Cataharry comma

Interval information

Ratio	19683/19600
Factorization	2-4 × 39 × 5-2 × 7-2
Monzo	[-4 9 -2 -2⟩
Size in cents	7.315767¢
Name	cataharry comma
Color name	Lrrgg-2, Labirugu comma
FJS name	[math]\text{m}{-2}_{5,5,7,7}[/math]
Special properties	reduced
Tenney height (log2 nd)	28.5232
Weil height (log2 max(n, d))	28.5293
Wilson height (sopfr(nd))	59
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.68393 bits
Comma size	small
S-expression	S26 * S272
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The cataharry comma (ratio: 19683/19600, monzo: [-4 9 -2 -2⟩) is a small 7-limit comma measuring about 6.1 cents. It is the difference between the septimal ultramajor second (81/70) and its fourth complement. In terms of commas, it is equal to (81/80)/(245/243) and to (81/80)²/(49/48). The latter equivalence implies that if the cataharry comma is tempered out and if neither 81/80 nor 49/48 are tempered out, there will be an interval ~81/80 above 8/7 and ~81/80 below 7/6, and analogously for 12/7 and 7/4.

Temperaments

Tempering out this comma leads to the rank-3 cataharry temperament, which splits the just perfect fourth (4/3) into two exact hemifourths, each representing 81/70~280/243. See Cataharry family for the rank-3 family where it is tempered out. See Cataharry temperaments for a collection of rank-2 temperaments where it is tempered out.

Etymology

The name cataharry was given by Gene Ward Smith in 2005 as a contraction of catakleismic and harry.