935edo: Difference between revisions

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The 935 equal division divides the octave into 935 parts of 1.283 cents 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 tricot comma {{~~monzo| 39 -29 3~~ }}~~, septendecima~~ {{~~monzo| -52 -17 34~~ }}, and astro {{monzo| 91 -12 -31 }}. 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.

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

== 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.

[[~~Category:Todo:expand~~]]

=== Prime harmonics ===

=== 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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-The 935 equal division divides the octave into 935 parts of 1.283 cents 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 tricot comma {{monzo| 39 -29 3 }}, septendecima {{monzo| -52 -17 34 }}, and astro {{monzo| 91 -12 -31 }}. 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.
+{{Infobox ET}}
+{{ED intro}}
-[[Category:Equal divisions of the octave]]
+== 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.
-[[Category:Todo:expand]]
+=== Prime harmonics ===
+{{Harmonics in equal|935}}
+=== 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.