Rastmic rank-3 clan: Difference between revisions
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* [[Jove]] (+441/440 or 540/539) → [[Breed family #Jove|Breed family]] | * [[Jove]] (+441/440 or 540/539) → [[Breed family #Jove|Breed family]] | ||
* ''[[Hagrid]]'' (+9801/9800) → [[Cataharry family #Hagrid|Cataharry family]] | * ''[[Hagrid]]'' (+9801/9800) → [[Cataharry family #Hagrid|Cataharry family]] | ||
Considered below are spectacle, mirwomo, mandos, cuckoo, parahemif, urania, and mirage. | Considered below are spectacle, mirwomo, mandos, cuckoo, parahemif, urania, rabic, and mirage. | ||
== Spectacle == | == Spectacle == | ||
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Scales: [[urania24]] | Scales: [[urania24]] | ||
== Rabic == | |||
If the rastma is added to the list of commas along with the [[Alpharabian comma]], you end up with rabic, which splits the octave into 24 equal parts. This temperament is named as such by [[Aura]] in 2022 because tempering out both the Alpharabian comma and the rastma automatically tempers out the [[Betarabian comma]]. | |||
[[Subgroup]]: 2.3.5.7.11 | |||
[[Comma list]]: 243/242, 131769/131072 | |||
{{Mapping|legend=1| 24 38 0 0 83 | 0 0 1 0 0 | 0 0 0 1 0 }} | |||
: mapping generators: ~33/32, ~5, ~7 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~33/32 = 50.0220{{c}}, ~5/4 = 385.0647{{c}}, ~7/4 = 967.3158{{c}} | |||
: [[error map]]: {{val| +0.538 -1.104 -0.002 -0.002 +0.541 }} | |||
* [[CWE]]: ~33/32 = 50.0000{{c}}, ~5/4 = 385.0647{{c}}, ~7/4 = 967.3158{{c}} | |||
: error map: {{val| 0.000 -1.955 -0.937 -1.133 -1.318 }} | |||
{{Optimal ET sequence|legend=1| 24, 48(d), 72, 264, 336b, 408b, 480bcde }} | |||
[[Badness]] (Sintel): 7.30 | |||
== Mirage == | == Mirage == | ||
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=== 17-limit === | === 17-limit === | ||
Mirage is very naturally a 17-limit temperament, relating 13 and 17 by tempering out [[273/272]], [[715/714]], [[833/832]], and [[936/935]]. Instead of 13/8, the second generator can also be the small comma tempered out by [[miraculous]]. | |||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
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Subgroup: 2.3.5.7.11.13.17.19 | Subgroup: 2.3.5.7.11.13.17.19 | ||
Comma list: 225/224, 243/242, 273/272, | Comma list: 210/209, 225/224, 243/242, 273/272, 343/342 | ||
{{Todo|complete temperament data|inline=1}} | {{Todo|complete temperament data|inline=1}} | ||
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Subgroup: 2.3.5.7.11.13.17.19.23 | Subgroup: 2.3.5.7.11.13.17.19.23 | ||
Comma list: 225/224, 243/242, 273/272, 300/299, 385/384 | Comma list: 210/209, 225/224, 243/242, 273/272, 300/299, 385/384 | ||
{{Todo|complete temperament data|inline=1}} | {{Todo|complete temperament data|inline=1}} | ||
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Subgroup: 2.3.5.7.11.13.17.19 | Subgroup: 2.3.5.7.11.13.17.19 | ||
Comma list: 225/224, 243/242, 273/272, 324/323, 385/384 | |||
{{Todo|complete temperament data|inline=1}} | {{Todo|complete temperament data|inline=1}} | ||
=== | === Prism 23-limit === | ||
Subgroup: 2.3.5.7.11.13.17.19.23 | Subgroup: 2.3.5.7.11.13.17.19.23 | ||
Comma list: 225/224, 243/242, 273/272, 300/299, 324/323, 385/384 | |||
{{Todo|complete temperament data|inline=1}} | |||
=== No-19 23-limit === | |||
Subgroup: 2.3.5.7.11.13.17.23 | |||
Comma list: 225/224, 243/242, 273/272, 300/299, 385/384 | |||
{{Todo|complete temperament data|inline=1}} | {{Todo|complete temperament data|inline=1}} | ||
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[[Category:Temperament clans]] | [[Category:Temperament clans]] | ||
[[Category:Rastmic rank-3 clan| ]] <!-- main article --> | [[Category:Rastmic rank-3 clan| ]] <!-- main article --> | ||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||