Gammic comma

Interval information

Ratio	95367431640625/95105071448064
Factorization	2-29 × 3-11 × 520
Monzo	[-29 -11 20⟩
Size in cents	4.769268¢
Name	gammic comma
FJS name	[math]\displaystyle{ \text{10d}{-5}^{5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} }[/math]
Special properties	reduced
Tenney height (log2 nd)	92.8731
Weil height (log2 max(n, d))	92.8771
Wilson height (sopfr(nd))	191
Comma size	small
Open this interval in xen-calc

The gammic comma (monzo: [-29 -11 20⟩) is a small 5-limit comma with a size of 4.769 cents. It is the difference between nine just major thirds and eleven just minor thirds, that is, (5/4)⁹/(6/5)¹¹. This can also be written as (3/2)/(25/24)¹⁰, that is, the difference between a stack of ten classic chromatic semitones and a classic major sixth; it is part of a series of Don Page commas between adjacent superparticulars, following the escapade comma, which follows the Pythagorean comma; and also the difference between the valentine comma and sycamore comma. It is additionally the difference between a diaschisma and three kleismas.

Temperaments

Temperaments in the gammic family temper out this comma.

Etymology

The gammic comma is named after the Carlos Gamma scale, nearly identical to 20edf, which the gammic temperament generates.