Aldebaran: Difference between revisions
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{{tdhat|No-twos subgroup temperaments#Aldebaran}} | {{tdhat|No-twos subgroup temperaments#Aldebaran}} | ||
'''Aldebaran''' is the rank | '''Aldebaran''' is the [[rank]]-2 [[regular temperament]] on 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. | ||
== Etymology == | |||
This temperament is named after the star {{w|Aldebaran}}, following a series of nonoctave temperaments that are named after stars. | |||
== Interval chain == | == Interval chain == | ||
{|class="wikitable" | {|class="wikitable" | ||
Revision as of 04:14, 23 August 2024
For technical data, see No-twos subgroup temperaments#Aldebaran. Aldebaran is the rank-2 regular temperament on 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.
Etymology
This temperament is named after the star Aldebaran, following a series of nonoctave temperaments that are named after stars.
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 |