9177/9176
| Interval information |
thisuthiwutwethonozo 2nd
reduced
(Shannon, [math]\sqrt{nd}[/math])
9177/9176, the donsaarisma, is a 37-limit superparticular ratio of about 0.19 cents.
Commatic relationships
This comma is the difference between the following superparticular pairs:
- 741/740 and 806/805
- 2295/2294 and 3060/3059
- 3220/3219 and 4960/4959
- 3553/3552 and 5797/5796
- 4186/4185 and 7696/7695
- 4256/4255 and 7936/7935
It can be factored into the following superparticular intervals:
- 9361/9360 and 466830/466829
- 10241/10240 and 88320/88319
- 12673/12672 and 33264/33263
Temperaments
Tempering out this comma in the full 37-limit leads to the rank-11 temperament donsaarismic. Using the 2.3.7.19.23.31.37 subgroup leads to the rank-6 temperament donsaaric.
Donsaaric
Subgroup: 2.3.7.19.23.31.37
Comma list: 9177/9176
| [⟨ | 1 | 1 | 2 | 4 | 4 | 4 | 4 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 1 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 1 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 1 | -1 | ]] |
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.950, ~7/4 = 968.811, ~19/16 = 297.479, ~23/16 = 628.236, ~31/16 = 1145.082
Optimal ET sequence: 5ik, 5, 7l, 9ikl, 10k, 10h, 12, 12ik, 14l, 17, 19, 22hkk, 26ik, 27, 31hk, 32, 36, 41l, 48, 53, 68l, 72, 77, 99k, 116l, 125, 130, 207k, 229, 265, 306, 395, 436, 653, 701, 783, 1012, 1089, 1219, 1614, 1920, 2118, 2347k, 2424, 2554, 3337, 3566, 3643, 4038, 4474, 5257, 6592, 7209, 7604, 8823, 10464i
Etymology
This comma was named by Francium in 2025. It refers to 9177 Donsaari, the asteroid, which in turn was named after Donald G. Saari, an American mathematician.