695edo: Difference between revisions

Revision as of 12:37, 2 November 2023

695edo is only consistent to the 5-odd-limit and the error of harmonic 3 is quite large. The equal temperament is most notable for tempering out 10976/10935, providing the optimal patent val for the hemimage temperament. It also tempers out the escapade comma, [32 -7 -9⟩ in the 5-limit; and [27 0 -8 -3⟩ and [-9 5 -8 7⟩ in the 7-limit.

Approximation of odd harmonics in 695edo
Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+0.779	+0.449	-0.193	-0.169	-0.527	+0.336	-0.499	+0.368	-0.535	+0.586	+0.215
Error	Relative (%)	+45.1	+26.0	-11.2	-9.8	-30.5	+19.4	-28.9	+21.3	-31.0	+33.9	+12.4
Steps (reduced)		1102 (407)	1614 (224)	1951 (561)	2203 (118)	2404 (319)	2572 (487)	2715 (630)	2841 (61)	2952 (172)	3053 (273)	3144 (364)

Since 695 factors into 5 × 139, 695edo contains 5edo and 139edo as subsets.

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 {{EDO intro|695}}
-In the 5-limit it [[tempering out|tempers out]] the [[escapade comma]], {{monzo| 32 -7 -9 }} in the 7-limit it tempers out [[10976/10935]] and 200120949/200000000, and provides the [[optimal patent val]] for the [[hemimage]] planar temperament, tempering out 10976/10935.
+edo is only [[consistent]] to the [[5-odd-limit]] and the error of [[harmonic]] [[3/1|3]] is quite large. The equal temperament is most notable for [[tempering out]] [[10976/10935]], providing the [[optimal patent val]] for the [[hemimage]] temperament. It also tempers out the [[escapade comma]], {{monzo| 32 -7 -9 }} in the 5-limit; and {{monzo| 27 0 -8 -3}} and {{monzo| -9 5 -8 7 }} in the 7-limit.
 === Odd harmonics ===
 {{Harmonics in equal|695}}
+=== Subsets and supersets ===
+Since 695 factors into {{factorization|695}}, 695edo contains [[5edo]] and [[139edo]] as subsets.
 [[Category:Hemimage]]