1224edo: Difference between revisions

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1224edo is [[~~Enfactoring~~|enfactored]] in the 11-limit, with the same tuning as [[612edo]], but it corrects the ~~harmonics~~ [[13/1|13]] and [[17/1|17]] to work better with the ~~other~~ harmonics. It provides the [[optimal patent val]] for the 19-limit semihemiennealimmal temperament with fine tunes of 23, 29 and 31.

1224edo is [[enfactoring|enfactored]] in the [[11-limit]], with the same tuning as [[612edo]], but it corrects the [[harmonic]]s [[13/1|13]] and [[17/1|17]] to work better with the flat tendency of the lower harmonics. It [[tempering out|tempers out]] [[4225/4224]], [[10648/10647]] in the 13-limit; [[2431/2430]], [[4914/4913]] in the 17-limit; [[1729/1728]], [[2926/2925]] among others in the 19-limit. It provides the [[optimal patent val]] for the 19-limit [[semihemiennealimmal]] temperament with fine tunes of [[23/1|23]], [[29/1|29]] and [[31/1|31]].

=== Prime harmonics ===

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=== Subsets and supersets ===

Since 1224 factors into ~~2<sup>3</sup> × 3<sup>2</sup> × 17~~, 1224edo has subset edos {{EDOs| 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72, 102, 136, 153, 204, 306, 408, and 612 }}.

Since 1224 factors into {{factorization|1224}}, 1224edo has subset edos {{EDOs| 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72, 102, 136, 153, 204, 306, 408, and 612 }}.

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 {{Infobox ET}}
-{{EDO intro|1224}}
+{{ED intro}}
-edo is [[Enfactoring|enfactored]] in the 11-limit, with the same tuning as [[612edo]], but it corrects the harmonics [[13/1|13]] and [[17/1|17]] to work better with the other harmonics. It provides the [[optimal patent val]] for the 19-limit semihemiennealimmal temperament with fine tunes of 23, 29 and 31.
+edo is [[enfactoring|enfactored]] in the [[11-limit]], with the same tuning as [[612edo]], but it corrects the [[harmonic]]s [[13/1|13]] and [[17/1|17]] to work better with the flat tendency of the lower harmonics. It [[tempering out|tempers out]] [[4225/4224]], [[10648/10647]] in the 13-limit; [[2431/2430]], [[4914/4913]] in the 17-limit; [[1729/1728]], [[2926/2925]] among others in the 19-limit. It provides the [[optimal patent val]] for the 19-limit [[semihemiennealimmal]] temperament with fine tunes of [[23/1|23]], [[29/1|29]] and [[31/1|31]].
 === Prime harmonics ===
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 === Subsets and supersets ===
-Since 1224 factors into 2<sup>3</sup> × 3<sup>2</sup> × 17, 1224edo has subset edos {{EDOs| 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72, 102, 136, 153, 204, 306, 408, and 612 }}.
+Since 1224 factors into {{factorization|1224}}, 1224edo has subset edos {{EDOs| 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72, 102, 136, 153, 204, 306, 408, and 612 }}.