935edo: Difference between revisions

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935edo 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]].

== 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 ===

=== ~~Divisors~~ ===

=== Subsets and supersets ===

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

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

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

== 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}}
-{{EDO intro|935}}
+{{ED intro}}
-edo 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]].
+== 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}}
-=== Divisors ===
+=== Subsets and supersets ===
-= 5 × 11 × 17, with subset edos 5, 11, 17, 55, 85, and 187.
+Since 935 factors into {{factorization|935}}, 935edo has subset edos {{EDOs| 5, 11, 17, 55, 85, and 187 }}.
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+== 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.