458edo: Difference between revisions

Revision as of 07:06, 3 November 2023

458edo is inconsistent to the 5-odd-limit and harmonic 5 is about halfway between its steps. The equal temperament is most notable for tempering out the kleisma, 15625/15552, in the 5-limit and provides the optimal patent val for the 5-limit kleismic temperament.

Approximation of prime harmonics in 458edo
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	+0.23	-1.16	+0.61	-1.10	+0.52	-0.15	+1.18	+0.55	+0.12	-0.06
Error	Relative (%)	+0.0	+8.7	-44.3	+23.1	-42.0	+19.9	-5.8	+44.9	+20.9	+4.5	-2.2
Steps (reduced)		458 (0)	726 (268)	1063 (147)	1286 (370)	1584 (210)	1695 (321)	1872 (40)	1946 (114)	2072 (240)	2225 (393)	2269 (437)

Since 458 factors into 2 × 229, 458edo contains 2edo and 229edo as subsets.

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-The '''458 equal division''' divides the octave into 458 equal parts of 2.620 cents each. It tempers out the kleisma, 15625/15552, in the 5-limit and provides the [[Optimal_patent_val|optimal patent val]] for the 5-limit planar kleismic temperament.
+{{EDO intro|458}}
+edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[5/1|5]] is about halfway between its steps. The equal temperament is most notable for [[tempering out]] the kleisma, [[15625/15552]], in the 5-limit and provides the [[optimal patent val]] for the 5-limit [[kleismic]] temperament.
+=== Odd harmonics ===
+{{Harmonics in equal|458}}
+=== Subsets and supersets ===
+Since 458 factors into {{factorization|458}}, 458edo contains [[2edo]] and [[229edo]] as subsets.
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
 [[Category:Kleismic]]