246edo: Difference between revisions

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== Theory ==

246 = 6 × 41, and 246edo shares its [[perfect fifth|fifth]] with 41edo. It is only [[consistent]] to the [[5-odd-limit]], but the [[patent val]] offers excellent approximations (within half a cent) of [[prime harmonic]]s [[11/1|11]], [[19/1|19]], and [[29/1|29]], and quite good approximations (within one cent) of [[5/1|5]] and [[23/1|23]]. It provides the [[optimal patent val]] for [[cata]], the 2.3.5.13 [[subgroup]] temperament [[~~tempering out~~]] [[~~325/324~~]] ~~and~~ [[~~625/624~~]].

246 = 6 × 41, and 246edo shares its [[perfect fifth|fifth]] with 41edo. It is only [[consistent]] to the [[5-odd-limit]], but the [[patent val]] offers excellent approximations (within half a cent) of [[prime harmonic]]s [[11/1|11]], [[19/1|19]], and [[29/1|29]], and quite good approximations (within one cent) of [[5/1|5]] and [[23/1|23]]. The same 11 and 19 are straight-up inherited by the monstrous [[2460edo]].

As an equal temperament, 246et [[tempering out|tempers out]] 15625/15552 ([[15625/15552|kleisma]]) in the 5-limit; [[5120/5103]] and 118098/117649 in the 7-limit; and [[540/539]], [[9801/9800]] in the 11-limit; [[325/324]], [[625/624]] in the 13-limit. It provides the [[optimal patent val]] for [[cata]], the 2.3.5.13 [[subgroup]] temperament tempering out 325/324 and 625/624. The 246d val [[support]]s [[tritikleismic]]. The 246ee val supports [[countercata]]. The 246f val supports [[supers]].

=== Prime harmonics ===

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=== Subsets and supersets ===

Since 246 factors into {{factorization|246}}, 246edo has subset edos {{EDOs| 2, 3, 6, 41, 82, and 123 }}.

A step of 246edo is exactly 10 [[mina]]s.

== Scales ==

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* [[Cata19]]

[[Category:~~Cata~~]]

[[Category:Kleismic]]

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 {{Infobox ET}}
-{{EDO intro}}
+{{ED intro}}
 == Theory ==
-= 6 × 41, and 246edo shares its [[perfect fifth|fifth]] with 41edo. It is only [[consistent]] to the [[5-odd-limit]], but the [[patent val]] offers excellent approximations (within half a cent) of [[prime harmonic]]s [[11/1|11]], [[19/1|19]], and [[29/1|29]], and quite good approximations (within one cent) of [[5/1|5]] and [[23/1|23]]. It provides the [[optimal patent val]] for [[cata]], the 2.3.5.13 [[subgroup]] temperament [[tempering out]] [[325/324]] and [[625/624]].
+= 6 × 41, and 246edo shares its [[perfect fifth|fifth]] with 41edo. It is only [[consistent]] to the [[5-odd-limit]], but the [[patent val]] offers excellent approximations (within half a cent) of [[prime harmonic]]s [[11/1|11]], [[19/1|19]], and [[29/1|29]], and quite good approximations (within one cent) of [[5/1|5]] and [[23/1|23]]. The same 11 and 19 are straight-up inherited by the monstrous [[2460edo]].
+As an equal temperament, 246et [[tempering out|tempers out]] 15625/15552 ([[15625/15552|kleisma]]) in the 5-limit; [[5120/5103]] and 118098/117649 in the 7-limit; and [[540/539]], [[9801/9800]] in the 11-limit; [[325/324]], [[625/624]] in the 13-limit. It provides the [[optimal patent val]] for [[cata]], the 2.3.5.13 [[subgroup]] temperament tempering out 325/324 and 625/624. The 246d val [[support]]s [[tritikleismic]]. The 246ee val supports [[countercata]]. The 246f val supports [[supers]].
 === Prime harmonics ===
@@ Line 9: / Line 11: @@
 === Subsets and supersets ===
 Since 246 factors into {{factorization|246}}, 246edo has subset edos {{EDOs| 2, 3, 6, 41, 82, and 123 }}.
+A step of 246edo is exactly 10 [[mina]]s.
 == Scales ==
@@ Line 19: / Line 23: @@
 * [[Cata19]]
-[[Category:Cata]]
+[[Category:Kleismic]]