352/351
Ratio | 352/351 |
Factorization | 2^{5} × 3^{-3} × 11 × 13^{-1} |
Monzo | [5 -3 0 0 1 -1⟩ |
Size in cents | 4.925278¢ |
Names | major minthma, major gentle comma, 11/13-kleisma |
Color name | 3u1o1, thulo 1sn, Thulo comma |
FJS name | [math]\text{P1}^{11}_{13}[/math] |
Special properties | superparticular, reduced |
Tenney height (log_{2} nd) | 16.9148 |
Weil height (log_{2} max(n, d)) | 16.9189 |
Wilson height (sopfr (nd)) | 43 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.50228 bits |
Comma size | small |
open this interval in xen-calc |
352/351, the major minthma, major gentle comma or 11/13-kleisma is a small 13-limit (also 2.3.11.13 subgroup) comma measuring about 4.9 ¢. This comma can be described in a number of ways. First, it is the difference between the tridecimal minor third of 13/11 and the Pythagorean minor third of 32/27, hence the name 11/13-kleisma. Second, it is the difference between various tridecimal intervals and their adjacent undecimal intervals such as:
- Between the tridecimal quartertone of 1053/1024 and the undecimal quartertone of 33/32;
- Between 16/13 and 27/22; and
- Between 39/32 and 11/9.
352/351 and 351/350, the ratwolfsma, are extremely close in size and make up a consecutive pair of 13-limit superparticular commas. Their difference is 123201/123200, the chalmersia, the smallest 13-limit superparticular comma; their sum is 176/175, the valinorsma, an 11-limit superparticular comma.
Temperaments
Tempering out this comma leads to a form of major minthmic temperament (full 13-limit rank-5) or majorminth temperament (2.3.11.13 subgroup rank-3), which enables major minthmic chords.
History and etymology
This comma was known as the minthma from 2011. The word minthma is a contraction of minor thirds comma into a single word. In 2022, Margo Schulter requested it should be changed to major/greater minthma to distinguish it from 364/363, which would gain the name minor/lesser minthma. The major gentle comma was also added to this comma in contrast to the minor gentle comma of 364/363. Both commas were essential to define the gentle temperament.