Elysia

Interval information

Ratio	117649/117612
Factorization	2-2 × 3-5 × 76 × 11-2
Monzo	[-2 -5 0 6 -2⟩
Size in cents	0.5445498¢
Name	elysia
Color name	1uuz64, Bilutrizo comma
FJS name	[math]\displaystyle{ \text{dd4}^{7,7,7,7,7,7}_{11,11} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	33.6878
Weil norm (log2 max(n, d))	33.6883
Wilson norm (sopfr(nd))	83
Comma size	unnoticeable
S-expression	S97⋅S982
Open this interval in xen-calc

The elysia (monzo: [-2 -5 0 6 -2⟩, ratio: 117649/117612) is an unnoticeable 11-limit (also 2.3.7.11-subgroup) comma measuring about 0.545 cents. It is the difference between 49/48 and two intervals of 99/98, and between the breedsma (2401/2400) and kalisma (9801/9800).

Temperaments

Tempering out this comma in the full 11-limit results in the rank-4 elysic temperament (→ Catalog of rank-4 temperaments #Elysic (117649/117612)), or in the 2.3.7.11 subgroup, the rank-3 elysian temperament. Alongside the olympia (131072/130977) and argyria (41503/41472), this comma is tempered out in the representation of 2.3.7.11 by 135edo. Any microtemperament including this comma can incorporate the prime 5 by tempering out 2401/2400 and 9801/9800.

Etymology

The elysia was named by Lériendil in 2024, on the pattern of the olympia, after Elysium Mons on Mars.