1375/1372

1375/1372, the moctdelisma or moctdelic comma is a small no-3's 11-limit comma with a size of 3.78 cents. It is the amount by which a stack of three 7/5's falls short of 11/4, the undecimal semi-augmented eleventh (one octave above 11/8).

Interval information

Ratio	1375/1372
Factorization	2-2 × 53 × 7-3 × 11
Monzo	[-2 0 3 -3 1⟩
Size in cents	3.781365 ¢
Names	moctdelisma, moctdelic comma
Color name	1or3y3-3, lotriruyo negative 3rd, Lotriruyo comma
FJS name	[math]\displaystyle{ \text{dd}{-3}^{5,5,5,11}_{7,7,7} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	20.8473
Weil norm (log2 max(n, d))	20.8504
Wilson norm (sopfr(nd))	51
Comma size	small
Open this interval in xen-calc

In terms of other commas, it is the difference between 50/49 and 56/55, between 99/98 and 126/125, and between 225/224 and 441/440. In the 13-limit, it factors into superparticular commas as (625/624)⋅(1716/1715), and in the 17-limit, (715/714)⋅(1275/1274).

Temperaments

Tempering out this comma in the full 11-limit leads to the rank-4 moctdelismic temperament, and in its minimal prime subgroup of 2.5.7.11, the moctdelic temperament. Some rank-2 temperaments such as miracle, octoid and grendel temper out this comma, and from this it derives its name.

In the 2.7/5.11 subgroup it creates a very efficient temperament with a generator of 7/5, two of which equals 55/28 and three of which equals 11/4 as discussed. If we split the generator in 3, we get ~28/25 which is notable as the difference between 5/4 and 7/5 so that two generator steps find 5/4, four find 11/7~25/16 and seven find 11/5, which is the (no-3's) 11-limit version of didacus, a very strong temperament of the 2.5.7.11 subgroup.

See Moctdelismic clan for the clan of temperaments where it is tempered out.