523edo: Difference between revisions

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@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|523}}
+{{ED intro}}
 == Theory ==
-et tempers out [[2401/2400]] in the 7-limit; 56723625/56689952, 26214400/26198073, 78675968/78594219, 759375/758912, 496125/495616, [[6250/6237]], 42875/42768, [[19712/19683]], 1479016/1476225, 16808715/16777216, 3294225/3294172, 43923/43904, 102487/102400 and 322102/321489 in the 11-limit.
+et tempers out [[2401/2400]] in the 7-limit; 56723625/56689952, 26214400/26198073, 78675968/78594219, 759375/758912, 496125/495616, [[6250/6237]], 42875/42768, [[19712/19683]], 1479016/1476225, 16808715/16777216, 3294225/3294172, 43923/43904, 102487/102400, and 322102/321489 in the 11-limit.
-===Prime harmonics===
+=== Prime harmonics ===
 {{Harmonics in equal|523}}
-===Subsets and supersets===
+=== Subsets and supersets ===
 edo is the 99th [[prime edo]].
-==Regular temperament properties==
+== Regular temperament properties ==
 {| class="wikitable center-4 center-5 center-6"
-! rowspan="2" |[[Subgroup]]
-! rowspan="2" |[[Comma list|Comma List]]
-! rowspan="2" |[[Mapping]]
-! rowspan="2" |Optimal<br>8ve Stretch (¢)
-! colspan="2" |Tuning Error
-|-
-![[TE error|Absolute]] (¢)
-![[TE simple badness|Relative]] (%)
 |-
-|2.3
+! rowspan="2" | [[Subgroup]]
-|{{monzo|829 -523}}
+! rowspan="2" | [[Comma list]]
-|{{mapping|523 829}}
+! rowspan="2" | [[Mapping]]
-| -0.0468
+! rowspan="2" | Optimal<br />8ve stretch (¢)
+! colspan="2" | Tuning error
+|-
+! [[TE error|Absolute]] (¢)
+! [[TE simple badness|Relative]] (%)
+|-
+| 2.3
+| {{monzo|829 -523}}
+| {{mapping|523 829}}
+| −0.0468
 | 0.0468
 | 2.04
 |-
-|2.3.5
+| 2.3.5
-|1600000/1594323, {{monzo|-101 11 36}}
+| 1600000/1594323, {{monzo|-101 11 36}}
-|{{mapping|523 829 1214}}
+| {{mapping|523 829 1214}}
 | +0.0901
 | 0.1974
 | 8.60
 |-
-|2.3.5.7
+| 2.3.5.7
-|2401/2400, 1600000/1594323, 341796875/339738624
+| 2401/2400, 1600000/1594323, 341796875/339738624
-|{{mapping|523 829 1214 1468}}
+| {{mapping|523 829 1214 1468}}
 | +0.1180
 | 0.1776
 | 7.74
 |-
-|2.3.5.7.11
+| 2.3.5.7.11
-|6250/6237, 2401/2400, 19712/19683, 166375/165888
+| 6250/6237, 2401/2400, 19712/19683, 166375/165888
-|{{mapping|523 829 1214 1468 1809}}
+| {{mapping|523 829 1214 1468 1809}}
 | +0.1319
 | 0.1613
 | 7.03
 |-
-|2.3.5.7.11.13
+| 2.3.5.7.11.13
-|2080/2079, 625/624, 4459/4455, 19712/19683, 50193/50176
+| 2080/2079, 625/624, 4459/4455, 19712/19683, 50193/50176
-|{{mapping|523 829 1214 1468 1809 1935}}
+| {{mapping|523 829 1214 1468 1809 1935}}
 | +0.1440
 | 0.1497
@@ Line 60: / Line 61: @@
 === 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
 |-
-|1
+| 1
-|37\523
+| 37\523
-|84.89
+| 84.89
-|21/20
+| 21/20
-|[[Amicable]]
+| [[Amicable]]
 |-
-|1
+| 1
-|52\523
+| 52\523
-|119.31
+| 119.31
-|15/14
+| 15/14
-|[[Septidiasemi]]
+| [[Septidiasemi]]
 |-
-|1
+| 1
-|148\523
+| 148\523
-|339.58
+| 339.58
-|243/200
+| 243/200
-|[[Amity]]
+| [[Amity]]
 |}
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
-<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
 == Music ==
 ; [[Francium]]
-* "(not) stuck" from ''hope in dark times'' – [https://open.spotify.com/track/1mgtvDuMtk980D6wDp9RH4 Spotify] | [https://francium223.bandcamp.com/track/not-stuck Bandcamp] | [https://www.youtube.com/watch?v=ZmPQHWLVCfQ YouTube]
+* "(not) stuck" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/1mgtvDuMtk980D6wDp9RH4 Spotify] | [https://francium223.bandcamp.com/track/not-stuck Bandcamp] | [https://www.youtube.com/watch?v=ZmPQHWLVCfQ YouTube]
+[[Category:Listen]]