299edo: Difference between revisions

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@@ Line 1: / Line 1: @@
-{{Infobox ET
+{{Infobox ET}}
-| Prime factorization = 13 × 23
+{{ED intro}}
-| Step size = 4.01338¢
-| Fifth = 175\299 (702.34¢)
-| Semitones = 29:22 (116.39¢ : 88.29¢)
-| Consistency = 7
-}}
-{{EDO intro|299}}
 == Theory ==
-In the 5-limit, 299et tempers out the [[kleisma]], 15625/15552, in the 7-limit [[10976/10935]], in the 11-limit [[385/384]]; and in the 13-limit [[325/324]], [[625/624]] and [[676/675]]. It provides the [[optimal patent val]] for the 13-limit rank-3 [[enlil]] temperament, and the rank-4 temperament tempering out 325/324 and 385/384.
+In the 5-limit, 299et [[tempering out|tempers out]] the [[kleisma]], 15625/15552, in the [[7-limit]] [[10976/10935]], in the [[11-limit]] [[385/384]]; and in the [[13-limit]] [[325/324]], [[625/624]] and [[676/675]]. It provides the [[optimal patent val]] for the 13-limit rank-3 [[enlil]] temperament, and the rank-4 temperament tempering out 325/324 and 385/384.
 === Prime harmonics ===
 {{Harmonics in equal|299}}
+=== Subsets and supersets ===
+Since 299 factors into 13 × 23, 299edo contains [[13edo]] and [[23edo]] as subsets.
 == Regular temperament properties ==
 {| class="wikitable center-4 center-5 center-6"
-! rowspan="2" | Subgroup
+|-
+! rowspan="2" | [[Subgroup]]
 ! rowspan="2" | [[Comma list]]
 ! rowspan="2" | [[Mapping]]
@@ Line 26: / Line 24: @@
 |-
 | 2.3
-| {{monzo| 474 -299 }}
+| {{Monzo| 474 -299 }}
-| [{{val| 299 474 }}]
+| {{Mapping| 299 474 }}
-| -0.1218
+| −0.1218
 | 0.1218
 | 3.04
@@ Line 34: / Line 32: @@
 | 2.3.5
 | 15625/15552, {{monzo| 80 -49 -1 }}
-| [{{val| 299 474 694 }}]
+| {{Mapping| 299 474 694 }}
 | +0.0665
 | 0.2844
@@ Line 41: / Line 39: @@
 | 2.3.5.7
 | 10976/10935, 15625/15552, 823543/819200
-| [{{val| 299 474 694 839 }}]
+| {{Mapping| 299 474 694 839 }}
 | +0.1925
 | 0.3291
@@ Line 48: / Line 46: @@
 | 2.3.5.7.11
 | 385/384, 6250/6237, 10976/10935, 12005/11979
-| [{{val| 299 474 694 839 1034 }}]
+| {{Mapping| 299 474 694 839 1034 }}
 | +0.2399
 | 0.3092
@@ Line 54: / Line 52: @@
 |-
 | 2.3.5.7.11.13
-| 325/324, 385/384, 676/675, 10648/10647, 10976/10935
+| 325/324, 385/384, 625/624, 10648/10647, 10976/10935
-| [{{val| 299 474 694 839 1034 1106 }}]
+| {{Mapping| 299 474 694 839 1034 1106 }}
 | +0.2779
 | 0.2948
@@ Line 62: / Line 60: @@
 | 2.3.5.7.11.13.17
 | 325/324, 385/384, 595/594, 625/624, 2058/2057, 8624/8619
-| [{{val| 299 474 694 839 1034 1106 1222 }}]
+| {{Mapping| 299 474 694 839 1034 1106 1222 }}
 | +0.2595
 | 0.2767
@@ Line 69: / Line 67: @@
 | 2.3.5.7.11.13.17.19
 | 325/324, 343/342, 385/384, 595/594, 625/624, 1216/1215, 1445/1444
-| [{{val| 299 474 694 839 1034 1106 1222 1270 }}]
+| {{Mapping| 299 474 694 839 1034 1106 1222 1270 }}
 | +0.2424
 | 0.2627
@@ Line 77: / Line 75: @@
 === 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 octave
+|-
-! Generator<br>(reduced)
+! Periods<br>per 8ve
-! Cents<br>(reduced)
+! Generator*
-! Associated<br>ratio
+! Cents*
+! Associated<br>ratio*
 ! Temperaments
+|-
+| 1
+| 25\299
+| 100.33
+| 1323/1250
+| [[Heptacot]] (7-limit)
 |-
 | 1
@@ Line 89: / Line 94: @@
 | 6/5
 | [[Hanson]]
+|-
+| 1
+| 124\299
+| 497.66
+| 4/3
+| [[Cotoneum]] (7-limit)
 |-
 | 1
@@ Line 96: / Line 107: @@
 | [[Marfifths]]
 |}
+<nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
 [[Category:Enlil]]
 [[Category:Keenanismic]]