8569/8568
| Interval information |
fowonosuloru negative 2nd
reduced
(Shannon, [math]\sqrt{nd}[/math])
8569/8568, the mamelisma, is a 41-limit superparticular comma of about 0.20 cents.
Commatic relationships
This comma is the difference between the following superparticular pairs:
- 205/204 and 210/209
- 451/450 and 476/475
- 1463/1462 and 1764/1763
- 2255/2254 and 3060/3059
- 2296/2295 and 3136/3135
It can be factored into the following superparticular ratios:
- 8625/8624 and 1319626/1319625
- 8671/8670 and 728365/728364
- 9361/9360 and 101270/101269
- 10241/10240 and 52480/52479
- 10660/10659 and 43681/43680
- 10830/10829 and 41041/41040
- 11935/11934 and 30381/30380
- 14145/14144 and 21736/21735
- 15457/15456 and 19228/19227
Temperaments
Tempering out this comma in the full 41-limit leads to the rank-12 temperament mamelismic. Using the 2.3.7.11.17.19.41 subgroup leads to the rank-6 temperament mamelic.
Mamelic
Subgroup: 2.3.7.11.17.19.41
Comma list: 8569/8568
| [⟨ | 1 | 1 | 2 | 3 | 4 | 4 | 4 | ], |
| ⟨ | 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 = 701.966, ~7/4 = 968.843, ~11/8 = 551.292, ~17/16 = 104.992, ~19/16 = 297.474
Optimal ET sequence: 5, 7dghm, 7, 9gmm, 9, 12, 14, 22h, 24m, 26, 29g, 31, 32m, 36e, 41, 48, 63, 89, 118, 166g, 193, 207, 311, 342, 400, 540, 549, 581, 629, 836, 971, 1178, 1371, 1489, 1578, 1807, 2207, 2549, 2667m, 3067m, 3130, 3759, 3966, 4937, 5144, 5337, 6426m, 6515, 7262m, 8004m, 10392m
Badness (Sintel): 0.048
Etymology
This comma was named by Francium in 2025. It refers to 8569 Mameli, which in turn was named after Goffredo Mameli, an Italian poet.