5632/5625
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| 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 nd) | 24.9171 |
| Weil height (log2 max(n, d)) | 24.9189 |
| Wilson height (sopfr (nd)) | 55 |
| 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 ET 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.