764edo: Difference between revisions

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VisualWikitext

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|764}}
+{{ED intro}}
 == Theory ==
@@ Line 15: / Line 15: @@
 == Regular temperament properties ==
 {| class="wikitable center-4 center-5 center-6"
+|-
 ! rowspan="2" | [[Subgroup]]
-! rowspan="2" | [[Comma list|Comma List]]
+! rowspan="2" | [[Comma list]]
 ! rowspan="2" | [[Mapping]]
-! rowspan="2" | Optimal<br>8ve Stretch (¢)
+! rowspan="2" | Optimal<br />8ve stretch (¢)
-! colspan="2" | Tuning Error
+! colspan="2" | Tuning error
 |-
 ! [[TE error|Absolute]] (¢)
@@ Line 27: / Line 28: @@
 | {{monzo| 1211 -764 }}
 | {{mapping| 764 1211 }}
-| -0.0439
+| −0.0439
 | 0.0439
 | 2.80
@@ Line 34: / Line 35: @@
 | {{monzo| 38 -2 -15 }}, {{monzo| 25 -48 22 }}
 | {{mapping| 764 1211 1774 }}
-| -0.0399
+| −0.0399
 | 0.0363
 | 2.31
@@ Line 41: / Line 42: @@
 | 4375/4374, 52734375/52706752, {{monzo| 31 -6 -2 -6 }}
 | {{mapping| 764 1211 1774 2145 }}
-| -0.0552
+| −0.0552
 | 0.0412
 | 2.62
@@ Line 48: / Line 49: @@
 | 3025/3024, 4375/4374, 131072/130977, 35156250/35153041
 | {{mapping| 764 1211 1774 2145 2643 }}
-| -0.0436
+| −0.0436
 | 0.0435
 | 2.77
@@ Line 55: / Line 56: @@
 | 1716/1715, 2080/2079, 3025/3024, 4096/4095, 10549994/10546875
 | {{mapping| 764 1211 1774 2145 2643 2827 }}
-| -0.0267
+| −0.0267
 | 0.0548
 | 3.49
@@ Line 62: / Line 63: @@
 | 1716/1715, 2080/2079, 2431/2430, 2500/2499, 4096/4095, 4914/4913
 | {{mapping| 764 1211 1774 2145 2643 2827 3123 }}
-| -0.0327
+| −0.0327
 | 0.0528
 | 3.36
+|-
+| 2.3.5.7.11.13.17.23
+| 1716/1715, 2080/2079, 2024/2023, 2431/2430, 2500/2499, 3520/3519, 4096/4095
+| {{mapping| 764 1211 1774 2145 2643 2827 3123 3456 }}
+| −0.0286
+| 0.0506
+| 3.22
 |}
 * 764et has lower absolute errors than any previous equal temperaments in the 13- and 17-limit. In the 13-limit it beats [[684edo|684]] and is only bettered by [[935edo|935]]. In the 17-limit it beats [[742edo|742]] and is only bettered by [[814edo|814]].
+* It is best at the no-19 23-limit, where it has a lower relative error than any previous equal temperaments, past [[494edo|494]] and before [[1578edo|1578]].
 === Rank-2 temperaments ===
 {| class="wikitable center-all left-5"
-|+Table of rank-2 temperaments by generator
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
-! Periods<br>per 8ve
+|-
+! Periods<br />per 8ve
 ! Generator*
 ! Cents*
-! Associated<br>Ratio*
+! Associated<br />ratio*
 ! Temperaments
 |-
@@ Line 96: / Line 106: @@
 |-
 | 2
-| 277\764<br>(105\764)
+| 277\764<br />(105\764)
-| 435.08<br>(164.92)
+| 435.08<br />(164.92)
-| 9/7<br>(11/10)
+| 9/7<br />(11/10)
 | [[Semisupermajor]]
 |}
-<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
 [[Category:Abigail]]