836edo: Difference between revisions

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== Theory ==

836edo is a strong 11-limit system, having the record of lowest absolute error and beating [[612edo]].

836edo is a strong 11-limit system, having the record of lowest absolute error and beating [[612edo]]. Its perfect fifth is notable as the midpoint between that of [[19edo]] and [[22edo]], which are nearly the same distance away from a pure 3/2 but in opposite directions, thus being quite an accurate approximation.

As an equal temperament, it [[tempering out|tempers out]] the [[counterschisma]] and the [[enneadeca]] in the 5-limit; [[4375/4374]], [[703125/702464]] in the 7-limit; [[3025/3024]] and [[9801/9800]] in the 11-limit. It supports [[enneadecal]] in the 7-limit as well as [[hemienneadecal]] in the 11-limit. It also tunes [[orga]] and [[quasithird]]. In addition, it is divisible by 44 and in light of that it tunes [[ruthenium]] in the 7-limit and also 11-limit.

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| [[Ruthenium]]

|}

<nowiki />* [[Normal ~~lists~~|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~|minimal form]] in parentheses if distinct

<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:Quasithird]]

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 {{Infobox ET}}
-{{EDO intro|836}}
+{{ED intro}}
 == Theory ==
-edo is a strong 11-limit system, having the record of lowest absolute error and beating [[612edo]].
+edo is a strong 11-limit system, having the record of lowest absolute error and beating [[612edo]]. Its perfect fifth is notable as the midpoint between that of [[19edo]] and [[22edo]], which are nearly the same distance away from a pure 3/2 but in opposite directions, thus being quite an accurate approximation.
 As an equal temperament, it [[tempering out|tempers out]] the [[counterschisma]] and the [[enneadeca]] in the 5-limit; [[4375/4374]], [[703125/702464]] in the 7-limit; [[3025/3024]] and [[9801/9800]] in the 11-limit. It supports [[enneadecal]] in the 7-limit as well as [[hemienneadecal]] in the 11-limit. It also tunes [[orga]] and [[quasithird]]. In addition, it is divisible by 44 and in light of that it tunes [[ruthenium]] in the 7-limit and also 11-limit.
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 | [[Ruthenium]]
 |}
-<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
+<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:Quasithird]]