1331/1323

Interval information

Ratio	1331/1323
Factorization	3-3 × 7-2 × 113
Monzo	[0 -3 0 -2 3⟩
Size in cents	10.437012¢
Name	aphrowe comma
Color name	trilo-aruru negative 2nd, 1o3rr-2 trilo-aruru comma
FJS name	[math]\text{M}{-2}^{11,11,11}_{7,7}[/math]
Special properties	reduced
Tenney height (log2 nd)	20.7479
Weil height (log2 max(n, d))	20.7566
Wilson height (sopfr(nd))	56
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~2.15237 bits
Comma size	small
S-expression	S222 × S23
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1331/1323, the aphrowe comma, is an 11-limit, and 3.7.11 subgroup, comma of approximately 10.4 cents. Tempering this out splits the interval of 7/1 into three major sevenths of 21/11, or 8/7 into three minor seconds of 22/21 (and therefore 12/11 into two of these intervals), the latter equivalence giving rise to this comma's S-expression as (S22 = 484/483)² × (S23 = 529/528). From a no-twos point of view, it can also be seen as splitting 27/7 into three minor sixths of 11/7 (and thus equating 27/11 to two of them).

Temperaments

Tempering it out in the 3.7.11 subgroup provides Mintaka temperament, which is one of the simplest temperaments in this subgroup with decent accuracy, and creates a 5L 2s macrodiatonic scale generated by 11/7 against the tritave.