3312/3311
| Interval information |
fothutwetholuru unison
reduced
(Shannon, [math]\sqrt{nd}[/math])
3312/3311, the pedersenisma, is a 43-limit superparticular comma of about 0.52 cents.
Commatic relationships
This comma is the difference between the following superparticular pairs:
It can be factored into the following superparticular intervals:
- 3381/3380 and 162240/162239
- 3510/3509 and 58696/58695
- 3565/3564 and 46656/46655
- 3774/3773 and 27048/27047
- 4000/3999 and 19251/19250
- 4301/4300 and 14400/14399
- 4761/4760 and 10880/10879
- 5083/5082 and 9504/9503
- 5376/5375 and 8625/8624
- 5720/5719 and 7866/7865
- 5888/5887 and 7569/7568
Temperaments
Tempering out this comma in the full 43-limit leads to the rank-13 temperament pedersenismic. Using the 2.3.7.11.23.43 subgroup leads to the rank-5 temperament pedersenic.
Pedersenic
Subgroup: 2.3.7.11.23.43
Comma list: 3312/3311
| [⟨ | 1 | 1 | 2 | 3 | 4 | 5 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | 2 | ], |
| ⟨ | 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 = 701.922, ~7/4 = 968.878, ~11/8 = 551.396, ~23/16 = 628.140
Optimal ET sequence: 5i, 7di, 7, 8din, 9in, 10, 12e, 12i, 14, 17, 22n, 24i, 31, 58i, 63, 89, 94, 113, 135, 152, 176, 176, 207, 165, 328, 342, 359, 535, 670, 701, 877, 1029, 1236, 1906n, 2607n, 3142n, 3843n
Etymology
This comma was named by Francium in 2025. It refers to 3312 Pedersen, the asteroid, which in turn was named after Holger Pedersen, a Danish astronomer.