935edo: Difference between revisions

935edo is a very strong 23-limit system, and is distinctly consistent through to the 27-odd-limit. It is also a zeta peak edo. The equal temperament tempers out the [39 -29 3⟩ (tricot comma), [-52 -17 34⟩ (septendecima), and [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.

Approximation of prime harmonics in 935edo
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.077	-0.004	+0.158	+0.554	+0.114	+0.285	+0.241	+0.603	-0.272	-0.223
Error	Relative (%)	+0.0	+6.0	-0.3	+12.3	+43.1	+8.9	+22.2	+18.8	+47.0	-21.2	-17.4
Steps (reduced)		935 (0)	1482 (547)	2171 (301)	2625 (755)	3235 (430)	3460 (655)	3822 (82)	3972 (232)	4230 (490)	4542 (802)	4632 (892)

Since 935 factors into 5 × 11 × 17, 935edo has subset edos 5, 11, 17, 55, 85, and 187.

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
 {{EDO intro|935}}
-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]].
+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]]. The equal temperament [[tempering out|tempers out]] the {{monzo| 39 -29 3 }} ([[tricot 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 -->

Revision as of 11:28, 2 November 2023