Very low accuracy temperaments: Difference between revisions

@@ Line 311: / Line 311: @@
 [[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 already quite accurately approximated by 5edo for its size, this temperament provides little improvement, so it is only provided below for bookkeeping purposes. 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: ~6/5, ~7
+[[Optimal tuning]]s:
+* [[WE]]: ~6/5 = 236.416{{c}}, ~7/4 = 1002.701{{c}} (~28/27 = 57.038{{c}})
+: [[error map]]: {{val| -17.921 -10.628 +50.676 -1.966 }}
+* [[CWE]]: ~6/5 = 240.000{{c}}, ~7/4 = 1005.135{{c}} (~28/27 = 45.135{{c}})
+: error map: {{val| 0.000 +18.045 +93.686 +36.309 }}
+{{Optimal ET sequence|legend=1| 5, 15ccd, 20cccd }}
+[[Badness]] (Sintel): 1.22
 == Geryon ==