Tridecapyth comma

Interval information
Ratio	3489660928/3486784401
Factorization	228 × 3-20 × 13
Monzo	[28 -20 0 0 0 1⟩
Size in cents	1.427644¢
Name	tridecapyth comma
Color name	s33o3, trisatho 3rd,; Trisatho comma
FJS name	[math]\displaystyle{ \text{ddd3}^{13} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	63.3997
Weil norm (log2 max(n, d))	63.4009
Wilson norm (sopfr(nd))	129
Comma size	unnoticeable
	Open this interval in xen-calc

The tridecapyth comma (monzo: [28 -20 0 0 0 1⟩, ratio: 3489660928/3486784401), also described as the tridecimal schisma, is an unnoticeable comma in 13-limit just intonation which measures roughly 1.43  ¢. It is the interval by which 13/8 exceeds a stack of twenty perfect fifths (3/2) octave reduced, and by which 16/13 falls short of a stack of four Pythagorean limmas (256/243). It is perhaps more easily conceptualized as reaching 13/4 through (9/8)¹⁰. In terms of commas, it is the amount by which tridecimal quartertone (1053/1024) is greater than a stack of two Pythagorean commas.

Etymology

This comma was named by Aura in 2021.