Augmented family: Difference between revisions

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 {{Optimal ET sequence|legend=1| 3b, 9bd, 12 }}
+[[Badness]] (Sintel): 3.50
 === 11-limit ===
-{{Todo|unify precision}}
 Subgroup: 2.3.5.7.11
@@ Line 656: / Line 657: @@
 Optimal tunings:
-* WE: ~5/4 = 397.495{{c}}, ~15/11 = 499.096{{c}} (~15/14 = 101.601{{c}})
+* WE: ~5/4 = 397.495{{c}}, ~15/11 = 499.096{{c}} (~12/11 = 101.601{{c}})
-* CWE: ~5/4 = 400.000{{c}}, ~15/11 = 500.775{{c}} (~15/14 = 100.775{{c}})
+* CWE: ~5/4 = 400.000{{c}}, ~15/11 = 500.775{{c}} (~12/11 = 100.775{{c}})
+{{Optimal ET sequence|legend=0| 3b, 9bde, 12 }}
+Badness (Sintel): 2.60
+== Subgroup extensions ==
+=== 2.3.5.19 subgroup (3 & 12) ===
+Augmented temperament works on the 2.3.5.19 subgroup very well, tempering out both [[76/75]] and [[96/95]], alongside the augmented comma.
+[[Subgroup]]: 2.3.5.19
+[[Comma list]]: 76/75, 96/95
+{{Mapping|legend=2| 3 0 7 8 | 0 1 0 1 }}
+: sval mapping generators: ~5/4, ~3
+[[Optimal tuning]]s:
+* [[WE]]: ~5/4 = 399.075{{c}}, ~3/2 = 705.062{{c}} (~19/16 = 305.986{{c}})
+* [[CWE]]: ~5/4 = 400.000{{c}}, ~3/2 = 705.107{{c}} (~19/16 = 305.107{{c}})
-{{Optimal ET sequence|legend=1| 3b, 9bde, 12 }}
+{{Optimal ET sequence|legend=1| 3, 9, 12, 27, 39 }}
-[[Badness]] (Sintel): 2.60
+[[Badness]] (Sintel): 0.264
 == External links ==