Tridecapyth comma

From Xenharmonic Wiki
Jump to navigation Jump to search
Interval information
Ratio 3489660928/3486784401
Factorization 228 × 3-20 × 13
Monzo [28 -20 0 0 0 1
Size in cents 1.4276445¢
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{n\cdot d}[/math])
~2.40679 bits
Comma size unnoticeable
open this interval in xen-calc

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.