Wesley comma

From Xenharmonic Wiki
Jump to navigation Jump to search
Interval information
Ratio 78125/73728
Factorization 2-13 × 3-2 × 57
Monzo [-13 -2 7
Size in cents 100.286¢
Name wesley comma
Color name Ly7-2, Lasepyo negative 2nd
FJS name [math]\text{ddd}{-2}^{5,5,5,5,5,5,5}[/math]
Special properties reduced
Tenney height (log2 nd) 32.4234
Weil height (log2 max(n, d)) 32.507
Wilson height (sopfr (nd)) 67
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~4.29122 bits
Comma size large
open this interval in xen-calc

The wesley comma (monzo: [-13 -2 7, ratio: 78125/73728) is a large 5-limit comma measuring about 100 cents. It is unchanged in Wesley Woolhouse's 7/26-comma meantone. It is the amount by which a stack of seven classical major thirds (5/4) octave-reduced exceeds the Pythagorean major second (9/8).


Tempering out this comma leads to the wesley temperament. See Wesley family for a collection of rank-2 temperaments, where it is tempered out.

Its 100-cent size is very close to a 12edo semitone, though it does not have the psychoacoustic significance as simpler intervals around it. It is tempered as such in the magnesium temperament in the 5-limit, with the tiny comma [-157 -24 84 being the difference between 12 wesley commas and 1 octave.