415edo: Difference between revisions

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-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]].
+{{Infobox ET}}
+{{ED intro}}
+If [[5/1|harmonic 5]] is used, 415edo tends very sharp. In the 5-limit the equal temperament [[tempering out|tempers out]] the [[parakleisma]], {{monzo| 8 14 -13 }}; in the 7-limit [[3136/3125]] and [[4375/4374]], so that it [[support]]s [[parakleismic]], the 99 & 316 temperament, and provides the [[optimal patent val]]. In the 11-limit it tempers out 12005/11979, [[16384/16335]], and [[41503/41472]]; and in the 13-limit, [[676/675]], [[1001/1000]], [[2080/2079]], 3584/3575, and [[10648/10647]].
+=== Odd harmonics ===
+{{Harmonics in equal|415}}
+=== Subsets and supersets ===
+Since 415 factors into {{factorization|415}}, 415edo contains [[5edo]] and [[83edo]] as subsets.
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
 [[Category:Parakleismic]]