246edo: Difference between revisions

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~~246edo divides the 2/1 (octave) into 246 equal steps of 4.878 [[cents|cents]].~~

~~The~~ patent val offers excellent approximations (within half a cent) of ~~primes 3,~~ 11, 19, and 29, and quite good approximations (within one cent) of ~~primes~~ 5 and 23.

== 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]]. The same 11 and 19 are straight-up inherited by the monstrous [[2460edo]].

~~=Scales=~~

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]].

[[~~cata7~~|~~cata7~~]]

~~[[cata11~~|~~cata11]]~~

=== Prime harmonics ===

~~[[cata15~~|~~cata15]]~~

=== Subsets and supersets ===

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

[[~~cata19|cata19~~]]

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

[[File:cata_246edo.jpg|alt=cata_246edo.jpg|~~cata_246edo.jpg~~]] [[~~Category:Equal divisions of the octave~~]]

== Scales ==

[[Category:~~scales~~]]

[[File:cata_246edo.jpg|thumb|alt=cata_246edo.jpg|Cata in 246edo]]

* [[Cata7]]

* [[Cata11]]

* [[Cata15]]

* [[Cata19]]

[[Category:Kleismic]]

@@ Line 1: / Line 1: @@
-edo divides the 2/1 (octave) into 246 equal steps of 4.878 [[cents|cents]].
+{{Infobox ET}}
+{{ED intro}}
-The patent val offers excellent approximations (within half a cent) of primes 3, 11, 19, and 29, and quite good approximations (within one cent) of primes 5 and 23.
+== 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]]. The same 11 and 19 are straight-up inherited by the monstrous [[2460edo]].
-=Scales=
+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]].
-[[cata7|cata7]]
-[[cata11|cata11]]
+=== Prime harmonics ===
+{{Harmonics in equal|246}}
-[[cata15|cata15]]
+=== Subsets and supersets ===
+Since 246 factors into {{factorization|246}}, 246edo has subset edos {{EDOs| 2, 3, 6, 41, 82, and 123 }}.
-[[cata19|cata19]]
+A step of 246edo is exactly 10 [[mina]]s.
-[[File:cata_246edo.jpg|alt=cata_246edo.jpg|cata_246edo.jpg]]      [[Category:Equal divisions of the octave]]
+== Scales ==
-[[Category:scales]]
+[[File:cata_246edo.jpg|thumb|alt=cata_246edo.jpg|Cata in 246edo]]
+* [[Cata7]]
+* [[Cata11]]
+* [[Cata15]]
+* [[Cata19]]
+[[Category:Kleismic]]