Very low accuracy temperaments: Difference between revisions

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 [[Badness]] (Sintel): 1.16
+== Quint ==
+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.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 16/15, 27/25
+{{Mapping|legend=1| 5 8 12 0 | 0 0 0 1 }}
+: Mapping generators: ~9/8, ~7
+[[Optimal tuning]]s:
+* [[POTE]]: ~9/8 = 1\5, ~7/4 = 1017.903 (~21/20 = 57.903)
+* [[CTE]]: ~9/8 = 1\5, ~7/4 = 968.8259 (~63/64 = 8.8259)
+{{Optimal ET sequence|legend=1| 5, 15ccd }}
+[[Badness]]: 0.048312
 == Geryon ==