Gaster comma
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Factorization | 2^{-70} × 3^{72} × 5^{-19} |
Monzo | [-70 72 -19⟩ |
Size in cents | 0.79949888¢ |
Name | gaster comma |
Color name | L^{8}g^{19}-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 (log_{2} nd) | 228.234 |
Weil height (log_{2} 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.
Temperaments
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.