Quintile comma

The quintile comma (monzo: [-28 25 -5⟩, ratio: 847 288 609 443 / 838 860 800 000) is a small 5-limit comma of about 17.306 cents. It is the amount by which a stack of five grave fourths of 320/243 falls short of two octaves, or the amount by which a stack of five acute fifths of 243/160 exceeds three octaves. It is also the amount by which a stack of five syntonic commas exceed a Pythagorean limma.

Interval information

Factorization	2-28 × 325 × 5-5
Monzo	[-28 25 -5⟩
Size in cents	17.30645¢
Name	Quintile comma
FJS name	[math]\displaystyle{ \text{m}{-2}_{5,5,5,5,5} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	79.2337
Weil norm (log2 max(n, d))	79.2481
Wilson norm (sopfr(nd))	156
Comma size	small
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Temperaments

Tempering out this comma leads to the quintile family of temperaments.