5632/5625

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 that the 11th harmonic overshoots two perfect fifths, four major thirds, and an octave combined. It is also the amount by which four major thirds falls short of 11/9 plus an octave. It is tempered out in 11-limit extensions of temperaments such as vishnu, grendel, quasiorwell, hemithirds, and decoid.

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
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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.

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