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]\text{ddd3}^{13}[/math]
Special properties	reduced
Tenney height (log2 nd)	63.3997
Weil height (log2 max(n, d))	63.4009
Wilson height (sopfr(nd))	129
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.21885 bits
Comma size	unnoticeable
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The tridecapyth comma (monzo: [28 -20 0 0 0 1⟩, ratio: 3489660928/3486784401) is an unnoticeable 13-limit comma which measures roughly 1.43 cents. It is the interval which separates 13/8 and a stack of twenty perfect fifths (3/2) octave reduced, and which separates 16/13 and 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 difference between the tridecimal quartertone (1053/1024) and a stack of two Pythagorean commas.