851edo: Difference between revisions

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851edo is [[consistent]] to the [[15-odd-limit]] or the no-17 no-23 [[25-odd-limit]]. As an equal temperament, it [[tempering out|tempers out]] 2401/2400 ([[breedsma]]) and 33554432/33480783 ([[garischisma]]) in the 7-limit; [[3025/3024]] and [[19712/19683]] in the 11-limit; and [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit. It provides the [[optimal patent val]] for 13-limit [[newt]], the 270 & 581 ~~temperament~~, as well as neonewt, its no-17 19-limit extension.

851edo is [[consistent]] to the [[15-odd-limit]] or the no-17 no-23 [[25-odd-limit]]. As an equal temperament, it [[tempering out|tempers out]] the [[luna comma]] in the 5-limit; 2401/2400 ([[breedsma]]) and 33554432/33480783 ([[garischisma]]) in the 7-limit; [[3025/3024]] and [[19712/19683]] in the 11-limit; and [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit. It provides the [[optimal patent val]] for 13-limit [[newt]], the 270 & 581 [[microtemperament]], as well as neonewt, its no-17 19-limit extension.

=== Prime harmonics ===

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=== Subsets and supersets ===

Since 851 factors into {{factorization|851}}, 851edo contains [[23edo]] and [[37edo]] as its subsets.

Since 851 factors into {{factorization|851}}, 851edo contains [[23edo]] and [[37edo]] as its subsets. [[1702edo]], which doubles it, provides a strong correction to the 17th and 23rd harmonics, making it notably good as a high-limit no-threes system.

[[Category:Newt]]

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 {{Infobox ET}}
-{{EDO intro}}
+{{ED intro}}
-edo is [[consistent]] to the [[15-odd-limit]] or the no-17 no-23 [[25-odd-limit]]. As an equal temperament, it [[tempering out|tempers out]] 2401/2400 ([[breedsma]]) and 33554432/33480783 ([[garischisma]]) in the 7-limit; [[3025/3024]] and [[19712/19683]] in the 11-limit; and [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit. It provides the [[optimal patent val]] for 13-limit [[newt]], the 270 & 581 temperament, as well as neonewt, its no-17 19-limit extension.
+edo is [[consistent]] to the [[15-odd-limit]] or the no-17 no-23 [[25-odd-limit]]. As an equal temperament, it [[tempering out|tempers out]] the [[luna comma]] in the 5-limit; 2401/2400 ([[breedsma]]) and 33554432/33480783 ([[garischisma]]) in the 7-limit; [[3025/3024]] and [[19712/19683]] in the 11-limit; and [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit. It provides the [[optimal patent val]] for 13-limit [[newt]], the 270 & 581 [[microtemperament]], as well as neonewt, its no-17 19-limit extension.
 === Prime harmonics ===
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 === Subsets and supersets ===
-Since 851 factors into {{factorization|851}}, 851edo contains [[23edo]] and [[37edo]] as its subsets.
+Since 851 factors into {{factorization|851}}, 851edo contains [[23edo]] and [[37edo]] as its subsets. [[1702edo]], which doubles it, provides a strong correction to the 17th and 23rd harmonics, making it notably good as a high-limit no-threes system.
 [[Category:Newt]]