E-shaped comma

Interval information

Ratio	31213/31212
Factorization	2-2 × 3-3 × 74 × 13 × 17-2
Monzo	[-2 -3 0 4 0 1 -2⟩
Size in cents	0.05546605¢
Name	E-shaped comma
Color name	17uu3oz42, susuthoquadzo 2nd
FJS name	[math]\text{m2}^{7,7,7,7,13}_{17,17}[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	29.8597
Weil height (log2 max(n, d))	29.8597
Wilson height (sopfr(nd))	88
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.19985 bits
Comma size	unnoticeable
S-expression	S49 / S51
open this interval in xen-calc

The E-shaped comma is a 17-limit unnoticeable comma of measuring 0.055 cents, with frequency ratio of 31213/31212. It is the amount by which a stack consisting of three 7/6s, one 26/17 and one 28/17 exceeds two octaves. By tempering it out is defined the E-shaped temperament, which splits 13/12 into two 51/49's.

Commatic relations

In terms of commas, it is the difference between the following superparticular pairs:

• 1225/1224 and 1275/1274
• 2401/2400 and 2601/2600
• 4914/4913 and 5832/5831
• 28561/28560 and 336141/336140

It factors into the following superparticular pair:

• 37180/37179 and 194481/194480

Etymology

This comma was named by Xenllium in 2023. It came from its numerator of the lowest terms, 31213, which constructs an E-shape by square tiling. Its denominator, 31212 also constructs another form of E-shape.

See also

• Unnoticeable comma
• List of superparticular intervals