Syntonic–kleismic equivalence continuum: Difference between revisions

@@ Line 62: / Line 62: @@
 |-
 | 9
-| 19 & 51c
+| [[Xenial]]
 | [[129140163/125000000]]
 | {{Monzo| -6 17 -9 }}
@@ Line 188: / Line 188: @@
 [[Badness]] (Sintel): 2.04
+== Xenial ==
+: ''For extensions, see [[Starling temperaments #Xenial]] and [[Sensamagic clan #Xenia]].''
+Named by [[User:Xenllium|Xenllium]] in 2026, xenial splits the [[8/3|perfect eleventh]] into nine equal parts, each for ~[[10/9]]. It corresponds to {{nowrap| ''n'' {{=}} 9 }}. Its [[ploidacot]] is zeta-enneacot, and from this it derives its name.
+[[Subgroup]]: 2.3.5
+[[Comma list]]: 129140163/125000000
+{{Mapping|legend=1| 1 -6 -12 | 0 9 17 }}
+: mapping generators: ~2, ~9/5
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.2802{{c}}, ~9/5 = 1011.2914{{c}}
+: [[error map]]: {{val| +0.280 -2.013 +2.278 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~9/5 = 1011.0762{{c}}
+: error map: {{val| 0.000 -2.269 +1.982 }}
+{{Optimal ET sequence|legend=1| 19, 70, 89, 108, 127 }}
+[[Badness]] (Sintel): 8.84
 == Lalasepyo (8c & 11) ==
@@ Line 227: / Line 249: @@
 [[Badness]] (Sintel): 10.8
-== Parakleismic (5-limit) ==
+== Parakleismic ==
 {{Main| Parakleismic }}
-: ''For extensions, see [[Ragismic microtemperaments #Parakleismic]].''
+: ''For extensions, see [[Ragismic microtemperaments #Parakleismic]] and [[Starling temperaments #Paraguay]].''
 The 5-limit version of parakleismic tempers out the [[parakleisma]]. It corresponds to {{nowrap| ''n'' {{=}} 13/2 }}, and 13 generator steps give the interval class of [[3/1|3]].