Cataharry comma
Ratio | 19683/19600 |
Factorization | 2^{-4} × 3^{9} × 5^{-2} × 7^{-2} |
Monzo | [-4 9 -2 -2⟩ |
Size in cents | 7.3157671¢ |
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 (log_{2} nd) | 28.5232 |
Weil height (log_{2} max(n, d)) | 28.5293 |
Wilson height (sopfr (nd)) | 59 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.65926 bits |
Comma size | small |
S-expression | S26 * S27^{2} |
open this interval in xen-calc |
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^{[1]}.