2814edo: Difference between revisions

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== 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 ===

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

! Periods<br>per 8ve

! Generator~~<br>(Reduced)~~

! Generator*

! Cents~~<br>(Reduced)~~

! Cents*

! Associated<br>Ratio

! Temperament

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| 252.878

| 53094899/45875200

| [[Double ~~Bastille~~]]

| [[Double bastille]]

|}

<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct

~~[[Category:Equal divisions of the octave|####]] ~~

[[Category:Jacobin]]

@@ Line 3: / Line 3: @@
 == 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 ===
@@ Line 19: / Line 15: @@
 {| class="wikitable center-all left-4"
 ! Periods<br>per 8ve
-! Generator<br>(Reduced)
+! Generator*
-! Cents<br>(Reduced)
+! Cents*
 ! Associated<br>Ratio
 ! Temperament
@@ Line 28: / Line 24: @@
 | 252.878
 | 53094899/45875200
-| [[Double Bastille]]
+| [[Double bastille]]
 |}
+<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
-[[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->
 [[Category:Jacobin]]