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 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: ~6/5, ~7
+[[Optimal tuning]]s:
+* [[WE]]: ~6/5 = 236.416, ~7/4 = 1002.701 (~28/27 = 57.038) <!-- Please review, last digit may be wrong -->
+: [[error map]]: {{val| -17.921 -10.628 +50.676 -1.966 }}
+* [[CWE]]: ~6/5 = 240.000, ~7/4 = 1005.135 (~28/27 = 45.135)
+: error map: {{val| 0.000 +18.045 +93.686 +36.309 }}
+{{Optimal ET sequence|legend=1| 5, 15ccd }}
+[[Badness]] (Sintel): 1.22
 == Geryon ==