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 height (log2 nd)	37.012
Weil height (log2 max(n, d))	37.0196
Wilson height (sopfr(nd))	101
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~1.9341 bits
Comma size	small
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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, 60, 77, 94, 171

Badness: 0.006431

See also

• Quinticular comma – another example of quintic-particular comma