2431/2430
Jump to navigation
Jump to search
Ratio | 2431/2430 |
Factorization | 2^{-1} × 3^{-5} × 5^{-1} × 11 × 13 × 17 |
Monzo | [-1 -5 -1 0 1 1 1⟩ |
Size in cents | 0.71229544¢ |
Name | heptacircle comma |
Color name | 17o3o1og2, sothologu 2nd, Sothologu comma |
FJS name | [math]\text{dd2}^{11,13,17}_{5}[/math] |
Special properties | superparticular, reduced |
Tenney height (log_{2} nd) | 22.4941 |
Weil height (log_{2} max(n, d)) | 22.4947 |
Wilson height (sopfr (nd)) | 63 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.20456 bits |
Comma size | unnoticeable |
open this interval in xen-calc |
2431/2430, the heptacircle comma is a 17-limit superparticular comma of about 0.71 cents. It is the amount by which 1215/512 (layo ninth, a stack consisting of major limma, Pythagorean whole tone and an octave) falls short of a stack consisting of 11/8, 13/8 and 17/16. By tempering it out is defined the heptacircle temperament, which enables the heptacircle chords.
Etymology
The name heptacircle was named by Xenllium in 2023, for the following reason - it is represented by monzo [-1 -5 -1 0 1 1 1⟩, using a zero value ("circle") in the mediant place of seven variables (17-limit no-seven subgroup comma). It is similar to the pentacircle comma, 896/891 (11-limit no-five subgroup comma).