Gaster comma

From Xenharmonic Wiki
Jump to navigation Jump to search
Interval information
Factorization 2-70 × 372 × 5-19
Monzo [-70 72 -19
Size in cents 0.79949888¢
Name gaster comma
Color name L8g19-3, quadbila-negu negative 3rd
FJS name [math]\text{M}{-3}_{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) 228.234
Weil height (log2 max(n, d)) 228.235
Wilson height (sopfr (nd)) 451
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~1.20578 bits
Comma size unnoticeable
open this interval in xen-calc

22528399544939174411840147874772641/22517998136852480000000000000000000, the gaster comma is a 5-limit unnoticeable comma measuring about 0.7995 cents. It is the difference between a stack of seventeen 9/8s and a stack of nineteen 10/9s, (9/8)17/(10/9)19 = [-70 72 -19 (quadbila-negu).

It can also be described as the difference between eighteen 81/80s and 5/4.


Equal temperaments which temper out this comma include 111, 113, 224, 335, 559, 783, 1342, 1901, 3243 and others.

The gaster comma is tempered out by the gaster temperament.