Wesley comma

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
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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).

Temperaments

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.