@@ Line 14: / Line 14: @@
 * [[Muggles]] (+525/512) → [[Magic family #Muggles|Magic family]]
 * [[Valentine]] (+1029/1024) → [[Gamelismic clan #Valentine|Gamelismic clan]]
-* ''[[Diaschismic]]'' (+2048/2025) → [[Diaschismic family #Septimal diaschismic|Diaschismic family]]
+* [[Diaschismic]] (+2048/2025) → [[Diaschismic family #Septimal diaschismic|Diaschismic family]]
-* ''[[Wollemia]]'' (+2240/2187) → [[Tetracot family #Wollemia|Tetracot family]]
+* [[Wollemia]] (+2240/2187) → [[Tetracot family #Wollemia|Tetracot family]]
 * ''[[Unicorn]]'' (+10976/10935) → [[Unicorn family #Unicorn|Unicorn family]]
 * ''[[Coblack]]'' (+16807/16384) → [[Trisedodge family #Coblack|Trisedodge family]] / [[Cloudy clan #Coblack|cloudy clan]]
@@ Line 323: / Line 323: @@
 Badness (Sintel): 1.23
+== Xenial ==
+{{Main| Xenial }}
+: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Xenial]].''
+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 [[2/1|octave]]s, so the [[ploidacot]] for the temperament is zeta-enneacot, and from this it derives its name.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 126/125, 177147/175616
+{{Mapping|legend=1| 1 -6 -12 -25 | 0 9 17 33 }}
+: mapping generators: ~2, ~9/5
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.0095{{c}}, ~9/5 = 1011.1532{{c}}
+: [[error map]]: {{val| +0.010 -1.634 +3.176 -1.009 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~9/5 = 1011.1456{{c}}
+: error map: {{val| 0.000 -1.644 +3.162 -1.021 }}
+{{Optimal ET sequence|legend=1| 19, 51cd, 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 = 1199.6137{{c}}, ~9/5 = 1010.8717{{c}}
+* CWE: ~2 = 1200.000{{c}}, ~9/5 = 1011.1915{{c}}
+{{Optimal ET sequence|legend=0| 19, 51cd, 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 = 1199.8559{{c}}, ~9/5 = 1011.0911{{c}}
+* CWE: ~2 = 1200.000{{c}}, ~9/5 = 1011.2102{{c}}
+{{Optimal ET sequence|legend=0| 19, 51cd, 70, 89 }}
+Badness (Sintel): 1.98
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 126/125, 169/168, 221/220, 256/255, 540/539
+Mapping: {{mapping| 1 -6 -12 -25 22 -14 26 | 0 9 17 33 -22 21 -26 }}
+Optimal tunings:
+* WE: ~2 = 1199.6970{{c}}, ~9/5 = 1010.9792{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~9/5 = 1011.2323{{c}}
+{{Optimal ET sequence|legend=0| 19, 51cd, 70, 89 }}
+Badness (Sintel): 2.06
+=== 19-limit ===
+Subgroup: 2.3.5.7.11.13.17.19
+Comma list: 126/125, 169/168, 171/170, 221/220, 256/255, 540/539
+Mapping: {{mapping| 1 -6 -12 -25 22 -14 26 27 | 0 9 17 33 -22 21 -26 -27 }}
+Optimal tunings:
+* WE: ~2 = 1199.7741{{c}}, ~9/5 = 1011.0334{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~9/5 = 1011.2230{{c}}
+{{Optimal ET sequence|legend=0| 19, 51cdh, 70, 89 }}
+Badness (Sintel): 2.03
+=== 23-limit ===
+Subgroup: 2.3.5.7.11.13.17.19.23
+Comma list: 126/125, 162/161, 169/168, 171/170, 208/207, 221/220, 231/230
+Mapping: {{mapping| 1 -6 -12 -25 22 -14 26 27 2 | 0 9 17 33 -22 21 -26 -27 3 }}
+Optimal tunings:
+* WE: ~2 = 1199.6628{{c}}, ~9/5 = 1010.9415{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~9/5 = 1011.2245{{c}}
+{{Optimal ET sequence|legend=0| 19, 51cdh, 70, 89 }}
+Badness (Sintel): 1.93
 == Kumonga ==
@@ Line 374: / Line 472: @@
 Badness (Sintel): 1.19
-== Cypress ==
+== Paraguay ==
-: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Cypress]].''
+: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Parakleismic]].''
+Named by [[User:Xenllium|Xenllium]] in 2026, paraguay tempers out [[12005/11664]] and may be described as the {{nowrap| 19 & 61 }} temperament. It is a variant of [[parakleismic]], mapping 7th harmonic to 16 generators.
