7696/7695
| Interval information |
sathisonuthogu 2nd
reduced
(Shannon, [math]\sqrt{nd}[/math])
7696/7695, the liebisma, is a 37-limit superparticular comma of about 0.22 cents.
Commatic relationships
This comma is the difference between the following superparticular pairs:
- 286/285 and 297/296
- 481/480 and 513/512
- 666/665 and 729/728
- 1216/1215 and 1444/1443
- 1369/1368 and 1665/1664
- 1540/1539 and 1925/1924
- 2431/2430 and 3553/3552
- 3136/3135 and 5292/5291
- 3367/3366 and 5985/5984
It can be factored into the following superparticular ratios:
- 7936/7935 and 254449/254448
- 8281/8280 and 108928/108927
- 9361/9360 and 43264/43263
- 9802/9801 and 35816/35815
- 10693/10692 and 27456/27455
- 11914/11913 and 21736/21735
- 12376/12375 and 20350/20349
- 12636/12635 and 19684/19683
- 13312/13311 and 18241/18240
- 14365/14364 and 16576/16575
Temperaments
Tempering out this comma in the full 37-limit leads to the rank-11 liebismic. Using the 2.3.5.13.19.37 subgroup leads to the rank-5 temperament liebic.
Liebic
Subgroup: 2.3.5.13.19.37
Comma list: 7696/7695
| [⟨ | 1 | 1 | 2 | 3 | 4 | 3 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | 4 | ], |
| ⟨ | 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 = 701.977, ~5/4 = 386.325, ~13/8 = 840.498, ~19/16 = 297.552
Optimal ET sequence: 5, 5hl, 7fh, 7, 9l, 10, 12, 15l, 19hl, 19, 24, 29, 34, 38fl, 41l, 43, 53, 164l, 183, 205, 217l, 258, 270, 311, 354, 407, 460, 677, 730, 829, 882, 935, 1395, 1947, 2000, 2053, 2935, 2988, 3395, 3448, 5395, 5448
Etymology
This comma was named by Francium in 2025. It refers to 7696 Liebe, the asteroid, which in turn was named after Bodo Liebe, a professor at the University of Siegen, Germany.