4774/4773
| Interval information |
fothuthisuthiwolozo negative 2nd
reduced
(Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])
4774/4773, the hobetsisma, is a 43-limit superparticular comma of about 0.36 cents.
Commatic relationships
This comma is the difference between the following superparticular pairs:
- 775/774 and 925/924
- 1333/1332 and 1849/1848
- 1463/1462 and 2109/2108
- 1936/1935 and 3256/3255
- 2108/2107 and 3774/3773
It can be factored into the following superparticular ratios:
- 4785/4784 and 2076256/2076255
- 4960/4959 and 127281/127280
- 5292/5291 and 48763/48762
- 5720/5719 and 28861/28860
- 5797/5796 and 27048/27047
- 6076/6075 and 22275/22274
- 7956/7955 and 11935/11934
Temperaments
Tempering out this comma in the full 43-limit leads to the rank-13 temperament hobetsismic. Using the 2.3.7.11.31.37.43 subgroup leads to the rank-6 temperament hobetsic.
Hobetsic
Subgroup: 2.3.7.11.31.37.43
Comma list: 4774/4773
| [⟨ | 1 | 1 | 2 | 3 | 4 | 5 | 4 | ], |
| ⟨ | 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 = 701.964, ~7/4 = 968.798, ~11/8 = 551.276, ~31/16 = 1144.950, ~37/32 = 251.439
Optimal ET sequence: 5, 8dn, 9kn, 10k, 10n, 12kn, 14l, 17, 17kn, 22, 24, 27e, 31k, 41, 48n, 55l, 63, 72, 82, 87, 89, 121kl, 135, 152, 176, 301, 383, 400, 477, 612, 701, 877, 940, 1084, 1241, 1417, 1641, 2118, 3202, 3814, 3966, 4142, 4843ln, 6872ln
Badness (Sintel): 0.060
Etymology
This comma was named by Francium in 2025. It refers to 4774 Hobetsu, the asteroid, which in turn was named after a town in Japan.