352/351
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Ratio | 352/351 |
Factorization | 2^{5} × 3^{-3} × 11 × 13^{-1} |
Monzo | [5 -3 0 0 1 -1⟩ |
Size in cents | 4.925278¢ |
Names | minthma, 11/13-kleisma |
Color name | 3u1o1, Thulo comma |
FJS name | [math]\text{P1}^{11}_{13}[/math] |
Special properties | superparticular, reduced |
Tenney height (log_{2} n⋅d) | 16.9148 |
Weil height (max(n, d)) | 352 |
Benedetti height (n⋅d) | 123552 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.50228 bits |
Comma size | small |
open this interval in xen-calc |
The minthma or 11/13-kleisma, 352/351, is a 13-limit (also 2.3.11.13 subgroup) small 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 chalmersma, the smallest 13-limit superparticular comma; their sum is 176/175, the valinorsma, an 11-limit superparticular comma.