2814edo: Difference between revisions
clarify and add rank 2 temp |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
2814edo has all the | 2814edo has all the [[harmonic]]s from 3 to 17 approximated below 1/3 relative error and it is as a corollary [[consistent]] in the [[17-odd-limit]]. | ||
In the 7-limit, it is | In the 7-limit, it is [[Enfactoring|enfactored]], with the same [[comma]]s [[Tempering out|tempered out]] as [[1407edo]]. In the 11-limit, it supports rank-3 [[odin]] temperament. In the 13-limit it tempers out [[6656/6655]] and supports the 2.5.7.11.13 [[subgroup]] [[double bastille]] temperament. | ||
In the 11-limit, it supports rank-3 [[odin]] temperament. | |||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|2814}} | {{Harmonics in equal|2814}} | ||
=== Subsets and supersets === | |||
Since 2814 factors into {{factorization|2814}}, 2814edo has subset edos {{EDOs| 2, 3, 6, 7, 14, 21, 42, 67, 134, 201, 402, 469, 938 and 1407 }}. | |||
== Regular temperament properties == | == Regular temperament properties == | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
Note: 7-limit temperaments represented by [[1407edo]] are not included. | Note: 7-limit temperaments represented by [[1407edo]] are not included. | ||
{| class="wikitable center-all left- | {| class="wikitable center-all left-5" | ||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |||
|- | |- | ||
|1 | ! Periods<br />per 8ve | ||
|593\2814 | ! Generator* | ||
|252.878 | ! Cents* | ||
|53094899/45875200 | ! Associated<br />ratio* | ||
|[[Double | ! Temperaments | ||
|}< | |- | ||
| 1 | |||
| 593\2814 | |||
| 252.878 | |||
| 53094899/45875200 | |||
| [[Double bastille]] | |||
|} | |||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | |||
[[Category:Jacobin]] | [[Category:Jacobin]] | ||