Syntonic–kleismic equivalence continuum: Difference between revisions

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@@ 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 226: / Line 248: @@
 [[Badness]] (Sintel): 10.8
-== Parakleismic (5-limit) ==
-{{Main| Parakleismic }}
-: ''For extensions, see [[Ragismic microtemperaments #Parakleismic]].''
-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]].
-[[Subgroup]]: 2.3.5
-[[Comma list]]: 1224440064/1220703125
-{{Mapping|legend=1| 1 -8 -8 | 0 13 14 }}
-: mapping generators: ~2, ~5/3
-[[Optimal tuning]]s:
-* [[WE]]: ~2 = 1199.971{{c}}, ~5/3 = 884.7383{{c}}
-: [[error map]]: {{val| -0.029 -0.127 +0.253 }}
-* [[CWE]]: ~2 = 1200.000{{c}}, ~5/3 = 884.8576{{c}}
-: error map: {{val| 0.000 -0.106 +0.293 }}
-{{Optimal ET sequence|legend=1| 19, 61, 80, 99, 118, 453, 571, 689, 1496 }}
-[[Badness]] (Sintel): 1.02
 == Mowgli ==
@@ Line 331: / Line 330: @@
 [[Badness]] (Sintel): 7.45
-== Oviminor ==
-{{See also| Ragismic microtemperaments #Oviminor }}
-Oviminor is named after the facts that it takes 184 minor thirds of 6/5 to reach 4/3, the Roman consul was Eggius in the year 184 AD, and the Latin word for egg is ovum, and with prefix ovi-. It sets a new record of complexity for a chain of nineteen 6/5's past [[egads]], though it is less accurate.
-[[Subgroup]]: 2.3.5
-[[Comma list]]: {{monzo| -134 -185 184 }}
-{{Mapping|legend=1| 1 -134 -134 | 0 184 185 }}
-: mapping generators: ~2, ~5/3
-[[Optimal tuning]]s:
-* [[WE]]: ~2 = 1200.0094{{c}}, ~5/3 = 884.2568{{c}}
-: [[error map]]: {{val| +0.009 +0.033 -0.069 }}
-* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/3 = 884.2499{{c}}
-: error map: {{val| 0.000 +0.026 -0.083 }}
-{{Optimal ET sequence|legend=1| 19, …, 1600, 3219, 4819 }}
-[[Badness]] (Sintel): 751
 [[Category:19edo]]
 [[Category:Equivalence continua]]