Aldebaran: Difference between revisions

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-'''Aldebaran''' is the rank two 3.5.13 temperament tempering out 3159/3125. It has a generator of [[5/3]] (similar to [[Arcturus]]) and equates 5 of them with [[13/9]]. It possesses non-trivial MOS of the families 2L 5s<3/1>, 2L 7s<3/1>, 2L 9s<3/1>, 2L 11s<3/1>, 13L 2s<3/1>, and 15L 13s<3/1>. Aldebaran temperament can accurately approximate the chord 9:13:15, which could be viewed as the "fundamental" chord of the 3.5.13 subgroup (similar to 4:5:6 for the 5-limit or 3:5:7 for the no-twos 7-limit) due to being tritave-equivalent to 3:5:13. [[15edt]]'s major sixth is near the optimal tuning for Aldebaran.
+'''Aldebaran''' is the [[non-octave]] [[rank-2 temperament|rank-2]] [[regular temperament|temperament]] of the 3.5.13 [[subgroup]] that [[tempering out|tempers out]] [[3159/3125]]. It has a generator of [[5/3]] (similar to [[arcturus]]) and equates 5 of them with [[13/9]]. It possesses non-trivial MOS of the families {{nowrap|2L 5s{{angbr|3/1}}|2L 7s{{angbr|3/1}}|2L 9s{{angbr|3/1}}|2L 11s{{angbr|3/1}}|13L 2s{{angbr|3/1}}|and 15L 13s{{angbr|3/1}}}}. Aldebaran temperament can accurately approximate the chord 9:13:15, which could be viewed as the "fundamental" chord of the 3.5.13 subgroup (similar to 4:5:6 for the 5-limit or 3:5:7 for the no-twos 7-limit) due to being tritave-equivalent to 3:5:13. [[15edt]]'s major sixth is near the optimal tuning for Aldebaran.
+{{Tdhat|No-twos subgroup temperaments #Aldebaran}}
+== Etymology ==
+This temperament is named after the star {{w|Aldebaran}}, following a series of non-octave temperaments that are named after stars.
+{{todo|add etymology|inline=1|text=Add name (person who coined the term) and year (when it was coined).}}
 == Interval chain ==
-{|class="wikitable"
+{| class="wikitable"
 |-
-|1393.52
+| 1393.52
-|379.32
+| 379.32
-|1267.08
+| 1267.08
-|252.88
+| 252.88
-|1140.64
+| 1140.64
-|126.44
+| 126.44
-|1014.20
+| 1014.20
-|0.00
+| 0.00
-|887.76
+| 887.76
-|1775.52
+| 1775.52
-|761.32
+| 761.32
-|1649.08
+| 1649.08
-|634.88
+| 634.88
-|1522.64
+| 1522.64
-|508.44
+| 508.44
 |-
-|729/325
+| 729/325
-|81/65
+| 81/65
-|[[27/13]]
+| [[27/13]]
-|[[15/13]]
+| [[15/13]]
-|243/125
+| 243/125
-|[[27/25]]
+| [[27/25]]
-|[[9/5]]
+| [[9/5]]
-|[[1/1]]
+| [[1/1]]
-|[[5/3]]
+| [[5/3]]
-|25/9
+| 25/9
-|125/81
+| 125/81
-|[[13/5]]
+| [[13/5]]
-|[[13/9]]
+| [[13/9]]
-|65/27
+| 65/27
-|325/243
+| 325/243
 |}
-== Temperament data ==
-[[Subgroup]]: 3.5.13
-[[Comma list]]: 3159/3125
-[[Mapping]]: [{{val|1 0 5}}, {{val|0 1 -2}}]
-[[Support]]ing [[ET]]s: 15, 17, 13, 32, 47, 28, 11[-13], 19[+13], 43, 9[-13], 7[-13], 49[+13], 21[+13], 41[-13]
-[[CTE tuning|CTE generator]]: ~[[5/3]] = 887.76
+[[Category:Aldebaran| ]] <!-- main article -->
+[[Category:Rank-2 temperaments]]
+[[Category:Non-octave temperaments]]