Gaster comma

Interval information

Factorization	2-70 × 372 × 5-19
Monzo	[-70 72 -19⟩
Size in cents	0.7994989¢
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
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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.

Ratio

22528399544939174411840147874772641 / 22517998136852480000000000000000000