Glacier comma

Interval information

Ratio	373248/371293
Factorization	29 × 36 × 13-5
Monzo	[9 6 0 0 0 -5⟩
Size in cents	9.091696¢
Name	glacier comma
Color name	3u5-2, quinthu negative 2nd
FJS name	[math]\displaystyle{ \text{ddd}{-2}_{13,13,13,13,13} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	37.012
Weil norm (log2 max(n, d))	37.0196
Wilson norm (sopfr(nd))	101
Comma size	small
Open this interval in xen-calc

The glacier comma is a 13-limit comma which is the difference between five small tridecimal neutral seconds of 13/12 and a perfect fifth (3/2). It is a quintic-particular^{[idiosyncratic term]} interval, that is, of the form ((n+5)/n) / ((n+3)/(n+2))⁵ = (S(n+1)×S(n+2)²) / (S(n+3)²×S(n+4)).

Temperaments

Tempering out this comma in the 13-limit leads to the glacier family.

Glacier (2.3.13)

Subgroup: 2.3.13

Mapping: [⟨1 1 3], ⟨0 5 6]]

Mapping generators: ~2, ~13/12

Optimal tuning (CTE): ~2 = 1200.0000, ~13/12 = 140.3277

Optimal ET sequence: 8, 9, 17, 26, 60, 77, 94, 111, 171

Badness: 0.383 (Sintel)

See also

• Quinticular comma – another example of quintic-particular comma