352/351

From Xenharmonic Wiki
Jump to navigation Jump to search
Interval information
Ratio 352/351
Factorization 25 × 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 (log2 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

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.

See also