8991/8990
| Interval information |
solidarity comma
thisothiwutwenugu 2nd
reduced
(Shannon, [math]\sqrt{nd}[/math])
8991/8990, the solidaritisma or solidarity comma, is a 37-limit superparticular comma of about 0.19 cents.
Commatic relationships
This comma is the difference between the following superparticular pairs:
- 2109/2108 and 2755/2754
- 2553/2552 and 3565/3564
- 3256/3255 and 5104/5103
- 3626/3625 and 6076/6075
- 3969/3968 and 7105/7104
It can be factored into the following superparticular ratios:
- 9177/9176 and 443556/443555
- 9361/9360 and 227448/227447
- 9801/9800 and 108780/108779
- 10557/10556 and 60606/60605
- 11340/11339 and 43401/43400
- 15873/15872 and 20736/20735
Temperaments
Tempering out this comma in the full 37-limit leads to the rank-11 temperament solidaritismic. Using the 2.3.5.29.31.37 subgroup leads to the rank-5 temperament solidaritic.
Solidaritic
Subgroup: 2.3.5.29.31.37
Comma list: 8991/8990
| [⟨ | 1 | 1 | 2 | 4 | 4 | 6 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | -5 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 1 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 1 | 1 | ]] |
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.938, ~5/4 = 386.321, ~29/16 = 1029.609, ~31/16 = 1145.069
Optimal ET sequence: 5, 5jl, 7jjkll, 7k, 10, 12l, 15k, 19kkl, 19, 34k, 41l, 46j, 60l, 65, 87, 99k, 106, 171, 205, 270, 376, 407, 506, 612, 1183, 1289, 3190, 4479, 5768, 7163, 8452, 9741, 10353, 10372
Badness (Sintel): 0.036
Etymology
This comma was named by Francium in 2025. It refers to 8991 Solidarity, the asteroid, which in turn was named to honor the victims of the September 11th attacks.