5632/5625

Interval information

Ratio	5632/5625
Factorization	29 × 3-2 × 5-4 × 11
Monzo	[9 -2 -4 0 1⟩
Size in cents	2.153085 ¢
Names	vishdelisma, vishdelic comma
Color name	s1og42, saloquadgu 2nd
FJS name	[math]\displaystyle{ \text{dd2}^{11}_{5,5,5,5} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	24.9171
Weil norm (log2 max(n, d))	24.9189
Wilson norm (sopfr(nd))	55
Comma size	unnoticeable
Open this interval in xen-calc

5632/5625, the vishdelisma or vishdelic comma, is an unnoticeable 11-limit (specifically 2.3.5.11-subgroup) comma with a size of about 2.15 cents. It is the amount by which a stack of four 5/4 major thirds falls short of 11/9 plus an octave. Equivalently, it is the amount by which 11/8 overshoots a stack of two 75/64 classical augmented seconds.

In terms of other commas, it is the difference between 176/175 and 225/224. In the 13-limit, it equals (676/675)/(4225/4224) and factors as (1001/1000)⋅(4096/4095). In the 19-limit it factors as (1216/1215)⋅(2376/2375).

Temperaments

Tempering out this comma in the full 11-limit gives the rank-4 vishdelismic temperament, or in the 2.3.5.11 subgroup, the rank-3 vishdelic temperament. It is tempered out in 11-limit extensions of temperaments such as vishnu, grendel, quasiorwell, hemithirds, and decoid.

Vishdelic

Subgroup: 2.3.5.11

Comma list: 5632/5625

Mapping: [⟨1 0 0 -9], ⟨0 1 0 2], ⟨0 0 1 4]]

mapping generators: ~2, ~3, ~5

Optimal tunings:

• WE: ~2 = 1199.8976 ¢, ~3/2 = 702.1145 ¢, ~5/4 = 386.7638 ¢

error map: ⟨-0.102 +0.057 +0.245 -0.136]

• CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.1309 ¢, ~5/4 = 386.7770 ¢

error map: ⟨0.000 +0.176 +0.463 +0.052]

Optimal ET sequence: 31, 34, 53, 65, 87, 118, 152, 270, 335, 605, 940, 1092, 1362c, 1697c, 2302c

Badness (Sintel): 0.183