451edo: Difference between revisions
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m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
451edo shares its [[3/2|fifth]] with [[41edo]]. Unlike 41, however, 451 is only [[consistent]] to the [[7-odd-limit]], though it has a reasonable approximation up to the [[13-limit]] using the [[patent val]]. The equal temperament [[tempering out|tempers out]] 390625000/387420489 ([[quartonic comma]]) in the 5-limit; [[2401/2400]], [[65625/65536]], [[703125/702464]], [[2100875/2097152]], in the 7-limit; [[6250/6237]], 42592/42525, 42875/42768, 43923/43904 in the 11-limit; and [[625/624]], [[2080/2079]], [[2200/2197]], [[4096/4095]], [[4225/4224]], 4459/4455, and 17303/17280 in the 13-limit. It [[support]]s [[tertiaseptal]], [[tertiseptisix]], and [[hemermacomp]], providing the [[optimal patent val]] for 5-limit [[quartonic]]. | |||
=== Prime harmonics === | === Prime harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 451 factors into | Since 451 factors into {{factorisation|451}}, 451edo has [[11edo]] and [[41edo]] as its subsets. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
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| [[Tertiaseptal]] | | [[Tertiaseptal]] | ||
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<nowiki />* [[Normal | <nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | ||
[[Category:Quartonic]] | [[Category:Quartonic]] | ||