122edo: Difference between revisions

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122 is flat in tendency, with the [[prime harmonic]]s from 3 to 13 tuned flat. ~~The~~ equal temperament [[tempering out|tempers out]] 78732/78125 in the [[5-limit]]; 225/224 in the [[7-limit]]; [[385/384]] and [[4000/3993]] in the [[11-limit]]; and [[351/350]] and [[364/363]] in the [[13-limit]]. It provides the [[optimal patent val]] for the 7-limit [[tritonic]] temperament and the 11-limit [[Marvel temperaments #Tritoni|tritoni]] temperament, and the [[rank-3 ~~temperament~~|planar]] [[squalentine]] ~~temperament~~.

122 is flat in tendency, with the [[prime harmonic]]s from 3 to 13 tuned flat. As an equal temperament, it [[tempering out|tempers out]] 78732/78125 ([[sensipent comma]]) in the [[5-limit]]; [[225/224]] in the [[7-limit]]; [[385/384]] and [[4000/3993]] in the [[11-limit]]; and [[351/350]] and [[364/363]] in the [[13-limit]]. It provides the [[optimal patent val]] for the 7-limit [[tritonic]] temperament and the 11-limit [[Marvel temperaments #Tritoni|tritoni]] temperament, and the [[rank-3|planar]] temperament [[squalentine]].

122 = [[55edo|55]] + [[67edo|67]], and so using the 122c val it is the convergent towards [[1/6-comma meantone]], with a fifth just a hundredth of a cent flatter.

122 = [[55edo|55]] + [[67edo|67]], and so using the 122c [[val]] it is the [[convergent]] towards [[1/6-comma meantone]], with a fifth just a hundredth of a cent flatter.

=== Odd harmonics ===

Harmonic 25 (two 5/4 major thirds) is about halfway between 122edo's steps.

=== Subsets and supersets ===

Since 122 factors into {{factorization|122}}, 122edo contains [[2edo]] and [[61edo]] as its subsets. 244edo (double 122edo) provides a good correction to ~~harmonic~~ 25.

Since 122 factors into {{factorization|122}}, 122edo contains [[2edo]] and [[61edo]] as its subsets. [[244edo]] (double 122edo) provides a good correction to harmonics 7 and 25.

[[Category:Tritonic]]

[[Category:Meantone]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro}}
+{{ED intro}}
-is flat in tendency, with the [[prime harmonic]]s from 3 to 13 tuned flat. The equal temperament [[tempering out|tempers out]] 78732/78125 in the [[5-limit]]; 225/224 in the [[7-limit]]; [[385/384]] and [[4000/3993]] in the [[11-limit]]; and [[351/350]] and [[364/363]] in the [[13-limit]]. It provides the [[optimal patent val]] for the 7-limit [[tritonic]] temperament and the 11-limit [[Marvel temperaments #Tritoni|tritoni]] temperament, and the [[rank-3 temperament|planar]] [[squalentine]] temperament.
+is flat in tendency, with the [[prime harmonic]]s from 3 to 13 tuned flat. As an equal temperament, it [[tempering out|tempers out]] 78732/78125 ([[sensipent comma]]) in the [[5-limit]]; [[225/224]] in the [[7-limit]]; [[385/384]] and [[4000/3993]] in the [[11-limit]]; and [[351/350]] and [[364/363]] in the [[13-limit]]. It provides the [[optimal patent val]] for the 7-limit [[tritonic]] temperament and the 11-limit [[Marvel temperaments #Tritoni|tritoni]] temperament, and the [[rank-3|planar]] temperament [[squalentine]].
-= [[55edo|55]] + [[67edo|67]], and so using the 122c val it is the convergent towards [[1/6-comma meantone]], with a fifth just a hundredth of a cent flatter.
+= [[55edo|55]] + [[67edo|67]], and so using the 122c [[val]] it is the [[convergent]] towards [[1/6-comma meantone]], with a fifth just a hundredth of a cent flatter.
 === Odd harmonics ===
-{{Harmonics in equal|122|23=}}
+{{Harmonics in equal|122}}
 Harmonic 25 (two 5/4 major thirds) is about halfway between 122edo's steps.
 === Subsets and supersets ===
-Since 122 factors into {{factorization|122}}, 122edo contains [[2edo]] and [[61edo]] as its subsets. 244edo (double 122edo) provides a good correction to harmonic 25.
+Since 122 factors into {{factorization|122}}, 122edo contains [[2edo]] and [[61edo]] as its subsets. [[244edo]] (double 122edo) provides a good correction to harmonics 7 and 25.
 [[Category:Tritonic]]
 [[Category:Meantone]]