342edo: Difference between revisions
m Update the prime error table; style |
Subsets and supersets; notability in the 11-limit |
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{{Harmonics in equal|342|columns=11}} | {{Harmonics in equal|342|columns=11}} | ||
=== | === Subset and supersets === | ||
342 factors as 2 × 3<sup>2</sup> × 19, with subset edos {{EDOs| 2, 3, 6, 9, 18, 19, 38, 57, 114, and 171 }}. | 342 factors as 2 × 3<sup>2</sup> × 19, with subset edos {{EDOs| 2, 3, 6, 9, 18, 19, 38, 57, 114, and 171 }}. | ||
[[684edo]], which doubles 342edo, provides an approximation of harmonic 13 that works well with the flat tendency of its 11-limit mapping. | |||
== Regular temperament properties == | == Regular temperament properties == | ||
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| style="border-top: double;" | 5.87 | | style="border-top: double;" | 5.87 | ||
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* 342et is lower in relative error than any previous equal temperaments in the 11-limit. Not until [[612edo|612]] do we find a better equal temperament in terms of absolute error, and not until [[1848edo|1848]] do we find one in terms of relative error. | * 342et is lower in relative error than any previous equal temperaments in the 11-limit, being the first to beat [[270edo|270]]. Not until [[612edo|612]] do we find a better equal temperament in terms of absolute error, and not until [[1848edo|1848]] do we find one in terms of relative error. | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
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| [[Hemienneadecal]] | | [[Hemienneadecal]] | ||
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