667/666
| Interval information |
thisutwenotwetho unison
reduced
(Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])
667/666, the denisisma, is a 37-limit superparticular comma of about 2.6 cents.
Commatic relationships
This comma is the difference between the following superparticular pairs:
It can be factored into the following superparticular ratios:
- 676/675 and 50025/50024
- 704/703 and 12673/12672
- 736/735 and 7105/7104
- 741/740 and 6670/6669
- 841/840 and 3220/3219
- 1000/999 and 2001/2000
Temperaments
Tempering out this comma in the full 37-limit leads to the rank-11 temperament denisismic. Using the 2.3.23.29.37 subgroup leads to the rank-4 temperament denisic.
Denisic
Subgroup: 2.3.23.29.37
Comma list: 667/666
| [⟨ | 1 | 1 | 4 | 4 | 5 | ], |
| ⟨ | 0 | 1 | 0 | 0 | -2 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 1 | 1 | ]] |
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.116, ~23/16 = 627.620, ~29/16 = 1028.823
Optimal ET sequence: 3, 5, 7i, 9ijl, 10, 12l, 17, 19, 22, 29, 48, 77, 99, 147, 176, 224, 323, 547, 706ij
Badness (Sintel): 0.036
Etymology
This comma was named by Francium in 2025. It refers to 667 Denise, the asteroid. The origin of the asteroid's name is unknown, it could be inspired by its provisional designation, containing the letters "DN".