224edo: Difference between revisions

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== Regular temperament properties ==

{~~{comma basis begin}}~~

{| class="wikitable center-4 center-5 center-6"

|-

! rowspan="2" | [[Subgroup]]

! rowspan="2" | [[Comma list]]

! rowspan="2" | [[Mapping]]

! rowspan="2" | Optimal<br />8ve stretch (¢)

! colspan="2" | Tuning error

|-

! [[TE error|Absolute]] (¢)

! [[TE simple badness|Relative]] (%)

|-

| 2.3

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| 0.2420

| 4.52

~~{{comma basis end}~~}

|}

* 224et has a lower relative error than any previous equal temperaments in the 13-limit, being the first to beat [[72edo|72]]. The next equal temperament that does better in terms of either absolute or relative error is [[270edo|270]].

* It is also notable in the 11- and 17-limit, with lower absolute errors than any previous equal temperaments. In the 11-limit it is the first to beat [[152edo|152]] and is superseded by [[239edo|239]]. In the 17-limit it is the first to beat [[217edo|217]] and is superseded by 270.

=== Rank-2 temperaments ===

{{rank-2 ~~begin}}~~

{| 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*

! Temperament

|-

| 1

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| 4/3<br>(126/125)

| [[Barium]]

~~{{rank-2 end}~~}

|}

~~{{orf}}~~

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

== Music ==

@@ Line 14: / Line 14: @@
 == Regular temperament properties ==
-{{comma basis begin}}
+{| class="wikitable center-4 center-5 center-6"
+|-
+! rowspan="2" | [[Subgroup]]
+! rowspan="2" | [[Comma list]]
+! rowspan="2" | [[Mapping]]
+! rowspan="2" | Optimal<br />8ve stretch (¢)
+! colspan="2" | Tuning error
+|-
+! [[TE error|Absolute]] (¢)
+! [[TE simple badness|Relative]] (%)
 |-
 | 2.3
@@ Line 57: / Line 66: @@
 | 0.2420
 | 4.52
-{{comma basis end}}
+|}
 * 224et has a lower relative error than any previous equal temperaments in the 13-limit, being the first to beat [[72edo|72]]. The next equal temperament that does better in terms of either absolute or relative error is [[270edo|270]].
 * It is also notable in the 11- and 17-limit, with lower absolute errors than any previous equal temperaments. In the 11-limit it is the first to beat [[152edo|152]] and is superseded by [[239edo|239]]. In the 17-limit it is the first to beat [[217edo|217]] and is superseded by 270.
 === Rank-2 temperaments ===
-{{rank-2 begin}}
+{| 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*
+! Temperament
 |-
 | 1
@@ Line 207: / Line 223: @@
 | 4/3<br>(126/125)
 | [[Barium]]
-{{rank-2 end}}
+|}
-{{orf}}
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
 == Music ==