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¢
Name	vishdel comma
Color name	s1og42, saloquadgu 2nd
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{nd}[/math])	~1.24219 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 in the full 11-limit gives the rank-4 vishdel temperament. Below is the rank-3 subgroup temperament as the vishdel comma doesn't have any 7's.

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.