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| Line 311: |
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| [[Badness]] (Sintel): 1.16 | | [[Badness]] (Sintel): 1.16 |
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| == Quint ==
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| Quint preserves the 5-limit mapping of 5edo, and harmonic 7 is mapped to an independent generator. As harmonic 7 is way more accurately approximated than 5 by 5edo, this temperament provides little improvement to 5edo'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 2.3.7-subgroup structure of 5edo and give prime 5 an independent generator instead, which is exactly what [[blackwood]] does.
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| [[Subgroup]]: 2.3.5.7
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| [[Comma list]]: 16/15, 27/25
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| {{Mapping|legend=1| 5 8 12 0 | 0 0 0 1 }}
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| : Mapping generators: ~6/5, ~7
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| [[Optimal tuning]]s:
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| * [[WE]]: ~6/5 = 236.416, ~7/4 = 1002.701 (~28/27 = 57.038) <!-- Please review, last digit may be wrong -->
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| : [[error map]]: {{val| -17.921 -10.628 +50.676 -1.966 }}
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| * [[CWE]]: ~6/5 = 240.000, ~7/4 = 1005.135 (~28/27 = 45.135)
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| : error map: {{val| 0.000 +18.045 +93.686 +36.309 }}
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| {{Optimal ET sequence|legend=1| 5, 15ccd }}
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| [[Badness]] (Sintel): 1.22
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| == Geryon == | | == Geryon == |