114edo: Difference between revisions

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In the [[~~5-limit|~~5-limit]] it [[~~tempering_out~~|tempers out]] 2048/2025, in the [[~~7-limit|~~7-limit]] 245/243, in the [[~~11-limit|~~11-limit]] 121/120, 176/175 and [[~~Quartisma|117440512/117406179~~]], in the [[~~13-limit|~~13-limit]] 196/195 and 325/324, in the [[~~17-limit|~~17-limit]] 136/135 and 154/153, in the [[~~19-limit|~~19-limit]] 286/285 and 343/342. These commas make for 114edo being an excellent tuning for [[~~Diaschismic_family|~~shrutar ~~temperament~~]]; it is in fact the [[~~Optimal_patent_val|~~optimal patent val]] for ~~[[Shrutar|~~shrutar]] in the 11- 13- 17- and 19-limit, as well as the rank ~~three~~ bisector temperament.

== Theory ==

In the [[5-limit]] the equal temperament [[tempering out|tempers out]] 2048/2025 ([[diaschisma]]), in the [[7-limit]] [[245/243]], in the [[11-limit]] [[121/120]], [[176/175]] and notably the [[quartisma]], in the [[13-limit]] [[196/195]] and [[325/324]], in the [[17-limit]] [[136/135]] and [[154/153]], in the [[19-limit]] [[286/285]] and [[343/342]]. These commas make for 114edo being an excellent tuning for the [[shrutar]] temperament; it is in fact the [[optimal patent val]] for shrutar in the 11-, 13-, 17-, and 19-limit, as well as the rank-3 [[bisector]] temperament.

== ~~Harmonics~~ ==

=== Odd harmonics ===

=== Subsets and supersets ===

Since 114 factors into {{factorization|114}}, 114 edo has subset edos {{EDOs| 2, 3, 6, 19, 38, and 57 }}.

== Intervals ==

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[[Category:Shrutar]]

[[Category:Bisector]]

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 {{Infobox ET}}
-{{EDO intro|114}}
+{{ED intro}}
-In the [[5-limit|5-limit]] it [[tempering_out|tempers out]] 2048/2025, in the [[7-limit|7-limit]] 245/243, in the [[11-limit|11-limit]] 121/120, 176/175 and [[Quartisma|117440512/117406179]], in the [[13-limit|13-limit]] 196/195 and 325/324, in the [[17-limit|17-limit]] 136/135 and 154/153, in the [[19-limit|19-limit]] 286/285 and 343/342. These commas make for 114edo being an excellent tuning for [[Diaschismic_family|shrutar temperament]]; it is in fact the [[Optimal_patent_val|optimal patent val]] for [[Shrutar|shrutar]] in the 11- 13- 17- and 19-limit, as well as the rank three bisector temperament.
+== Theory ==
+In the [[5-limit]] the equal temperament [[tempering out|tempers out]] 2048/2025 ([[diaschisma]]), in the [[7-limit]] [[245/243]], in the [[11-limit]] [[121/120]], [[176/175]] and notably the [[quartisma]], in the [[13-limit]] [[196/195]] and [[325/324]], in the [[17-limit]] [[136/135]] and [[154/153]], in the [[19-limit]] [[286/285]] and [[343/342]]. These commas make for 114edo being an excellent tuning for the [[shrutar]] temperament; it is in fact the [[optimal patent val]] for shrutar in the 11-, 13-, 17-, and 19-limit, as well as the rank-3 [[bisector]] temperament.
-== Harmonics ==
+=== Odd harmonics ===
 {{Harmonics in equal|114}}
+=== Subsets and supersets ===
+Since 114 factors into {{factorization|114}}, 114 edo has subset edos {{EDOs| 2, 3, 6, 19, 38, and 57 }}.
 == Intervals ==
@@ Line 11: / Line 15: @@
 [[Category:Shrutar]]
+[[Category:Bisector]]