Barium comma

Interval information

Factorization	2-225 × 3224 × 5-56
Monzo	[-225 224 -56⟩
Size in cents	4.352217¢
Name	Barium comma
Color name	L24g56-8, quadtribila-sepquadbigu negative octave
FJS name	[math]\displaystyle{ - }[/math]
Special properties	reduced
Tenney height (log2 nd)	710.06
Weil height (log2 max(n, d))	710.063
Wilson height (sopfr(nd))	1402
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~1.37413 bits
Comma size	small
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Barium comma is a 5-limit interval that sets the difference between 56 syntonic commas and the octave, marking the closest approximation of the octave by stacking syntonic commas.

Tempering it out results in the barium temperament, which splits the octave into 56 equal parts. Some notable edos tempering out the barium comma are 224edo which is a zeta edo, and 2520edo which is a highly composite edo. The tuning systems which are not divisible by 56 cannot temper it out.