * WE: ~2 = 1134.018{{c}}, ~3/2 = 670.285{{c}}
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| * CWE: ~2 = 1200.000{{c}}, ~3/2 = 667.893{{c}}
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| {{Optimal ET sequence|legend=0| 2 }}
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| Badness (Sintel): 0.629
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| ==== 11-limit ====
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| Subgroup: 2.3.5.7.11
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| Comma list: 6/5, 8/7, 11/10
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| Mapping: {{mapping| 1 0 1 3 2 | 0 1 1 0 1 }}
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| Optimal tunings:
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| * WE: ~2 = 1136.109{{c}}, ~3/2 = 672.403{{c}}
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| * CWE: ~2 = 1200.000{{c}}, ~3/2 = 668.374{{c}}
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| {{Optimal ET sequence|legend=0| 2 }}
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| Badness (Sintel): 0.681
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| == Sixseven ==
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| Sixseven tempers out the [[7/6|septimal minor third (7/6)]], equating the [[6/1|sixth]] and [[7/1|seventh harmonic]]s. It was named by [[User:Xenllium|Xenllium]] in 2026.
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| [[Subgroup]]: 2.3.7
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| [[Comma list]]: 7/6
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| {{Mapping|legend=1| 1 0 1 | 0 1 1 }}
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| [[Optimal tuning]]s:
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| * [[WE]]: ~2 = 1218.135{{c}}, ~3/2 = 734.187{{c}}
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| : [[error map]]: {{val| +18.135 +50.367 -198.368 }}
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| * [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 738.927{{c}}
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| : error map: {{val| 0.000 +36.972 -229.899 }}
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| {{Optimal ET sequence|legend=1| 1, 2d, 3, 5dd }}
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| [[Badness]] (Sintel): 0.329
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| === 2.3.7.13 subgroup ===
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| This temperament is extended to the 2.3.7.13 subgroup naturally, tempering out both [[13/12]] and [[14/13]], tridecimal neutral seconds.
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| Subgroup: 2.3.7.13
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| Comma list: 7/6, 13/12
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| Mapping: {{mapping| 1 0 1 2 | 0 1 1 1 }}
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| Optimal tunings:
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| * WE: ~2 = 1220.937{{c}}, ~3/2 = 734.003{{c}}
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| * CWE: ~2 = 1200.000{{c}}, ~3/2 = 739.780{{c}}
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| {{Optimal ET sequence|legend=0| 1, 2d, 3, 5ddf }}
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| Badness (Sintel): 0.422
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| === Heaven ===
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| Heaven tempers out [[11/9]] and [[22/21]] in the 2.3.7.11 subgroup.
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| Subgroup: 2.3.7.11
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| Comma list: 7/6, 11/9
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| Mapping: {{mapping| 1 0 1 0 | 0 1 1 2 }}
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| Optimal tunings:
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| * WE: ~2 = 1210.810{{c}}, ~3/2 = 783.079{{c}}
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| * CWE: ~2 = 1200.000{{c}}, ~3/2 = 785.173{{c}}
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| {{Optimal ET sequence|legend=0| 1e, 2de, 3 }}
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| Badness (Sintel): 0.577
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| ==== 2.3.7.11.13 subgroup ====
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| Subgroup: 2.3.7.11.13
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| Comma list: 7/6, 11/9, 13/12
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| Mapping: {{mapping| 1 0 1 0 2 | 0 1 1 2 1 }}
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| Optimal tunings:
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| * WE: ~2 = 1210.595{{c}}, ~3/2 = 783.176{{c}}
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| * CWE: ~2 = 1200.000{{c}}, ~3/2 = 784.989{{c}}
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| {{Optimal ET sequence|legend=0| 1e, 2de, 3 }}
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| Badness (Sintel): 0.627
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| [[Category:Temperament collections]]
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