Aldebaran: Difference between revisions
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'''Aldebaran''' is the [[rank]]-2 [[regular temperament]] of the 3.5.13 [[subgroup]] that [[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 2L 5s | '''Aldebaran''' is the [[non-octave]] [[rank]]-2 [[regular temperament]] of the 3.5.13 [[subgroup]] that [[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}} | {{tdhat|No-twos subgroup temperaments #Aldebaran}} | ||
== Etymology == | == Etymology == | ||
This temperament is named after the star {{w|Aldebaran}}, following a series of | 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).}} | {{todo|add etymology|inline=1|text=Add name (person who coined the term) and year (when it was coined).}} | ||
== Interval chain == | == 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 | ||
|} | |} | ||
Revision as of 20:47, 23 November 2024
Aldebaran is the non-octave rank-2 regular temperament of the 3.5.13 subgroup that 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 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.
For technical data, see No-twos subgroup temperaments #Aldebaran.
Etymology
This temperament is named after the star Aldebaran, following a series of non-octave temperaments that are named after stars.
|
Todo: add etymology
Add name (person who coined the term) and year (when it was coined). |
Interval chain
| 1393.52 | 379.32 | 1267.08 | 252.88 | 1140.64 | 126.44 | 1014.20 | 0.00 | 887.76 | 1775.52 | 761.32 | 1649.08 | 634.88 | 1522.64 | 508.44 |
| 729/325 | 81/65 | 27/13 | 15/13 | 243/125 | 27/25 | 9/5 | 1/1 | 5/3 | 25/9 | 125/81 | 13/5 | 13/9 | 65/27 | 325/243 |