Miscellaneous 7-limit temperaments: Difference between revisions
+ triwellismic |
+ scheme. Officialize canopic as the sole name for {16875/16807}. Schismean -> aberdietic and review its optimal ET sequence |
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[[Badness]] (Sintel): 0.661 | [[Badness]] (Sintel): 0.661 | ||
== | == Scheme == | ||
[[Subgroup]]: 2.3.5.7 | |||
[[Comma list]]: 14348907/14336000 | |||
{{Mapping|legend=1| 1 0 0 -14 | 0 1 0 15 | 0 0 1 -3 }} | |||
: Mapping generators: ~2, ~3, ~5 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1200.0267{{c}}, ~3/2 = 701.8565{{c}}, ~5/4 = 386.2912{{c}} | |||
: [[Error map]]: {{val| +0.027 -0.072 +0.031 +0.015 }} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8494{{c}}, ~5/4 = 386.3135{{c}} | |||
: Error map: {{val| 0.000 -0.106 -0.000 -0.025 }} | |||
{{Optimal ET sequence|legend=1| 53, 111, 118, 171, 742, 795, 913, 966, 1137, 1308, 2050, 2221, 2392, 3358, 3529, 7229b, 10758bbd }} | |||
[[Badness]] (Sintel): 1.47 | |||
== Canopic == | |||
: ''For extensions, see [[Swetismic temperaments #Indra]].'' | : ''For extensions, see [[Swetismic temperaments #Indra]].'' | ||
Canopic | Canopic (formerly ''mirkwai'') tempers out the [[canopic comma]] in the 7-limit. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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[[Projection pair]]: <code>5 2401/486</code> to 2.3.7 | [[Projection pair]]: <code>5 2401/486</code> to 2.3.7 | ||
== | == Aberdietic == | ||
Aberdietic tempers out the [[3645/3584|aberdiesis]] in the 7-limit. It equates [[7/5]] with a stack of three [[9/8]]'s. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 697.459{{c}}, ~5/4 = 383.104{{c}} | * [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 697.459{{c}}, ~5/4 = 383.104{{c}} | ||
{{Optimal ET sequence|legend=1| 5c, 7d, 12, 19, 31, 81 }} | {{Optimal ET sequence|legend=1| 5c, 7d, 12, 19, 31, 81, 98c, 117c, 129c, 148bc, 160bc, 179bcd }} | ||
[[Badness]] (Sintel): 2.96 | [[Badness]] (Sintel): 2.96 | ||