457edo: Difference between revisions

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@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|457}}
+{{ED intro}}
 == Theory ==
-edo is [[consistent]] to the [[7-odd-limit]], but the error of [[harmonic]] [[3/1|3]] is quite large. The equal temperament [[tempering out|tempers out]] [[19683/19600]] and [[65625/65536]] in the 7-limit; [[540/539]], [[8019/8000]], and 43923/43904 in the 11-limit.
+edo is [[consistent]] to the [[7-odd-limit]], but the error of [[harmonic]] [[3/1|3]] is quite large. As an equal temperament, it [[tempering out|tempers out]] [[19683/19600]] and [[65625/65536]] in the [[7-limit]]; [[540/539]], [[8019/8000]], and 43923/43904 in the [[11-limit]].
 === Odd harmonics ===
@@ Line 9: / Line 9: @@
 === Subsets and supersets ===
 edo is the 88th [[prime edo]].
 == 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
 | {{monzo| -724 457 }}
 | {{mapping| 457 724 }}
-| 0.2716
+| +0.2716
 | 0.2716
 | 10.34
@@ Line 24: / Line 33: @@
 | {{monzo| -36 11 8 }}, {{monzo| -5 31 -19 }}
 | {{mapping| 457 724 1061 }}
-| 0.2267
+| +0.2267
 | 0.2307
 | 8.79
@@ Line 31: / Line 40: @@
 | 19683/19600, 65625/65536, 7381125/7340032
 | {{mapping| 457 724 1061 1283 }}
-| 0.1609
+| +0.1609
 | 0.2300
 | 8.76
@@ Line 38: / Line 47: @@
 | 540/539, 8019/8000, 19683/19600, 43923/43904
 | {{mapping| 457 724 1061 1283 1581 }}
-| 0.1227
+| +0.1227
 | 0.2194
 | 8.36
@@ Line 45: / Line 54: @@
 | 540/539, 1716/1715, 4225/4224, 41067/40960, 43940/43923
 | {{mapping| 457 724 1061 1283 1581 1691 }}
-| 0.1142
+| +0.1142
 | 0.2012
 | 7.66
@@ Line 52: / Line 61: @@
 | 936/935, 1089/1088, 1275/1274, 1575/1573, 2601/2600, 4225/4224
 | {{mapping| 457 724 1061 1283 1581 1691 1868 }}
-| 0.0952
+| +0.0952
 | 0.1920
 | 7.31
-{{comma basis end}}
+|}
 === 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 77: / Line 93: @@
 | 864/625
 | [[Tritriple]]
-{{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
 == Music ==
 ; [[Francium]]
-* "Less and Less" from ''Take Advantage'' (2024) &ndash; [https://open.spotify.com/track/5w3K1Q6VhCkUPMXmuh5pVt Spotify] | [https://francium223.bandcamp.com/track/less-and-less Bandcamp] | [https://www.youtube.com/watch?v=y4MGhHE20b4 YouTube]
+* "Less and Less" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/5w3K1Q6VhCkUPMXmuh5pVt Spotify] | [https://francium223.bandcamp.com/track/less-and-less Bandcamp] | [https://www.youtube.com/watch?v=y4MGhHE20b4 YouTube]
-* "Porcelain Stoneware" from ''Scoop'' (2024) &ndash; [https://open.spotify.com/track/055lRdMBKr37MU8HQqlvus Spotify] | [https://francium223.bandcamp.com/track/porcelain-stoneware Bandcamp] | [https://www.youtube.com/watch?v=bzycN6PYMQQ YouTube]
+* "Porcelain Stoneware" from ''Scoop'' (2024) – [https://open.spotify.com/track/055lRdMBKr37MU8HQqlvus Spotify] | [https://francium223.bandcamp.com/track/porcelain-stoneware Bandcamp] | [https://www.youtube.com/watch?v=bzycN6PYMQQ YouTube]
 [[Category:Listen]]