Parakleismic family: Difference between revisions

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 Badness (Sintel): 1.67
+== Counterpara ==
+Counterpara tempers out the [[horwell comma]], covering the range between [[118edo]] and [[137edo]], and [[373edo]] makes for a recommendable tuning. It was named by [[Flora Canou]] in 2026 by analog to ''[[countercata]]''.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 65625/65536, 100442349/100000000
+{{Mapping|legend=1| 1 -8 -8 64 | 0 13 14 -83 }}
+: mapping generators: ~2, ~5/3
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.1717{{c}}, ~5/3 = 884.8468{{c}}
+: [[error map]]: {{val| +0.172 -0.321 +0.167 -0.117 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/3 = 884.7196{{c}}
+: error map: {{val| 0.000 -0.600 -0.240 -0.552 }}
+{{Optimal ET sequence|legend=1| 118, 255, 373, 1237bd, 1610bd, 1983bd }}
+[[Badness]] (Sintel): 4.40
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 3025/3024, 8019/8000, 65625/65536
+Mapping: {{mapping| 1 -8 -8 64 | 0 13 14 -83 -36 }}
+: mapping generators: ~2, ~5/3
+Optimal tunings:
+* WE: ~2 = 1200.2039{{c}}, ~5/3 = 884.8695{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 884.7182{{c}}
+{{Optimal ET sequence|legend=0| 118, 255, 373 }}
+Badness (Sintel): 1.52
 == Paraguay ==
-Named by [[Xenllium]] in 2026, paraguay tempers out [[12005/11664]] and may be described as the {{nowrap| 19 & 61 }} temperament. It is a variant of septimal parakleismic, mapping 7th harmonic to 16 generators.
+Named by [[Xenllium]] in 2026, paraguay tempers out [[126/125]] and may be described as the {{nowrap| 19 & 61 }} temperament. It is a variant of septimal parakleismic, mapping 7th harmonic to 16 generators.
 [[Subgroup]]: 2.3.5.7
@@ Line 243: / Line 279: @@
 [[Badness]] (Sintel): 2.47
-=== 11-limit ===
+== Maviloid ==
-Subgroup: 2.3.5.7.11
+[[Subgroup]]: 2.3.5.7
-Comma list: 56/55, 100/99, 12005/11664
+[[Comma list]]: 2401/2400, 1224440064/1220703125
-Mapping: {{mapping| 1 -8 -8 -9 2 | 0 13 14 16 2 }}
+{{Mapping|legend=1| 1 -21 -22 -15 | 0 52 56 41 }}
+: mapping generators: ~2, ~875/648
-Optimal tunings:
+[[Optimal tuning]]s:
-* WE: ~2 = 1197.7783{{c}}, ~5/3 = 883.6140{{c}}
+* [[WE]]: ~2 = 1199.9863{{c}}, ~875/648 = 521.1837{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 885.1383{{c}}
+: [[error map]]: {{val| -0.014 -0.115 +0.274 -0.089 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~875/648 = 521.1894{{c}}
-{{Optimal ET sequence|legend=0| 19, 42e, 61e }}
+: error map: {{val| 0.000 -0.106 +0.293 -0.060 }}
-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 -8 -8 -9 2 -14 | 0 13 14 16 2 24 }}
-Optimal tunings:
-* WE: ~2 = 1197.7848{{c}}, ~5/3 = 883.6431{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 885.1623{{c}}
-{{Optimal ET sequence|legend=0| 19, 42ef, 61e }}
+{{Optimal ET sequence|legend=1| 76, 99, 274, 373, 472, 571, 1043, 1614 }}
-Badness (Sintel): 1.86
+[[Badness]] (Sintel): 1.46
 [[Category:Parakleismic family| ]] <!-- main article -->
 [[Category:Temperament families]]
-[[Category:Rank 2]]
+[[Category:Catalogs of rank-2 temperaments]]