285edo: Difference between revisions

← Older edit

VisualWikitext

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|285}}
+{{ED intro}}
 == Theory ==
-edo has a sharp tendency. It tempers out the [[misty comma]] and the [[enneadeca]] in the 5-limit; [[3136/3125]] and [[5120/5103]] in the 7-limit; [[3025/3024]] and [[3388/3375]] in the 11-limit; [[352/351]], [[676/675]], [[847/845]], [[1001/1000]], and [[2080/2079]] in the 13-limit. It supports the 13-limit [[hemimist]] temperament.
+edo has a sharp tendency. The equal temperament [[tempering out|tempers out]] the [[misty comma]] and the [[enneadeca]] in the 5-limit; [[3136/3125]] and [[5120/5103]] in the 7-limit; [[3025/3024]] and [[3388/3375]] in the 11-limit; [[352/351]], [[676/675]], [[847/845]], [[1001/1000]], and [[2080/2079]] in the 13-limit. It supports the 13-limit [[hemimist]] temperament.
 === Prime harmonics ===
-{{Harmonics in equal|285}}
+{{Harmonics in equal|285|intervals=prime}}
 === Subsets and supersets ===
-Since 285 factors into 3 × 5 × 19, 285edo has subset edos {{EDOs| 3, 5, 15, 19, 57, and 95 }}.
+Since 285 factors into {{factorisation|285}}, 285edo has subset edos {{EDOs| 3, 5, 15, 19, 57, and 95 }}.
 == 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| 452 -285 }}
-| [{{val| 285 452 }}]
+| {{mapping| 285 452 }}
-| -0.3795
+| −0.3795
 | 0.3794
 | 9.01
@@ Line 31: / Line 32: @@
 | 2.3.5
 | 67108864/66430125, {{monzo| -14 -19 19 }}
-| [{{val| 285 452 662 }}]
+| {{mapping| 285 452 662 }}
-| -0.4043
+| −0.4043
 | 0.3117
 | 7.41
@@ Line 38: / Line 39: @@
 | 2.3.5.7
 | 3136/3125, 5120/5103, 40353607/39858075
-| [{{val| 285 452 662 800 }}]
+| {{mapping| 285 452 662 800 }}
-| -0.2673
+| −0.2673
 | 0.3596
 | 8.54
@@ Line 45: / Line 46: @@
 | 2.3.5.7.11
 | 3025/3024, 3136/3125, 5120/5103, 12005/11979
-| [{{val| 285 452 662 800 986 }}]
+| {{mapping| 285 452 662 800 986 }}
-| -0.2289
+| −0.2289
 | 0.3307
 | 7.85
@@ Line 52: / Line 53: @@
 | 2.3.5.7.11.13
 | 352/351, 676/675, 847/845, 3025/3024, 12005/11979
-| [{{val| 285 452 662 800 986 1055 }}]
+| {{mapping| 285 452 662 800 986 1055 }}
-| -0.2618
+| −0.2618
 | 0.3107
 | 7.38
@@ Line 60: / Line 61: @@
 === 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 74: / Line 76: @@
 |-
 | 3
-| 59\285<br>(36\285)
+| 59\285<br />(36\285)
-| 248.42<br>(151.58)
+| 248.42<br />(151.58)
-| 15/13<br>(12/11)
+| 15/13<br />(12/11)
 | [[Hemimist]]
 |-
 | 3
-| 59\285<br>(23\285)
+| 59\285<br />(23\285)
-| 496.84<br>(96.84)
+| 496.84<br />(96.84)
-| 4/3<br>(256/243)
+| 4/3<br />(256/243)
 | [[Misty]]
 |-
 | 19
-| 118\285<br>(2\285)
+| 118\285<br />(2\285)
-| 496.84<br>(8.42)
+| 496.84<br />(8.42)
-| 4/3<br>(15625/15552)
+| 4/3<br />(15625/15552)
 | [[Enneadecal]] (5-limit)
 |}
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct