Elysia: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
BudjarnLambeth (talk | contribs)
m Etymology: added link
m Linking & bold lemma
 
(One intermediate revision by the same user not shown)
Line 5: Line 5:
| Comma = yes
| Comma = yes
}}
}}
The '''elysia''' ([[monzo]]: {{monzo| -2 -5 0 6 -2 }}, [[ratio]]: 117649/117612) is an [[unnoticeable comma|unnoticeable]] [[11-limit]] (also 2.3.7.11 [[subgroup]]) [[comma]] measuring about 0.545 [[cent]]s. It is the difference between [[49/48]] and two intervals of [[99/98]], and between the [[breedsma]] (2401/2400) and [[kalisma]] (9801/9800).
The '''elysia''' ([[monzo]]: {{monzo| -2 -5 0 6 -2 }}, [[ratio]]: 117649/117612) is an [[unnoticeable comma|unnoticeable]] [[11-limit]] (also [[2.3.7.11 subgroup|2.3.7.11-subgroup]]) [[comma]] measuring about 0.545 [[cent]]s. It is the difference between [[49/48]] and two intervals of [[99/98]], and between the [[breedsma]] (2401/2400) and [[kalisma]] (9801/9800).


== Temperaments ==
== Temperaments ==
Alongside the [[olympia]] (131072/130977) and [[41503/41472|argyria]] (41503/41472), this comma is tempered 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.
[[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 ==
== Etymology ==
The elysia was named by [[Lériendil]] in 2024, on the pattern of the [[olympia]], after Elysium Mons on Mars.
The elysia was named by [[Lériendil]] in 2024, on the pattern of the olympia, after Elysium Mons on Mars.


[[Category:Elysic]]
[[Category:Commas named after place names]]
[[Category:Commas named after place names]]

Latest revision as of 05:09, 5 June 2026

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.