3773/3772
| Interval information |
fowutwethulotrizo 2nd
reduced
(Shannon, [math]\sqrt{nd}[/math])
3773/3772, the smithsonianisma, is a 41-limit superparticular comma of about 0.46 cents.
Commatic relationships
This comma is the difference between the following superparticular pairs:
It can be factored into the following superparticular ratios:
- 3774/3773 and 14235529/14235528
- 3969/3968 and 76384/76383
- 4675/4674 and 19551/19550
- 4785/4784 and 17836/17835
- 5577/5576 and 11662/11661
- 5929/5928 and 10374/10373
- 6930/6929 and 8281/8280
Temperaments
Tempering out this comma in the full 41-limit leads to the rank-12 temperament smithsonianismic. Using the 2.7.11.23.41 subgroup leads to the rank-4 temperament smithsonianic.
Smithsonianic
Subgroup: 2.7.11.23.41
Comma list: 3773/3772
| [⟨ | 1 | 2 | 3 | 4 | 3 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 3 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 1 | -1 | ]] |
Optimal tuning (CTE): ~2 = 1\1, ~7/4 = 968.744, ~11/8 = 551.276, ~23/16 = 628.345
Optimal ET sequence: 4, 6m, 7, 9i, 11, 20, 31, 46, 63, 67, 78, 109, 187, 296, 529, 638, 825, 1759, 2584, 3705, 4530, 6278d
Etymology
This comma was named by Francium in 2025. It refers to 3773 Smithsonian, the asteroid, which in turn was named after the Smithsonian Institution.