129edo: Difference between revisions

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'''129edo''' is the [[~~Equal_division_of_the_octave|~~equal division of the octave]] into 129 parts of 9.302 [[~~cent|~~cent]]s each. It provides the [[~~Optimal_patent_val|~~optimal patent val]] for the 11-limit rank ~~three~~ [[~~Didymus_rank_three_family|~~clio ~~temperament~~]]. It [[~~tempering_out~~|tempers out]] 81/80 ~~in the~~ [[5-limit~~|5-limit]];~~ 1029/1024 and 1728/1715 in the [[~~7-limit|~~7-limit]]; 176/175 and 540/539 in the [[~~11-limit|~~11-limit]]; 507/500, 676/675 and 847/845 in the [[~~13-limit|~~13-limit]]; 221/220 in the [[~~17-limit|~~17-limit]]; 171/170 and 286/285 in the [[~~19-limit|~~19-limit]].

'''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]].

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

=== Odd harmonics ===

=== Miscellany ===

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

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

[[Category:Clio]]

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 {{Infobox ET}}
-'''129edo''' is the [[Equal_division_of_the_octave|equal division of the octave]] into 129 parts of 9.302 [[cent|cent]]s each. It provides the [[Optimal_patent_val|optimal patent val]] for the 11-limit rank three [[Didymus_rank_three_family|clio temperament]]. It [[tempering_out|tempers out]] 81/80 in the [[5-limit|5-limit]]; 1029/1024 and 1728/1715 in the [[7-limit|7-limit]]; 176/175 and 540/539 in the [[11-limit|11-limit]]; 507/500, 676/675 and 847/845 in the [[13-limit|13-limit]]; 221/220 in the [[17-limit|17-limit]]; 171/170 and 286/285 in the [[19-limit|19-limit]].
+'''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]].
-The factorization of 129 is [[3edo|3]] and [[43edo|43]]
+=== Odd harmonics ===
+{{Harmonics in equal|129}}
+=== Miscellany ===
+The factorization of 129 is [[3edo|3]] and [[43edo|43]].
 [[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
 [[Category:Clio]]