981edo: Difference between revisions

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@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|981}}
+{{ED intro}}
 == Theory ==
-edo is a good 13- and 17-limit system, [[consistent]] to the [[17-odd-limit]]. The equal temperament [[Tempering out|tempers out]] [[2080/2079]], [[2401/2400]], [[2431/2430]], [[4096/4095]], [[4225/4224]], [[4375/4374]], 4459/4455 and [[4914/4913]] in the 17-limit. It provides the [[optimal patent val]] for 13-limit [[ennealimmic]], the rank-3 temperament tempering out 2080/2079, 2401/2400, and 4375/4374, and for 13-limit [[ennealimmia]], which also tempers out 4096/4095.
+edo is a good 13- and 17-limit system, [[consistent]] to the [[17-odd-limit]]. As an equal temperament, it [[tempering out|tempers out]] [[2080/2079]], [[2401/2400]], [[2431/2430]], [[4096/4095]], [[4225/4224]], [[4375/4374]], 4459/4455 and [[4914/4913]] in the 17-limit. It provides the [[optimal patent val]] for 13-limit [[ennealimmic]], the rank-3 temperament tempering out 2080/2079, 2401/2400, and 4375/4374, and for 13-limit [[ennealimmia]], which also tempers out 4096/4095.
 === Prime harmonics ===
@@ Line 9: / Line 9: @@
 === Subsets and supersets ===
-Since 981 = {{factorization|981}}, 981edo has subset edos 3, 9, 109, and 327.
+Since 981 factors into primes as 3<sup>2</sup> × 109, 981edo has subset edos 3, 9, 109, and 327.
 == 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| 1555 -981 }}
 | {{mapping| 981 1555 }}
-| &minus;0.0586
+| −0.0586
 | 0.0586
 | 4.79
@@ Line 24: / Line 33: @@
 | {{monzo| 1 -27 18 }}, {{monzo| 85 -17 -25 }}
 | {{mapping| 981 1555 2278 }}
-| &minus;0.0722
+| −0.0722
 | 0.0515
 | 4.21
@@ Line 31: / Line 40: @@
 | 2401/2400, 4375/4374, {{monzo| 79 -25 -23 5 }}
 | {{mapping| 981 1555 2278 2754 }}
-| &minus;0.0385
+| −0.0385
 | 0.0562
 | 4.59
@@ Line 38: / Line 47: @@
 | 2401/2400, 4375/4374, 131072/130977, 1771561/1771470
 | {{mapping| 981 1555 2278 2754 3394 }}
-| &minus;0.0630
+| −0.0630
 | 0.0545
 | 4.46
@@ Line 45: / Line 54: @@
 | 2080/2079, 2401/2400, 4096/4095, 4375/4374, 1771561/1771470
 | {{mapping| 981 1555 2278 2754 3394 3630 }}
-| &minus;0.0453
+| −0.0453
 | 0.0636
 | 5.20
@@ Line 52: / Line 61: @@
 | 2080/2079, 2401/2400, 2431/2430, 4096/4095, 4375/4374, 4914/4913
 | {{mapping| 981 1555 2278 2754 3394 3630 4010 }}
-| &minus;0.0473
+| −0.0473
 | 0.0591
 | 4.83
-{{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 71: / Line 87: @@
 | 6/5<br />(36/35)
 | [[Ennealimmal]] / ennealimmia
-{{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
 [[Category:Ennealimmic]]
 [[Category:Ennealimmia]]