5632/5625

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Interval information
Ratio 5632/5625
Factorization 29 × 3-2 × 5-4 × 11
Monzo [9 -2 -4 0 1
Size in cents 2.1530852¢
Name vishdel comma
FJS name [math]\text{dd2}^{11}_{5,5,5,5}[/math]
Special properties reduced
Tenney height (log2 n⋅d) 24.9171
Weil height (max(n, d)) 5632
Benedetti height (n⋅d) 31680000
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~2.4185 bits
Comma size unnoticeable
open this interval in xen-calc

The vishdel comma is an 11-limit unnoticeable comma with a ratio of 5632/5625, a monzo of [9 -2 -4 0 1, and a size of 2.1531 cents. It is the amount that the eleventh harmonic overshoots two perfect fifths, four major thirds, and an octave combined. It is tempered out in 11-limit extensions of temperaments such as vishnu, grendel, quasiorwell, hemithirds, and decoid.

Temperament

Tempering this comma out gives the rank-4 vishdel temperament. Below however, is a rank-3 subgroup temperament since the vishdel comma doesn't have any sevens in it.

118 & 65 & 152

Subgroup: 2.3.5.11

Comma list: 5632/5625

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

POTE generators: ~3/2 = 702.1744, ~5/4 = 386.7968

Optimal GPV sequence: 31, 34, 53, 65, 87, 118, 152, 183, 217, 270

See also