574edo: Difference between revisions

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@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|574}}
+{{ED intro}}
 == Theory ==
-= 14 × 41, and 574edo shares the [[harmonic]] [[3/1|3]] with [[41edo]]. Unfortunately, it is only [[consistent]] to the [[5-odd-limit]], and the [[patent val]] and the 574d [[val]] are about equally viable.
+edo shares the [[harmonic]] [[3/1|3]] with [[41edo]]. Unfortunately, it is only [[consistent]] to the [[5-odd-limit]], and the [[patent val]] and the 574d [[val]] are about equally viable.
 The 574d val [[tempering out|tempers out]] 4375/4374 ([[ragisma]]), 29360128/29296875 (quasiorwellisma), and 40500000/40353607 in the 7-limit; [[3025/3024]], [[5632/5625]], [[9801/9800]], and [[19712/19683]] in the 11-limit; [[676/675]], [[4225/4224]], and [[10648/10647]] in the 13-limit.
@@ Line 13: / Line 13: @@
 === Subsets and supersets ===
-Since 574 factors into {{factorization|574}}, 574edo has subset edos {{EDOs| 2, 7, 14, 41, 82, and 287 }}.
+Since 574 factors into 2 × 7 × 41, 574edo has subset edos {{EDOs| 2, 7, 14, 41, 82, and 287 }}.
 == 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
 | {{monzo| 23 6 -14 }}, {{monzo| 42 -47 14 }}
 | {{mapping| 574 910 1333 }}
-| &minus;0.1658
+| −0.1658
 | 0.1260
 | 6.03
@@ Line 28: / Line 37: @@
 | 4375/4374, 29360128/29296875, 40500000/40353607
 | {{mapping| 574 910 1333 1612 }} (574d)
-| &minus;0.2320
+| −0.2320
 | 0.1583
 | 7.57
@@ Line 35: / Line 44: @@
 | 3025/3024, 4375/4374, 5632/5625, 40500000/40353607
 | {{mapping| 574 910 1333 1612 1986 }} (574d)
-| &minus;0.2202
+| −0.2202
 | 0.1435
 | 6.87
@@ Line 42: / Line 51: @@
 | 676/675, 3025/3024, 4225/4224, 4375/4374, 41600/41503
 | {{mapping| 574 910 1333 1612 1986 2124 }} (574d)
-| &minus;0.1786
+| −0.1786
 | 0.1607
 | 7.69
@@ Line 49: / Line 58: @@
 | 10976/10935, 2100875/2097152, 49009212/48828125
 | {{mapping| 574 910 1333 1611 }} (574)
-| &minus;0.0459
+| −0.0459
 | 0.2347
 | 11.23
@@ Line 56: / Line 65: @@
 | 5632/5625, 10976/10935, 131072/130977, 166698/166375
 | {{mapping| 574 910 1333 1611 1986 }} (574)
-| &minus;0.0713
+| −0.0713
 | 0.2160
 | 10.33
@@ Line 63: / Line 72: @@
 | 676/675, 1001/1000, 4096/4095, 10976/10935, 166698/166375
 | {{mapping| 574 910 1333 1611 1986 2124 }} (574)
-| &minus;0.0544
+| −0.0544
 | 0.2007
 | 9.60
-{{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
 |-
 | 2
@@ Line 76: / Line 92: @@
 | 25/24
 | [[Vishnu]] (574d)
-{{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