Parakleismic family: Difference between revisions
→Paraguay: - very dubious 11-limit extension |
+ counterpara |
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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 [[ | 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 | ||