E-shaped comma
(Redirected from 31213/31212)
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Ratio | 31213/31212 |
Factorization | 2^{-2} × 3^{-3} × 7^{4} × 13 × 17^{-2} |
Monzo | [-2 -3 0 4 0 1 -2⟩ |
Size in cents | 0.055466049¢ |
Name | E-shaped comma |
Color name | 17uu3oz^{4}2, susuthoquadzo 2nd |
FJS name | [math]\text{m2}^{7,7,7,7,13}_{17,17}[/math] |
Special properties | superparticular, reduced |
Tenney height (log_{2} nd) | 29.8597 |
Weil height (log_{2} 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:
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.