2814edo: Difference between revisions

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@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|2814}}
+{{ED intro}}
 == Theory ==
-edo has all the harmonics from 3 to 17 approximated below 1/3 relative error and it is as a corollary [[consistent]] in the [[17-odd-limit]].
+edo 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 contorted, with the same commas tempered out as [[1407edo]].
+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 ===
+{{Harmonics in equal|2814}}
-It is also a tuning for the [[Double Bastille]] temperament in the 2.5.7.11.13 subgroup.
+=== 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 }}.
-=== Prime harmonics ===
+== Regular temperament properties ==
-{{Harmonics in equal|2814}}
+=== Rank-2 temperaments ===
+Note: 7-limit temperaments represented by [[1407edo]] are not included.
+{| class="wikitable center-all left-5"
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
+|-
+! Periods<br />per 8ve
+! Generator*
+! Cents*
+! Associated<br />ratio*
+! 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:Equal divisions of the octave|####]]<!-- 4-digit number -->
 [[Category:Jacobin]]