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]\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
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.40819 bits
Comma size	small
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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 perfect fifth; 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 three kleismas (15625/15552) and a diaschisma (2048/2025).

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.