5632/5625
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Ratio | 5632/5625 |
Factorization | 2^{9} × 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 (log_{2} 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
- Unnoticeable comma
- Rank-4 temperament, where this comma's rank-4 temperament should be added to.