129edo: Difference between revisions
+overview to its harmonic quality, before going on to talk about the patent val. Misc. cleanup |
Note its patent val is the same as 43et |
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{{EDO intro|129}} | {{EDO intro|129}} | ||
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. It is the last | 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 === | === Odd harmonics === | ||