415edo: Difference between revisions

Revision as of 04:11, 16 June 2023

If harmonic 5 is used, 415edo tends very sharp. In the 5-limit the equal temperament tempers out the parakleisma, [8 14 -13⟩; in the 7-limit 3136/3125 and 4375/4374, so that it supports the parakleismic temperament and provides the optimal patent val.

Approximation of odd harmonics in 415edo
Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+0.70	+1.16	-0.15	+1.39	+0.97	+0.92	-1.04	-0.86	+0.32	+0.54	-0.80
Error	Relative (%)	+24.1	+40.0	-5.2	+48.1	+33.6	+31.8	-36.0	-29.7	+11.0	+18.8	-27.8
Steps (reduced)		658 (243)	964 (134)	1165 (335)	1316 (71)	1436 (191)	1536 (291)	1621 (376)	1696 (36)	1763 (103)	1823 (163)	1877 (217)

415edo has subset edos 5 and 83.

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-The '''415 equal division''' divides the octave into 415 equal parts of 2.892 cents each. In the 5-limit it tempers out the parakleisma, |8 14 -13&gt;; in the 7-limit 3136/3125 and 4375/4374, so that it [[support]]s parakleismic temperament and provides the [[Optimal_patent_val|optimal patent val]].
+{{EDO intro|415}}
+If [[5/1|harmonic 5]] is used, 415edo tends very sharp. In the 5-limit the equal temperament tempers out the [[parakleisma]], {{monzo| 8 14 -13 }}; in the 7-limit [[3136/3125]] and [[4375/4374]], so that it [[support]]s the [[parakleismic]] temperament and provides the [[optimal patent val]].
+=== Odd harmonics ===
+{{Harmonics in equal|415}}
+=== Subsets and supersets ===
+edo has subset edos {{EDOs| 5 and 83 }}.
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
 [[Category:Parakleismic]]