129edo: Difference between revisions

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~~'''~~129edo~~'''~~ is the [[~~equal division of the octave~~]] ~~into 129 parts of 9.302~~ [[~~cent~~]]s ~~each~~. ~~It provides the~~ [[~~optimal~~ patent val]] ~~for~~ the 11-limit ~~rank-3~~ [[~~clio~~]] ~~temperament~~. It is the last [[patent val]] that [[tempering out|tempers out]] 81/80 so as to support [[meantone]] and its higher-limit expansions. It also tempers out [[1029/1024]] and [[1728/1715]] in the [[7-limit]]; [[176/175]] and [[540/539]] in the [[11-limit]]; [[507/500]], [[676/675]] and [[847/845]] in the [[13-limit]]; [[221/220]] in the [[17-limit]]; [[171/170]] and [[286/285]] in the [[19-limit]].

129edo is in[[consistent]] to the [[5-odd-limit]] and both [[harmonic]]s [[3/1|3]] and [[5/1|5]] are about halfway between its steps. The [[patent val]] is [[enfactoring|enfactored]] in the 5-limit, with the same tuning as [[43edo]]. It is the last patent val that [[tempering out|tempers out]] [[81/80]] so as to [[support]] [[meantone]] and its higher-limit expansions. It also tempers out [[1029/1024]] and [[1728/1715]] in the [[7-limit]]; [[176/175]] and [[540/539]] in the [[11-limit]]; [[507/500]], [[676/675]] and [[847/845]] in the [[13-limit]]; [[221/220]] in the [[17-limit]]; [[171/170]] and [[286/285]] in the [[19-limit]]. It provides the [[optimal patent val]] for the 11-limit rank-3 [[clio]] temperament.

=== Odd harmonics ===

=== ~~Miscellany~~ ===

=== Subsets and supersets ===

~~The~~ factorization of 129 is [[3edo|3]] and [[43edo~~|43~~]].

Since 129 factors into {{factorization|129}}, 129edo contains [[3edo]] and [[43edo]] as its subsets. [[258edo]], which doubles it, provides a good correction for the 3rd and 5th harmonics.

== Instruments ==

* [[Lumatone mapping for 129edo]]

~~[[Category:Equal divisions of the octave|###]] ~~

[[Category:Clio]]

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 {{Infobox ET}}
-'''129edo''' is the [[equal division of the octave]] into 129 parts of 9.302 [[cent]]s each. It provides the [[optimal patent val]] for the 11-limit rank-3 [[clio]] temperament. It is the last [[patent val]] that [[tempering out|tempers out]] 81/80 so as to support [[meantone]] and its higher-limit expansions. It also tempers out [[1029/1024]] and [[1728/1715]] in the [[7-limit]]; [[176/175]] and [[540/539]] in the [[11-limit]]; [[507/500]], [[676/675]] and [[847/845]] in the [[13-limit]]; [[221/220]] in the [[17-limit]]; [[171/170]] and [[286/285]] in the [[19-limit]].
+{{ED intro}}
+edo is in[[consistent]] to the [[5-odd-limit]] and both [[harmonic]]s [[3/1|3]] and [[5/1|5]] are about halfway between its steps. The [[patent val]] is [[enfactoring|enfactored]] in the 5-limit, with the same tuning as [[43edo]]. It is the last patent val that [[tempering out|tempers out]] [[81/80]] so as to [[support]] [[meantone]] and its higher-limit expansions. It also tempers out [[1029/1024]] and [[1728/1715]] in the [[7-limit]]; [[176/175]] and [[540/539]] in the [[11-limit]]; [[507/500]], [[676/675]] and [[847/845]] in the [[13-limit]]; [[221/220]] in the [[17-limit]]; [[171/170]] and [[286/285]] in the [[19-limit]]. It provides the [[optimal patent val]] for the 11-limit rank-3 [[clio]] temperament.
 === Odd harmonics ===
 {{Harmonics in equal|129}}
-=== Miscellany ===
+=== Subsets and supersets ===
-The factorization of 129 is [[3edo|3]] and [[43edo|43]].
+Since 129 factors into {{factorization|129}}, 129edo contains [[3edo]] and [[43edo]] as its subsets. [[258edo]], which doubles it, provides a good correction for the 3rd and 5th harmonics.
+== Instruments ==
+* [[Lumatone mapping for 129edo]]
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
 [[Category:Clio]]