Cataharry comma

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Interval information
Ratio 19683/19600
Monzo [-4 9 -2 -2
Size in cents 7.31577
Name(s) cataharry comma
open this interval in xen-calc

The cataharry comma (19683/19600) is a 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 family of temperaments, which splits the just perfect fourth (4/3) into two exact hemifourths, each representing 81/70~280/243.

See also