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: 126/125, 19683/19208
+[[Comma list]]: 126/125, 12005/11664
-{{Mapping|legend=1| 1 -5 -7 -12 | 0 12 17 27 }}
+{{Mapping|legend=1| 1 -8 -8 -9 | 0 13 14 16 }}
+: mapping generators: ~2, ~5/3
 [[Optimal tuning]]s:
-* [[WE]]: ~2 = 1200.1652{{c}}, ~196/135 = 658.2622{{c}}
+* [[WE]]: ~2 = 1200.6421{{c}}, ~5/3 = 885.3232{{c}}
-: [[error map]]: {{val| +0.165 -3.634 +2.988 +2.272 }}
+: [[error map]]: {{val| +0.642 +2.110 +3.074 -9.434 }}
-* [[CWE]]: ~2 = 1200.0000{{c}}, ~196/135 = 658.1814{{c}}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/3 = 884.8949{{c}}
-: error map: {{val| 0.000 -3.779 +2.769 +2.071 }}
+: error map: {{val| 0.000 +1.678 +2.214 -10.508 }}
-{{Optimal ET sequence|legend=1| 11cd, 20cd, 31 }}
+{{Optimal ET sequence|legend=1| 19, 61, 80d, 99d }}
-[[Badness]] (Sintel): 2.53
+[[Badness]] (Sintel): 2.47
 === 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 99/98, 126/125, 243/242
+Comma list: 56/55, 100/99, 12005/11664
+Mapping: {{mapping| 1 -8 -8 -9 2 | 0 13 14 16 2 }}
+Optimal tunings:
+* WE: ~2 = 1197.7783{{c}}, ~5/3 = 883.6140{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 885.1383{{c}}
+{{Optimal ET sequence|legend=0| 19, 42e, 61e }}
+Badness (Sintel): 2.49
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 56/55, 91/90, 100/99, 343/338
-Mapping: {{mapping| 1 -5 -7 -12 -13 | 0 12 17 27 30 }}
+Mapping: {{mapping| 1 -8 -8 -9 2 -14 | 0 13 14 16 2 24 }}
 Optimal tunings:
-* WE: ~2 = 1200.1117{{c}}, ~22/15 = 658.2892{{c}}
+* WE: ~2 = 1197.7848{{c}}, ~5/3 = 883.6431{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 658.2345{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 885.1623{{c}}
-{{Optimal ET sequence|legend=0| 11cdee, 20cde, 31, 144cd }}
+{{Optimal ET sequence|legend=0| 19, 42ef, 61e }}
-Badness (Sintel): 1.41
+Badness (Sintel): 1.86
-=== 13-limit ===
+==== Uruguay ====
 Subgroup: 2.3.5.7.11.13
-Comma list: 66/65, 99/98, 126/125, 243/242
+Comma list: 56/55, 78/77, 100/99, 1183/1152
-Mapping: {{mapping| 1 -5 -7 -12 -13 -10 | 0 12 17 27 30 25 }}
+Mapping: {{mapping| 1 -8 -8 -9 2 0 | 0 13 14 16 2 5 }}
 Optimal tunings:
-* WE: ~2 = 1199.4328{{c}}, ~22/15 = 657.9111{{c}}
+* WE: ~2 = 1199.6132{{c}}, ~5/3 = 884.7325{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 658.1886{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 885.0005{{c}}
-{{Optimal ET sequence|legend=0| 11cdeef, 20cdef, 31 }}
+{{Optimal ET sequence|legend=0| 19, 42e }}
-Badness (Sintel): 1.56
+Badness (Sintel): 2.51
 == Bisemidim ==
@@ Line 472: / Line 588: @@
 Badness (Sintel): 0.987
+== Cypress ==
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Cypress]].''
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 126/125, 19683/19208
+{{Mapping|legend=1| 1 -5 -7 -12 | 0 12 17 27 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.1652{{c}}, ~196/135 = 658.2622{{c}}
+: [[error map]]: {{val| +0.165 -3.634 +2.988 +2.272 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~196/135 = 658.1814{{c}}
+: error map: {{val| 0.000 -3.779 +2.769 +2.071 }}
+{{Optimal ET sequence|legend=1| 11cd, 20cd, 31 }}
+[[Badness]] (Sintel): 2.53
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 99/98, 126/125, 243/242
+Mapping: {{mapping| 1 -5 -7 -12 -13 | 0 12 17 27 30 }}
+Optimal tunings:
+* WE: ~2 = 1200.1117{{c}}, ~22/15 = 658.2892{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 658.2345{{c}}
+{{Optimal ET sequence|legend=0| 11cdee, 20cde, 31, 144cd }}
+Badness (Sintel): 1.41
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 66/65, 99/98, 126/125, 243/242
+Mapping: {{mapping| 1 -5 -7 -12 -13 -10 | 0 12 17 27 30 25 }}
+Optimal tunings:
+* WE: ~2 = 1199.4328{{c}}, ~22/15 = 657.9111{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 658.1886{{c}}
+{{Optimal ET sequence|legend=0| 11cdeef, 20cdef, 31 }}
+Badness (Sintel): 1.56
 == Casablanca ==
@@ Line 712: / Line 877: @@
 == Cobalt ==
+: ''For the 5-limit version, see [[27th-octave temperaments #Cobalt]].''
 Cobalt has a period of 1/27 octave and tempers out 126/125 and 540/539 as in the [[aplonis]] temperament. It may be described as {{nowrap| 27 & 81 }}.

Starling temperaments: Difference between revisions