1092edo: Difference between revisions

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1092edo is related to [[364edo]], but it differs in mapping for [[5/1|5]] and [[11/1|11]]. Despite having large errors on ~~harmonics~~, it is [[consistent]] in the [[13-odd-limit]]~~. It is not consistent higher than that as its mapping~~ for [[15/8]] ~~is off by one step of a stack of~~ [[3/2]] and [[~~5/4~~]]~~. It provides~~ the [[~~optimal patent val]] for the [[sextile]] temperament and the rank~~-~~3 [[loki~~]] ~~temperament~~.

1092edo is related to [[364edo]], but it differs in mapping for [[5/1|5]] and [[11/1|11]]. Despite having large errors on the [[harmonic]]s, it is [[consistent]] in the [[13-odd-limit]], and except for [[15/8]], [[21/16]] and their [[octave complement]]s, the [[23-odd-limit]].

In higher limits, 1092edo is ~~good at~~ the 2.13.29.31.53.59 subgroup.

It provides the [[optimal patent val]] for [[sextile]], the 270 & 822 temperament, the rank-3 [[loki]] temperament, and the rank-4 [[vishdelismic]] temperament, which tempers out [[5632/5625]], as well as its no-7 [[retraction]] thereof.

In higher limits, 1092edo is accurate in the 2.13.29.31.53.59 subgroup.

=== Odd harmonics ===

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=== Subsets and supersets ===

Since 1092 factors into {{~~factorization~~|~~1092~~}}, 1092edo has subset edos {{EDOs| 2, 3, 4, 6, 7, 12, 13, 14, 21, 26, 28, 39, 42, 52, 78, 84, 91, 156, 182, 273, 364, and 546 }}.

Since 1092 factors into primes as {{nowrap| 2<sup>2</sup> × 3 × 7 × 13 }}, 1092edo has subset edos {{EDOs| 2, 3, 4, 6, 7, 12, 13, 14, 21, 26, 28, 39, 42, 52, 78, 84, 91, 156, 182, 273, 364, and 546 }}.

[[Category:Sextile]]

[[Category:Loki]]

[[Category:Vishdelismic]]

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 {{ED intro}}
-edo is related to [[364edo]], but it differs in mapping for [[5/1|5]] and [[11/1|11]]. Despite having large errors on harmonics, it is [[consistent]] in the [[13-odd-limit]]. It is not consistent higher than that as its mapping for [[15/8]] is off by one step of a stack of [[3/2]] and [[5/4]]. It provides the [[optimal patent val]] for the [[sextile]] temperament and the rank-3 [[loki]] temperament.
+edo is related to [[364edo]], but it differs in mapping for [[5/1|5]] and [[11/1|11]]. Despite having large errors on the [[harmonic]]s, it is [[consistent]] in the [[13-odd-limit]], and except for [[15/8]], [[21/16]] and their [[octave complement]]s, the [[23-odd-limit]].
-In higher limits, 1092edo is good at the 2.13.29.31.53.59 subgroup.
+It provides the [[optimal patent val]] for [[sextile]], the 270 & 822 temperament, the rank-3 [[loki]] temperament, and the rank-4 [[vishdelismic]] temperament, which tempers out [[5632/5625]], as well as its no-7 [[retraction]] thereof.
+In higher limits, 1092edo is accurate in the 2.13.29.31.53.59 subgroup.
 === Odd harmonics ===
@@ Line 10: / Line 12: @@
 === Subsets and supersets ===
-Since 1092 factors into {{factorization|1092}}, 1092edo has subset edos {{EDOs| 2, 3, 4, 6, 7, 12, 13, 14, 21, 26, 28, 39, 42, 52, 78, 84, 91, 156, 182, 273, 364, and 546 }}.
+Since 1092 factors into primes as {{nowrap| 2<sup>2</sup> × 3 × 7 × 13 }}, 1092edo has subset edos {{EDOs| 2, 3, 4, 6, 7, 12, 13, 14, 21, 26, 28, 39, 42, 52, 78, 84, 91, 156, 182, 273, 364, and 546 }}.
 [[Category:Sextile]]
 [[Category:Loki]]
+[[Category:Vishdelismic]]