742edo: 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]] (%)

|-

| 2.3.5

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| 0.0699

| 4.32

~~{{comma basis end}~~}

|}

* 742et has a lower 19-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any previous equal temperaments. It is only bettered by [[935edo|935]] in terms of absolute error, and by [[1178edo|1178]] in terms of relative error.

* 742et (742i val) is also notable in the 17- and 23-limit, where it has lower absolute errors than any previous equal temperaments. In the 17-limit it beats [[581edo|581]] and is bettered by [[764edo|764]]; in the 23-limit it beats [[718edo|718]] and is bettered by [[814edo|814]].

=== 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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| 441/260<br />(196/195)

| [[Iodine]]

~~{{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

@@ Line 12: / Line 12: @@
 == 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]] (%)
 |-
 | 2.3.5
@@ Line 62: / Line 71: @@
 | 0.0699
 | 4.32
-{{comma basis end}}
+|}
 * 742et has a lower 19-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any previous equal temperaments. It is only bettered by [[935edo|935]] in terms of absolute error, and by [[1178edo|1178]] in terms of relative error.
 * 742et (742i val) is also notable in the 17- and 23-limit, where it has lower absolute errors than any previous equal temperaments. In the 17-limit it beats [[581edo|581]] and is bettered by [[764edo|764]]; in the 23-limit it beats [[718edo|718]] and is bettered by [[814edo|814]].
 === 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 104: / Line 120: @@
 | 441/260<br />(196/195)
 | [[Iodine]]
-{{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