616/615
| Interval information |
fowulozogu 2nd
reduced
(Shannon, [math]\sqrt{nd}[/math])
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:
- 621/620 and 76384/76383
- 638/637 and 17836/17835
- 651/650 and 11440/11439
- 676/675 and 6930/6929
- 704/703 and 4921/4920
- 726/725 and 4060/4059
- 736/735 and 3773/3772
- 780/779 and 2926/2925
- 784/783 and 2871/2870
- 1001/1000 and 1600/1599
- 1026/1025 and 1540/1539
- 1190/1189 and 1276/1275
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.