E-shaped comma

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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 0.055466049¢
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{n\cdot d}[/math])
~2.39832 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:

It factors into the following superparticular pair:

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