Aksial comma

Interval information

Ratio	336141/336140
Factorization	2-2 × 32 × 5-1 × 7-5 × 133 × 17
Monzo	[-2 2 -1 -5 0 3 1⟩
Size in cents	0.0051503287¢
Name	Aksial comma
Color name	17o3o3r5g-2, sotritho-aquinru-agu negative 2nd
FJS name	[math]\text{A}{-2}^{13,13,13,17}_{5,7,7,7,7,7}[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	36.7174
Weil height (log2 max(n, d))	36.7174
Wilson height (sopfr(nd))	106
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.19982 bits
Comma size	unnoticeable
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The aksial comma is an unnoticeable 17-limit comma measuring 0.0052 cents, with a frequency ratio of 336141/336140. It is the smallest superparticular 17-limit interval.

Commatic relations

This comma is the difference between the following superparticular pairs:

• 28561/28560 and 31213/31212
• 123201/123200 and 194481/194480

Etymology

It is named, together with the lateral comma, by Akselai in 2024. The name is a blend of "axial" and "Akselai".

Originally, 194481/194480 was intended to be named the axial comma, based on the factorization of 31213/31212, the E-shaped comma, into 37180/37179 (lateral comma) and 194481/194480, referring to the rectilinear shape of the letter E. However, the latter was already named as the scintillisma.

See also

• List of superparticular intervals