# 352/351

 Ratio 352/351 Factorization 25 × 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 $\text{P1}^{11}_{13}$ Special properties superparticular,reduced Tenney height (log2 nd) 16.9148 Weil height (log2 max(n, d)) 16.9189 Wilson height (sopfr (nd)) 43 Harmonic entropy(Shannon, $\sqrt{nd}$) ~1.42367 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:

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.