566edo: Difference between revisions

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== Theory ==

566edo is [[consistency|distinctly consistent]] in the [[15-odd-limit]]. ~~The~~ equal temperament [[tempering out|tempers out]] the [[schisma]] in the 5-limit; 4375/4374 ([[ragisma]]), 65625/65536 ([[horwell comma]]), and 14348907/14336000 ([[skeetsma]]) in the 7-limit; [[3025/3024]] in the 11-limit; [[1716/1715]] and [[2080/2079]] in the 13-limit. It notably supports [[pontiac]] and [[orga]].

566edo is [[consistency|distinctly consistent]] in the [[15-odd-limit]]. As an equal temperament, it [[tempering out|tempers out]] the [[schisma]] in the 5-limit; 4375/4374 ([[ragisma]]), 65625/65536 ([[horwell comma]]), and 14348907/14336000 ([[skeetsma]]) in the 7-limit; [[3025/3024]] in the 11-limit; [[1716/1715]] and [[2080/2079]] in the 13-limit. It notably supports [[pontiac]] and [[orga]].

The 566g val is interesting in the higher limits, and in the 23-limit in particular it has a great rating in terms of absolute error. It tempers out [[1156/1155]], 1275/1274, 2431/2430, [[2500/2499]] and [[2601/2600]] in the 17-limit; [[1445/1444]], [[1521/1520]] and [[1729/1728]] in the 19-limit; 1105/1104 and 2025/2024 in the 23-limit.

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=== Subsets and supersets ===

Since 566 factors into ~~{{factorization|566}}~~, 566edo contains [[2edo]] and [[283edo]] as subsets.

Since 566 factors into 2 × 283, 566edo contains [[2edo]] and [[283edo]] as subsets.

== 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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| 0.1047

| 4.94

~~{{comma basis end}~~}

|}

* 566et (566g val) has a lower absolute error in the 23-limit than any previous equal temperaments, past [[525edo|525]] and followed by [[581edo|581]].

=== 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*

! Temperaments

|-

| 1

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| 8/7

| [[Orga]]

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

|}

~~{{orf}}~~

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

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|566}}
+{{ED intro}}
 == Theory ==
-edo is [[consistency|distinctly consistent]] in the [[15-odd-limit]]. The equal temperament [[tempering out|tempers out]] the [[schisma]] in the 5-limit; 4375/4374 ([[ragisma]]), 65625/65536 ([[horwell comma]]), and 14348907/14336000 ([[skeetsma]]) in the 7-limit; [[3025/3024]] in the 11-limit; [[1716/1715]] and [[2080/2079]] in the 13-limit. It notably supports [[pontiac]] and [[orga]].
+edo is [[consistency|distinctly consistent]] in the [[15-odd-limit]]. As an equal temperament, it [[tempering out|tempers out]] the [[schisma]] in the 5-limit; 4375/4374 ([[ragisma]]), 65625/65536 ([[horwell comma]]), and 14348907/14336000 ([[skeetsma]]) in the 7-limit; [[3025/3024]] in the 11-limit; [[1716/1715]] and [[2080/2079]] in the 13-limit. It notably supports [[pontiac]] and [[orga]].
 The 566g val is interesting in the higher limits, and in the 23-limit in particular it has a great rating in terms of absolute error. It tempers out [[1156/1155]], 1275/1274, 2431/2430, [[2500/2499]] and [[2601/2600]] in the 17-limit; [[1445/1444]], [[1521/1520]] and [[1729/1728]] in the 19-limit; 1105/1104 and 2025/2024 in the 23-limit.
@@ Line 11: / Line 11: @@
 === Subsets and supersets ===
-Since 566 factors into {{factorization|566}}, 566edo contains [[2edo]] and [[283edo]] as subsets.
+Since 566 factors into 2 × 283, 566edo contains [[2edo]] and [[283edo]] as subsets.
 == 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 50: / Line 59: @@
 | 0.1047
 | 4.94
-{{comma basis end}}
+|}
 * 566et (566g val) has a lower absolute error in the 23-limit than any previous equal temperaments, past [[525edo|525]] and followed by [[581edo|581]].
 === 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*
+! Temperaments
 |-
 | 1
@@ Line 67: / Line 83: @@
 | 8/7
 | [[Orga]]
-{{rank-2 end}}
+|}
-{{orf}}
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct