1342edo: Difference between revisions

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1342edo is [[consistent]] to the 9-odd-limit, but there is a large relative delta for ~~the 7th~~ and ~~the 11th harmonics~~. Its notability lies in the utility as every other step of the full 13-limit ~~monster –~~ [[2684edo]], so it probably makes more sense as a 2.3.5.13 [[subgroup]] temperament. In the 5-limit it tempers out kwazy, {{monzo| -53 10 16 }}, senior {{monzo| -17 62 -35 }}, and egads, {{monzo| -36 52 51 }}; in the 2.3.5.13 subgroup it tempers out 140625/140608.

1342edo is [[consistent]] to the [[9-odd-limit]], but there is a large relative delta for [[harmonic]]s [[7/1|7]] and [[11/1|11]]. Its notability lies in the utility as every other step of the full 13-limit monster—[[2684edo]], so it probably makes more sense as a [[2.3.5.13 subgroup|2.3.5.13]] [[subgroup]] temperament. In the 5-limit it tempers out [[kwazy comma|kwazy]], {{monzo| -53 10 16 }}, [[senior]] {{monzo| -17 62 -35 }}, and [[egads]], {{monzo| -36 52 51 }}; in the 2.3.5.13 subgroup it tempers out [[Catasma|140625/140608]], providing the optimal patent val for [[Very high accuracy temperaments#Catabolic|catabolic]].

=== Prime harmonics ===

=== ~~Divisors~~ ===

=== Subsets and supersets ===

Since 1342 factors as ~~2 × 11 × 61~~, 1342edo has subset edos {{EDOs| 2, 11, 22, 61, 122, and 671 }}.

Since 1342 factors as {{factorization|1342}}, 1342edo has subset edos {{EDOs| 2, 11, 22, 61, 122, and 671 }}. 2684edo, which doubles it, corrects the harmonics 7 and 11 to near-just qualities.

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 {{Infobox ET}}
-{{EDO intro|1342}}
+{{ED intro}}
-edo is [[consistent]] to the 9-odd-limit, but there is a large relative delta for the 7th and the 11th harmonics. Its notability lies in the utility as every other step of the full 13-limit monster – [[2684edo]], so it probably makes more sense as a 2.3.5.13 [[subgroup]] temperament. In the 5-limit it tempers out kwazy, {{monzo| -53 10 16 }}, senior {{monzo| -17 62 -35 }}, and egads, {{monzo| -36 52 51 }}; in the 2.3.5.13 subgroup it tempers out 140625/140608.
+edo is [[consistent]] to the [[9-odd-limit]], but there is a large relative delta for [[harmonic]]s [[7/1|7]] and [[11/1|11]]. Its notability lies in the utility as every other step of the full 13-limit monster—[[2684edo]], so it probably makes more sense as a [[2.3.5.13 subgroup|2.3.5.13]] [[subgroup]] temperament. In the 5-limit it tempers out [[kwazy comma|kwazy]], {{monzo| -53 10 16 }}, [[senior]] {{monzo| -17 62 -35 }}, and [[egads]], {{monzo| -36 52 51 }}; in the 2.3.5.13 subgroup it tempers out [[Catasma|140625/140608]], providing the optimal patent val for [[Very high accuracy temperaments#Catabolic|catabolic]].
 === Prime harmonics ===
 {{Harmonics in equal|1342|columns=11}}
-=== Divisors ===
+=== Subsets and supersets ===
-Since 1342 factors as 2 × 11 × 61, 1342edo has subset edos {{EDOs| 2, 11, 22, 61, 122, and 671 }}.
+Since 1342 factors as {{factorization|1342}}, 1342edo has subset edos {{EDOs| 2, 11, 22, 61, 122, and 671 }}. 2684edo, which doubles it, corrects the harmonics 7 and 11 to near-just qualities.