Parakleismic family: Difference between revisions

Paraguay: - very dubious 11-limit extension
+ counterpara
Line 222: Line 222:


Badness (Sintel): 1.67
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 ==
== 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
[[Subgroup]]: 2.3.5.7