616/615
| Interval information |
fowulozogu 2nd
reduced
616/615, the ellisma, is a 41-limit superparticular comma of about 2.8 cents.
Commatic relationships
This comma is the difference between the following superparticular pairs:
- 42/41 and 45/44
- 154/153 and 205/204
- 165/164 and 225/224
- 176/175 and 246/245
- 196/195 and 287/286
- 231/230 and 369/368
- 288/287 and 540/539
It can be factored into the following superparticular intervals:
Temperaments
Tempering out this comma in the full 41-limit leads to the rank-12 temperament ellismic. Using the 2.3.5.7.11.41 subgroup leads to the rank-5 temperament ellic.
Ellic
Subgroup: 2.3.5.7.11.41
Comma list: 616/615
| [⟨ | 1 | 1 | 2 | 2 | 3 | 5 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | -1 | ], |
| ⟨ | 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 = 702.080, ~5/4 = 386.582, ~7/4 = 968.433, ~11/8 = 550.722
Optimal ET sequence: 5e, 7dm, 8d, 9, 10, 12e, 12m, 15, 19em, 19, 22, 27e, 31, 53, 58, 72, 80, 87, 99em, 111, 118, 152m, 198, 239m, 270
Etymology
This comma was named by Francium in 2025. It refers to 616 Elly, the asteroid, which in turn was named after Elly Boehm, wife of German mathematician Karl Boehm.