Cataharry comma

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Interval information
Ratio 19683/19600
Factorization 2-4 × 39 × 5-2 × 7-2
Monzo [-4 9 -2 -2
Size in cents 7.3157671¢
Name cataharry comma
FJS name [math]\text{m}{-2}_{5,5,7,7}[/math]
Special properties reduced
Tenney height (log2 n⋅d) 28.5232
Weil height (max(n, d)) 19683
Benedetti height (n⋅d) 385786800
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~2.62219 bits
Comma size small
S-expression S26 * S272
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