3367/3366
| Interval information |
thisosutholuzo 2nd
reduced
(Shannon, [math]\sqrt{nd}[/math])
3367/3366, the alexisma, is a 37-limit superparticular comma of about 0.51 cents.
= Commatic relationships
This comma is the difference between the following superparticular pairs:
- 273/272 and 297/296
- 364/363 and 408/407
- 481/480 and 561/560
- 925/924 and 1275/1274
- 936/935 and 1296/1295
- 1225/1224 and 1925/1924
It can be factored into the following superparticular ratios:
- 3381/3380 and 812890/812889
- 3510/3509 and 82621/82620
- 3520/3519 and 77441/77440
- 3565/3564 and 60606/60605
- 3626/3625 and 47125/47124
- 3774/3773 and 31213/31212
- 4186/4185 and 17205/17204
- 4225/4224 and 16576/16575
- 4625/4624 and 12376/12375
- 4693/4692 and 11914/11913
- 4914/4913 and 10693/10692
- 5985/5984 and 7696/7695
Temperaments
Tempering out this comma in the full 37-limit leads to the rank-11 temperament alexismic. Using the 2.3.7.11.13.17.37 subgroup leads to the rank-6 temperament alexic.
Alexic
Subgroup: 2.3.7.11.13.17.37
Comma list: 3367/3366
| [⟨ | 1 | 1 | 2 | 3 | 3 | 4 | 5 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | 0 | 2 | ], |
| ⟨ | 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 = 701.985, ~7/4 = 968.780, ~11/8 = 551.388, ~13/8 = 840.447, ~17/16 = 105.054
Optimal ET sequence: 5f, 7dg, 7, 8d, 9gl, 10e, 10l, 12el, 12fg, 14fggl, 14f, 15, 17l, 17g, 24, 26, 32f, 36el, 41, 46, 58, 67, 72, 104, 121l, 140, 147, 149, 157, 171, 181, 207, 311, 328, 400, 477, 535, 607, 788, 935, 971, 1188, 1371, 1395, 1759, 2159, 2366l, 4525l
Etymology
This comma was named by Francium in 2025. It refers to 3367 Alex, the asteroid, which in turn was named after the grandson of the discoverer.