575/574
Interval information |
fowutwethoruyoyo unison
reduced
575/574, the renatisma, is a 41-limit superparticular interval superparticular comma of about 3.0 cents.
Commatic relationships
This comma is the difference between the following superparticular pairs:
It can be factored into the following superparticular ratios:
Temperaments
Tempering out this comma in the full 41-limit leads to the rank-12 temperament renatismic. Using the 2.5.7.23.41 subgroup leads to the rank-4 temperament renatic.
Renatic
Subgroup: 2.5.7.23.41
Comma list: 575/574
[⟨ | 1 | 2 | 2 | 4 | 5 | ], |
⟨ | 0 | 1 | 0 | 0 | 2 | ], |
⟨ | 0 | 0 | 1 | 0 | -1 | ], |
⟨ | 0 | 0 | 0 | 1 | 1 | ]] |
Optimal tuning (CTE): ~ 2 = 1\1, ~5/4 = 385.900, ~7/4 = 969.128, ~23/16 = 627.490
Optimal ET sequence: 4, 6, 10m, 15m, 18im, 19, 21, 25, 31, 56, 74m, 78, 84, 109, 249, 358, 432m, 541m, 650m
Badness (Sintel): 0.045
Etymology
This comma was named by Francium in 2025. It refers to 575 Renate, the asteroid. The name's origin is unknown, it may be inspired by the asteroid's provisional designation, containing the letters "RE".