3256/3255
| Interval information |
thisothiwulorugu 2nd
reduced
(Shannon, [math]\sqrt{nd}[/math])
3256/3255, the daguerrisma, is a 37-limit superparticular comma of about 0.53 cents.
Commatic relationships
This comma is the difference between the following superparticular pairs:
- 148/147 and 155/154
- 176/175 and 186/185
- 407/406 and 465/464
- 666/665 and 837/836
- 962/961 and 1365/1364
- 1210/1209 and 1925/1924
- 1036/1035 and 1519/1518
- 1184/1183 and 1860/1859
It can be factored into the following superparticular intervals:
- 3367/3366 and 98736/98735
- 3520/3519 and 43401/43400
- 3626/3625 and 31900/31899
- 3774/3773 and 23716/23715
- 3876/3875 and 20350/20349
- 4096/4095 and 15873/15872
- 4186/4185 and 14652/14651
- 4992/4991 and 9361/9360
- 5104/5103 and 8991/8990
- 5291/5290 and 8464/8463
- 5643/5642 and 7696/7695
Temperaments
Tempering out this comma in the full 37-limit leads to the rank-11 temperament daguerrismic. Using the 2.3.5.7.11.31.37 subgroup leads to the rank-6 temperament daguerric.
Daguerric
Subgroup: 2.3.5.7.11.31.37
Comma list: 3256/3255
| [⟨ | 1 | 1 | 2 | 2 | 3 | 4 | 3 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 1 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 1 | 0 | -1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 1 | 1 | ]] |
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.972, ~5/4 = 386.350, ~7/4 = 968.879, ~11/8 = 551.238, ~31/16 = 1145.200
Optimal ET sequence: 5e, 6l, 7dkll, 7k, 8dll, 9kl, 10ek, 10, 12l, 12k, 15, 19ekkl, 19e, 22, 27e, 31k, 41l, 46, 58kl, 72kll, 72, 87, 99ek, 103l, 121kl, 125, 130, 152, 212, 224, 270, 301, 311, 342l, 400, 525, 612, 1164, 1376, 1776, 2000k, 2612k
Badness (Sintel): 0.126
Etymology
This comma was named by Francium in 2025. It refers to 3256 Daguerre, the asteroid, which in turn was named after Louis Daguerre, a French chemist, artist and pioneer of photography.