Chrysia

Interval information

Ratio	43923/43904
Factorization	2-7 × 3 × 7-3 × 114
Monzo	[-7 1 0 -3 4⟩
Size in cents	0.7490509¢
Name	chrysia
Color name	Qualo-atriruma, 4*1ua3*rM
FJS name	[math]\displaystyle{ \text{m}{-3}^{11,11,11,11}_{7,7,7} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	30.8448
Weil norm (log2 max(n, d))	30.8454
Wilson norm (sopfr(nd))	82
Comma size	unnoticeable
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The chrysia (monzo: [-7 1 0 -3 4⟩, ratio: 43923/43904) is an unnoticeable 11-limit (also 2.3.7.11-subgroup) comma measuring about 0.749 cents. It is the amount by which three intervals of 11/7 and 33/32 exceed two octaves.

It factors into simpler superparticular commas as (3025/3024)⋅(9801/9800).

Temperaments

Tempering out this comma in the full 11-limit results in the rank-4 chrysic temperament (→ Catalog of rank-4 temperaments #Chrysic (43923/43904)), and in the 2.3.7.11 subgroup, the rank-3 chrysian temperament.

Alongside the olympia (131072/130977) and argyria (41503/41472), this comma is tempered out in the representation of the 2.3.7.11 subgroup by 135edo. Among the various 2.3.7.11-subgroup micro-commas of 135edo, this comma is notable for having only a single power of 3 in it, allowing 3 to be represented by 2.7.11-subgroup intervals. One notable example is given by chrysanthemum temperament, which tempers out the chrysia alongside the amaranthine comma to provide a 2.3.7.11 interpretation of a chain of nearly pure 7/4's with errors less than 0.1 cents.

Etymology

The chrysia was named by VIxen in 2025, on the pattern of the argyria, after Chryse Planitia on Mars and the legendary island of Chryse.

It was previously named the hemigail comma by an unknown wiki contributor some time before 2025 (the name appeared on the page Unnoticeable commas).