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. It 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 ===
-{{Harmonics in equal|981|columns=11}}
+{{Harmonics in equal|981}}
-=== Miscellaneous properties ===
+=== Subsets and supersets ===
-Since 981 = 3<sup>2</sup> × 109, 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 ==
 {| class="wikitable center-4 center-5 center-6"
+|-
 ! rowspan="2" | [[Subgroup]]
-! rowspan="2" | [[Comma list|Comma List]]
+! rowspan="2" | [[Comma list]]
 ! rowspan="2" | [[Mapping]]
-! rowspan="2" | Optimal<br>8ve Stretch (¢)
+! rowspan="2" | Optimal<br />8ve stretch (¢)
-! colspan="2" | Tuning Error
+! colspan="2" | Tuning error
 |-
 ! [[TE error|Absolute]] (¢)
@@ Line 24: / Line 25: @@
 | 2.3
 | {{monzo| 1555 -981 }}
-| [{{val| 981 1555 }}]
+| {{mapping| 981 1555 }}
-| -0.0586
+| −0.0586
 | 0.0586
 | 4.79
@@ Line 31: / Line 32: @@
 | 2.3.5
 | {{monzo| 1 -27 18 }}, {{monzo| 85 -17 -25 }}
-| [{{val| 981 1555 2278 }}]
+| {{mapping| 981 1555 2278 }}
-| -0.0722
+| −0.0722
 | 0.0515
 | 4.21
@@ Line 38: / Line 39: @@
 | 2.3.5.7
 | 2401/2400, 4375/4374, {{monzo| 79 -25 -23 5 }}
-| [{{val| 981 1555 2278 2754 }}]
+| {{mapping| 981 1555 2278 2754 }}
-| -0.0385
+| −0.0385
 | 0.0562
 | 4.59
@@ Line 45: / Line 46: @@
 | 2.3.5.7.11
 | 2401/2400, 4375/4374, 131072/130977, 1771561/1771470
-| [{{val| 981 1555 2278 2754 3394 }}]
+| {{mapping| 981 1555 2278 2754 3394 }}
-| -0.0630
+| −0.0630
 | 0.0545
 | 4.46
@@ Line 52: / Line 53: @@
 | 2.3.5.7.11.13
 | 2080/2079, 2401/2400, 4096/4095, 4375/4374, 1771561/1771470
-| [{{val| 981 1555 2278 2754 3394 3630 }}]
+| {{mapping| 981 1555 2278 2754 3394 3630 }}
-| -0.0453
+| −0.0453
 | 0.0636
 | 5.20
@@ Line 59: / Line 60: @@
 | 2.3.5.7.11.13.17
 | 2080/2079, 2401/2400, 2431/2430, 4096/4095, 4375/4374, 4914/4913
-| [{{val| 981 1555 2278 2754 3394 3630 4010 }}]
+| {{mapping| 981 1555 2278 2754 3394 3630 4010 }}
-| -0.0473
+| −0.0473
 | 0.0591
 | 4.83
@@ Line 67: / Line 68: @@
 === Rank-2 temperaments ===
 {| class="wikitable center-all left-5"
-! Periods<br>per 8ve
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
-! Generator<br>(Reduced)
+|-
-! Cents<br>(Reduced)
+! Periods<br />per 8ve
-! Associated<br>Ratio
+! Generator*
+! Cents*
+! Associated<br />ratio*
 ! Temperaments
 |-
@@ Line 77: / Line 80: @@
 | 500.306
 | 8192/6137
-| [[Langwidge]] (2.17.19)
+| [[Protolangwidge]]
 |-
 | 9
-| 258\981<br>(40\981)
+| 258\981<br />(40\981)
-| 315.60<br>(48.93)
+| 315.60<br />(48.93)
-| 6/5<br>(36/35)
+| 6/5<br />(36/35)
 | [[Ennealimmal]] / ennealimmia
 |}
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
 [[Category:Ennealimmic]]
 [[Category:Ennealimmia]]