487edo: Difference between revisions

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@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|487}}
+{{ED intro}}
 == Theory ==
-edo is [[consistency|distinctly consistent]] to the [[13-odd-limit]]. The equal temperament [[tempering out|tempers out]] {{monzo| 24 -21 4 }} ([[vulture comma]]) and {{monzo| 55 -1 -23 }} (counterwürschmidt comma) in the 5-limit, 4375/4374 ([[ragisma]]), 235298/234375 ([[triwellisma]]), and 33554432/33480783 ([[garischisma]]) in the 7-limit, [[5632/5625]], [[12005/11979]], [[19712/19683]], [[41503/41472]] in the 11-limit, [[676/675]], [[1001/1000]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit. It supports [[semidimfourth]], [[seniority]], and [[vulture]].
+edo is [[consistency|distinctly consistent]] to the [[13-odd-limit]]. As an equal temperament, it [[tempering out|tempers out]] {{monzo| 24 -21 4 }} ([[vulture comma]]) and {{monzo| 55 -1 -23 }} (counterwürschmidt comma) in the 5-limit, 4375/4374 ([[ragisma]]), 235298/234375 ([[triwellisma]]), and 33554432/33480783 ([[garischisma]]) in the 7-limit, [[5632/5625]], [[12005/11979]], [[19712/19683]], [[41503/41472]] in the 11-limit, [[676/675]], [[1001/1000]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit. It supports [[semidimfourth]], [[seniority]], and [[vulture]].
 === Prime harmonics ===
-{{Harmonics in equal|487|columns=11}}
+{{Harmonics in equal|487}}
 === Subsets and supersets ===
 edo is the 93rd [[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| 772 -487 }}
 | {{mapping| 487 772 }}
-| &minus;0.0958
+| −0.0958
 | 0.0958
 | 3.89
@@ Line 24: / Line 33: @@
 | {{monzo| 24 -21 4 }}, {{monzo| 55 -1 -23 }}
 | {{mapping| 487 772 1131 }}
-| &minus;0.1421
+| −0.1421
 | 0.1020
 | 4.14
@@ Line 31: / Line 40: @@
 | 4375/4374, 235298/234375, 33554432/33480783
 | {{mapping| 487 772 1131 1367 }}
-| &minus;0.0667
+| −0.0667
 | 0.1577
 | 6.40
@@ Line 38: / Line 47: @@
 | 4375/4374, 5632/5625, 12005/11979, 41503/41472
 | {{mapping| 487 772 1131 1367 1685 }}
-| &minus;0.0899
+| −0.0899
 | 0.1485
 | 6.03
@@ Line 45: / Line 54: @@
 | 676/675, 1001/1000, 4096/4095, 4375/4374, 12005/11979
 | {{mapping| 487 772 1131 1367 1685 1802 }}
-| &minus;0.0623
+| −0.0623
 | 0.1490
 | 6.05
-{{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 88: / Line 104: @@
 | 864/625
 | [[Tritriple]] (5-limit)
-{{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
 == Scales ==