1331/1323
| 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 |
| open this interval in xen-calc | |
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.