E-shaped comma
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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
| Interval information |
susuthoquadzo 2nd
reduced
(Shannon, [math]\sqrt{nd}[/math])
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:
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.