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 equivalent to the 3rd, 5th and 13th harmonics tritave-reduced. | '''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 equivalent to the 3rd, 5th and 13th harmonics tritave-reduced. | ||
== Interval chain == | |||
{|class="wikitable" | |||
|- | |||
|505.76 | |||
|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 | |||
|1396.2 | |||
|} | |||
Revision as of 07:53, 23 May 2023
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 equivalent to the 3rd, 5th and 13th harmonics tritave-reduced.
Interval chain
| 505.76 | 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 | 1396.2 |