935edo: Difference between revisions

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The '''935 equal divisions of the octave''' ('''935edo''') divides the [[octave]] into 935 parts of 1.283 [[cent]]s each. It is a very strong 23-limit system, and distinctly [[consistent]] through to the [[27-odd-limit]]. It is also a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak tuning]]. In the 5-limit it tempers out the {{~~monzo| 39 -29 3~~ }} ([[tricot comma]]), {{monzo| -52 -17 34 }} ([[septendecima]]), and {{monzo| 91 -12 -31 }} (astro). In the 7-limit it tempers out [[4375/4374]] and 52734375/52706752, in the 11-limit 161280/161051 and 117649/117612, and in the 13-limit [[2080/2079]], [[4096/4095]] and [[4225/4224]].

~~935~~ = ~~5 × 11 ×~~ 17, ~~with subset edos~~ 5, 11, ~~17, 55, 85,~~ and ~~187~~.

== Theory ==

935edo is a very strong 23-limit system, and is [[consistency|distinctly consistent]] through to the [[27-odd-limit]]. It is also a [[zeta peak edo]]. It [[tempering out|tempers out]] the {{monzo| 39 -29 3 }} ([[alphatricot comma]]), {{monzo| -52 -17 34 }} ([[septendecima]]), and {{monzo| 91 -12 -31 }} (astro) in the 5-limit; [[4375/4374]] and 52734375/52706752 in the 7-limit; 161280/161051 and 117649/117612 in the 11-limit; and [[2080/2079]], [[4096/4095]] and [[4225/4224]] in the 13-limit.

=== Prime harmonics ===

[[~~Category:Equal divisions of~~ the ~~octave~~|~~###~~]] 

=== Subsets and supersets ===

Since 935 factors into {{factorization|935}}, 935edo has subset edos {{EDOs| 5, 11, 17, 55, 85, and 187 }}.

== Regular temperament properties ==

935et has lower absolute errors than any previous equal temperaments in the 13-, 17-, 19- and 23-limit. It is the first to beat [[764edo|764]] in the 13-limit, [[814edo|814]] in the 17- and 23-limit, and [[742edo|742]] in the 19-limit, only to be bettered by [[954edo|954h]] in all of those subgroups.

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 {{Infobox ET}}
-The '''935 equal divisions of the octave''' ('''935edo''') divides the [[octave]] into 935 parts of 1.283 [[cent]]s each. It is a very strong 23-limit system, and distinctly [[consistent]] through to the [[27-odd-limit]]. It is also a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak tuning]]. In the 5-limit it tempers out the {{monzo| 39 -29 3 }} ([[tricot comma]]), {{monzo| -52 -17 34 }} ([[septendecima]]), and {{monzo| 91 -12 -31 }} (astro). In the 7-limit it tempers out [[4375/4374]] and 52734375/52706752, in the 11-limit 161280/161051 and 117649/117612, and in the 13-limit [[2080/2079]], [[4096/4095]] and [[4225/4224]].
+{{ED intro}}
-= 5 × 11 × 17, with subset edos 5, 11, 17, 55, 85, and 187.
+== Theory ==
+edo is a very strong 23-limit system, and is [[consistency|distinctly consistent]] through to the [[27-odd-limit]]. It is also a [[zeta peak edo]]. It [[tempering out|tempers out]] the {{monzo| 39 -29 3 }} ([[alphatricot comma]]), {{monzo| -52 -17 34 }} ([[septendecima]]), and {{monzo| 91 -12 -31 }} (astro) in the 5-limit; [[4375/4374]] and 52734375/52706752 in the 7-limit; 161280/161051 and 117649/117612 in the 11-limit; and [[2080/2079]], [[4096/4095]] and [[4225/4224]] in the 13-limit.
 === Prime harmonics ===
 {{Harmonics in equal|935}}
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+=== Subsets and supersets ===
+Since 935 factors into {{factorization|935}}, 935edo has subset edos {{EDOs| 5, 11, 17, 55, 85, and 187 }}.
+== Regular temperament properties ==
+et has lower absolute errors than any previous equal temperaments in the 13-, 17-, 19- and 23-limit. It is the first to beat [[764edo|764]] in the 13-limit, [[814edo|814]] in the 17- and 23-limit, and [[742edo|742]] in the 19-limit, only to be bettered by [[954edo|954h]] in all of those subgroups.