Xenial comma

The xenial comma (monzo: [-6 17 -9⟩, ratio: 129140163/125000000) is a 5-limit comma of about 56.4 cents. It belongs to the syntonic–kleismic equivalence continuum and is equal to the difference between a stack of nine ptolemaic whole tones and the perfect eleventh ((8/3)/(10/9)⁹), or in terms of commas, between a stack of three syntonic commas and a kleisma ((81/80)³/(15625/15552)).

Interval information

Ratio	129140163/125000000
Factorization	2-6 × 317 × 5-9
Monzo	[-6 17 -9⟩
Size in cents	56.41159¢
Name	xenial comma
Color name	Lg92, latritrigu 2nd, Latritrigu comma
FJS name	[math]\displaystyle{ \text{dd2}_{5,5,5,5,5,5,5,5,5} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	53.8417
Weil norm (log2 max(n, d))	53.8887
Wilson norm (sopfr(nd))	108
Comma size	medium
Open this interval in xen-calc

Temperaments

Tempering out this comma leads to the xenial family of temperaments. Patent vals which temper it out include those for 19, 70, 89, 108, 127, 146 and 235.

Etymology

The comma was named by Xenllium in 2026, in terms of the corresponding temperament, xenial, come from ξενία (Greek for hospitable), after its temperament property.