Quintile comma

Interval information

Factorization	2-28 × 325 × 5-5
Monzo	[-28 25 -5⟩
Size in cents	17.30645¢
Name	Quintile comma
FJS name	[math]\text{m}{-2}_{5,5,5,5,5}[/math]
Special properties	reduced
Tenney height (log2 nd)	79.2337
Weil height (log2 max(n, d))	79.2481
Wilson height (sopfr(nd))	156
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~3.36099 bits
Comma size	small
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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 exceeds a Pythagorean limma.

Temperaments

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

Etymology

The corresponding temperament was discovered first, called pental by Petr Pařízek in 2012 for the fact that it splits the octave in five equal parts. In 2024, the community has decided to rename it to quintile for fear of confusion with the more common usage of the term pental to refer to the 5-limit.