2814edo: Difference between revisions

(7 intermediate revisions by 2 users not shown)

Line 1:

== Theory ==

2814edo 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]].

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 ~~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.

In the 13-limit it tempers out [[6656/6655]] and supports the 2.5.7.11.13 subgroup [[~~Double Bastille~~]] temperament.

=== Prime harmonics ===

=== 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 ==

=== Rank-2 temperaments ===

Note: 7-limit temperaments represented by [[1407edo]] are not included.

{| class="wikitable center-all left-4"

{| class="wikitable center-all left-5"

! Periods per 8ve

|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator

! Generator~~ (Reduced)~~

|-

! Cents~~ (Reduced)~~

! Periods per 8ve

! Associated ~~Ratio~~

! Generator*

! ~~Temperament~~

! Cents*

! Associated ratio*

! Temperaments

|-

| 1

Line 28:

Line 29:

| 252.878

| 53094899/45875200

| [[Double ~~Bastille~~]]

| [[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|####]] ~~

[[Category:Jacobin]]

@@ 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.
-In the 13-limit it tempers out [[6656/6655]] and supports the 2.5.7.11.13 subgroup [[Double Bastille]] temperament.
 === Prime harmonics ===
 {{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 ==
 === Rank-2 temperaments ===
 Note: 7-limit temperaments represented by [[1407edo]] are not included.
-{| class="wikitable center-all left-4"
+{| class="wikitable center-all left-5"
-! Periods<br>per 8ve
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
-! Generator<br>(Reduced)
+|-
-! Cents<br>(Reduced)
+! Periods<br />per 8ve
-! Associated<br>Ratio
+! Generator*
-! Temperament
+! Cents*
+! Associated<br />ratio*
+! Temperaments
 |-
 | 1
@@ Line 28: / Line 29: @@
 | 252.878
 | 53094899/45875200
-| [[Double Bastille]]
+| [[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]]