316edo: Difference between revisions

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@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|316}}
+{{ED intro}}
 == Theory ==
-While not highly accurate for its size, 316et is the point where a few important temperaments meet, and is distinctly [[consistent]] in the [[11-odd-limit]]. It tempers out the [[parakleisma]], {{monzo| 8 14 -13 }}, the [[undim comma]], {{monzo| 41 -20 -4 }}, and the [[maquila comma]], {{monzo| 49 -6 -17 }} in the 5-limit; [[3136/3125]], [[4375/4374]], [[10976/10935]] in the 7-limit; [[3025/3024]], [[3388/3375]], [[9801/9800]] and [[14641/14580]] in the 11-limit; and using the [[patent val]], [[1716/1715]], [[2080/2079]] and [[4096/4095]] in the 13-limit; notably supporting [[abigail]] and [[semiparakleismic]].
+While not highly accurate for its size, 316et is the point where a few important temperaments meet, and is [[consistency|distinctly consistent]] in the [[11-odd-limit]]. It [[tempering out|tempers out]] the [[parakleisma]], {{monzo| 8 14 -13 }}, the [[undim comma]], {{monzo| 41 -20 -4 }}, and the [[maquila comma]], {{monzo| 49 -6 -17 }} in the 5-limit; [[3136/3125]], [[4375/4374]], [[10976/10935]] in the 7-limit; [[3025/3024]], [[3388/3375]], [[9801/9800]], and [[14641/14580]] in the 11-limit; and using the [[patent val]], [[1716/1715]], [[2080/2079]], [[2197/2187]], [[4096/4095]], [[4225/4224]], [[6656/6655]], and [[10648/10647]] in the 13-limit; notably supporting [[Abigail]] and [[semiparakleismic]].
 It provides the [[optimal patent val]] for the rank-4 temperament tempering out 3388/3375, and [[triglav]], which also tempers out 3025/3024.
@@ Line 11: / Line 11: @@
 === Subsets and supersets ===
-factors into 2<sup>2</sup> × 79, with subset edos {{EDOs| 2, 4, 79, and 158 }}.
+factors into {{factorisation|316}}, with subset edos {{EDOs| 2, 4, 79, and 158 }}.
 == 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 8ve <br>Stretch (¢)
+! rowspan="2" | Optimal<br />8ve stretch (¢)
-! colspan="2" | Tuning Error
+! colspan="2" | Tuning error
 |-
 ! [[TE error|Absolute]] (¢)
@@ Line 26: / Line 27: @@
 | 2.3
 | {{monzo| 501 -316 }}
-| [{{val| 316 501 }}]
+| {{mapping| 316 501 }}
-| -0.182
+| −0.182
 | 0.182
 | 4.79
@@ Line 33: / Line 34: @@
 | 2.3.5
 | {{monzo| 8 14 -13 }}, {{monzo| 41 -20 -4 }}
-| [{{val| 316 501 734 }}]
+| {{mapping| 316 501 734 }}
-| -0.269
+| −0.269
 | 0.193
 | 5.08
@@ Line 40: / Line 41: @@
 | 2.3.5.7
 | 3136/3125, 4375/4374, {{monzo| -26 -1 1 9 }}
-| [{{val| 316 501 734 887 }}]
+| {{mapping| 316 501 734 887 }}
-| -0.160
+| −0.160
 | 0.252
 | 6.64
@@ Line 47: / Line 48: @@
 | 2.3.5.7.11
 | 3025/3024, 3136/3125, 4375/4374, 131072/130977
-| [{{val| 316 501 734 887 1093 }}]
+| {{mapping| 316 501 734 887 1093 }}
-| -0.088
+| −0.088
 | 0.267
 | 7.04
 |-
 | 2.3.5.7.11.13
-| 1716/1715, 2080/2079, 3025/3024, 3136/3125, 4096/4095
+| 1716/1715, 2080/2079, 2197/2187, 3025/3024, 3136/3125
-| [{{val| 316 501 734 887 1093 1169 }}]
+| {{mapping| 316 501 734 887 1093 1169 }}
-| -0.016
+| −0.016
 | 0.293
 | 7.72
@@ Line 62: / Line 63: @@
 === Rank-2 temperaments ===
 {| class="wikitable center-all left-5"
-|+Table of rank-2 temperaments by generator
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
-! Periods<br>per 8ve
+|-
-! Generator<br>(Reduced)
+! Periods<br />per 8ve
-! Cents<br>(Reduced)
+! Generator*
-! Associated<br>Ratio
+! Cents*
+! Associated<br />ratio*
 ! Temperaments
 |-
@@ Line 92: / Line 94: @@
 | 512/375
 | [[Maquila]] (5-limit)
+|-
+| 1
+| 149\316
+| 565.82
+| 18/13
+| [[Threedic]]
 |-
 | 1
@@ Line 106: / Line 114: @@
 |-
 | 2
-| 83\316<br>(75\316)
+| 83\316<br />(75\316)
-| 315.19<br>(284.81)
+| 315.19<br />(284.81)
-| 6/5<br>(33/28)
+| 6/5<br />(33/28)
 | [[Semiparakleismic]]
 |-
 | 4
-| 131\316<br>(27\316)
+| 131\316<br />(27\316)
-| 497.47<br>(102.53)
+| 497.47<br />(102.53)
-| 4/3<br>(35/33)
+| 4/3<br />(35/33)
-| [[Undim]] / [[unlit]]
+| [[Unlit]]
 |}
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
 [[Category:Parakleismic]]
 [[Category:Semiparakleismic]]
 [[Category:Triglav]]