Orwellismic family: Difference between revisions
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: 7/6 length = 0.7526, 3/2 length = 1.3931 | : 7/6 length = 0.7526, 3/2 length = 1.3931 | ||
: Angle (7/6, 3/2) = 97.5081 | : Angle (7/6, 3/2) = 97.5081 | ||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1199.4176{{c}}, ~3/2 = 701.8055{{c}}, ~12/7 = 928.9445{{c}} | |||
: [[error map]]: {{val| -0.582 -0.732 +0.520 +2.288 }} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.6429{{c}}, ~12/7 = 929.2316{{c}} | |||
: error map: {{val| 0.000 -0.312 +1.381 +3.585 }} | |||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
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== Guanyin == | == Guanyin == | ||
{{See also|Subgroup temperaments#Guanyintet}} | |||
Guanyin is the most natural [[11-limit]] extension of orwellismic, where two ~7/6 generators make [[15/11]], tempering out [[540/539]], and two sharpened ~[[5/4]]'s make [[11/7]], tempering out [[176/175]]. | Guanyin is the most natural [[11-limit]] extension of orwellismic, where two ~7/6 generators make [[15/11]], tempering out [[540/539]], and two sharpened ~[[5/4]]'s make [[11/7]], tempering out [[176/175]]. | ||
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: 7/6 length = 0.5167, 3/2 length = 1.3055 | : 7/6 length = 0.5167, 3/2 length = 1.3055 | ||
: Angle (7/6, 3/2) = 79.0940 | : Angle (7/6, 3/2) = 79.0940 | ||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1199.2336{{c}}, ~3/2 = 702.4159{{c}}, ~12/7 = 929.3128{{c}} | |||
: [[error map]]: {{val| -0.7664 -0.3055 +1.6247 +1.9781 -1.5717 }} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.2876{{c}}, ~12/7 = 929.7608{{c}} | |||
: error map: {{val| 0.0000 +0.3326 +2.9688 +3.7009 -0.2261 }} | |||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
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Comma list: 176/175, 351/350, 540/539 | Comma list: 176/175, 351/350, 540/539 | ||
{{Mapping|legend=0| 1 0 0 2 -2 3 | 0 1 0 1 1 -2 | 0 0 3 -1 5 5 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1199.2015{{c}}, ~3/2 = 702.4954{{c}}, ~12/7 = 929.2881{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.6821{{c}}, ~12/7 = 929.7296{{c}} | |||
{{Optimal ET sequence|legend=0| 22, 27e, 31, 53, 58, 80, 111, 280cdf }} | {{Optimal ET sequence|legend=0| 22, 27e, 31, 53, 58, 80, 111, 280cdf }} | ||
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Comma list: 144/143, 176/175, 196/195 | Comma list: 144/143, 176/175, 196/195 | ||
{{Mapping|legend=0| 1 0 0 2 -2 6 | 0 1 0 1 1 1 | 0 0 3 -1 5 -5 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1198.4320{{c}}, ~3/2 = 702.7802{{c}}, ~12/7 = 929.4834{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.5889{{c}}, ~12/7 = 930.5977{{c}} | |||
{{Optimal ET sequence|legend=0| 22f, 27e, 31, 49f, 58, 138cdeff, 196cdefff, 254ccdeeffff }} | {{Optimal ET sequence|legend=0| 22f, 27e, 31, 49f, 58, 138cdeff, 196cdefff, 254ccdeeffff }} | ||
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{{Mapping|legend=1| 1 0 0 2 5 | 0 1 0 1 0 | 0 0 3 -1 -2 }} | {{Mapping|legend=1| 1 0 0 2 5 | 0 1 0 1 0 | 0 0 3 -1 -2 }} | ||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1200.7839{{c}}, ~3/2 = 699.6996{{c}}, ~12/7 = 928.6481{{c}} | |||
: [[error map]]: {{val| +0.784 -1.471 -0.369 +4.577 -4.695 }} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 699.6270{{c}}, ~12/7 = 928.0978{{c}} | |||
: error map: {{val| 0.000 -2.328 -2.020 +2.703 -7.514 }} | |||
{{Optimal ET sequence|legend=1| 4, 5, 9, 17, 22, 31, 53, 84e }} | {{Optimal ET sequence|legend=1| 4, 5, 9, 17, 22, 31, 53, 84e }} | ||
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Scales: [[orwellian chromatic]] | Scales: [[orwellian chromatic]] | ||
[[Category:Orwellismic family| ]] <!-- main article --> | |||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category: | [[Category:Catalogs of rank-3 temperaments]] | ||
[[Category:Listen]] | [[Category:Listen]] | ||