Starling temperaments: Difference between revisions

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 : ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Xenial]].''
-Xenial may be described as the {{nowrap| 19 & 70 }} temperament, splitting the [[8/3|perfect eleventh]] into nine equal parts, each for ~[[10/9]]. Equivalently, a stack of nine [[9/5]]s is equated with the [[3/2|perfect fifth]] above 7 octaves, so the [[ploidacot]] for the temperament is zeta-enneacot, and from this it derives its name (named by [[User:Xenllium|Xenllium]] in 2026).
+Named by [[User:Xenllium|Xenllium]] in 2026, xenial may be described as the {{nowrap| 19 & 70 }} temperament, splitting the [[8/3|perfect eleventh]] into nine equal parts, each for ~[[10/9]]. Equivalently, a stack of nine [[9/5]]s is equated with the [[3/2|perfect fifth]] above 7 octaves, so the [[ploidacot]] for the temperament is zeta-enneacot, and from this it derives its name.
 [[Subgroup]]: 2.3.5.7
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 [[Optimal tuning]]s:
 * [[WE]]: ~2 = 1200.0095{{c}}, ~9/5 = 1011.1532{{c}}
-: [[error map]]: {{val| +0.0095, -1.6335, +3.1760, -1.0091 }}
+: [[error map]]: {{val| +0.010 -1.634 +3.176 -1.009 }}
 * [[CWE]]: ~2 = 1200.0000{{c}}, ~9/5 = 1011.1456{{c}}
-: error map: {{val| 0.0000 -1.6444, +3.1618, -1.0205 }}
+: error map: {{val| 0.000 -1.644 +3.162 -1.021 }}
 {{Optimal ET sequence|legend=1| 19, 70, 89 }}
 [[Badness]] (Sintel): 2.13
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 126/125, 540/539, 16384/16335
+Mapping: {{mapping| 1 -6 -12 -25 22 | 0 9 17 33 -22 }}
+Optimal tunings:
+* WE: ~2 = 1199.614{{c}}, ~9/5 = 1010.872{{c}}
+* CWE: ~2 = 1200.000{{c}}, ~9/5 = 1011.192{{c}}
+{{Optimal ET sequence|legend=0| 19, 70, 89 }}
+Badness (Sintel): 2.31
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 126/125, 169/168, 540/539, 729/728
+Mapping: {{mapping| 1 -6 -12 -25 22 -14 | 0 9 17 33 -22 21 }}
+Optimal tunings:
+* WE: ~2 = 1199.856{{c}}, ~9/5 = 1011.091{{c}}
+* CWE: ~2 = 1200.000{{c}}, ~9/5 = 1011.210{{c}}
+{{Optimal ET sequence|legend=0| 19, 70, 89 }}
+Badness (Sintel): 1.98
 == Kumonga ==