Euzenius comma
Ratio | 78125000/78121827 |
Factorization | 2^{3} × 3^{-13} × 5^{10} × 7^{-2} |
Monzo | [3 -13 10 -2⟩ |
Size in cents | 0.07031446¢ |
Name | euzenius comma |
Color name | srry^{10}-3, Sabiruquinyo comma |
FJS name | [math]\text{dddd}{-3}^{5,5,5,5,5,5,5,5,5,5}_{7,7}[/math] |
Special properties | reduced |
Tenney height (log_{2} nd) | 52.4385 |
Weil height (log_{2} max(n, d)) | 52.4386 |
Wilson height (sopfr (nd)) | 109 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.19986 bits |
Comma size | unnoticeable |
open this interval in xen-calc |
The euzenius comma is an unnoticeable 7-limit comma with a ratio of 78125000/78121827, a monzo of [3 -13 10 -2⟩, and a size of 0.070314 cents. It is the difference between two 6250/5103 intervals and the perfect fifth. In terms of commas, it is the difference between a ragisma and a stack of two breedsmas, relating the two smallest 7-limit superparticular commas.
Temperament
Tempering out this comma gives the euzenius temperament (→ Very high accuracy temperaments #Euzenius or Sabiruquinyo). In any tuning of euzenius, the breedsma is split in two, and the perfect fifth as well. Ennealimmal is an obvious rank-2 temperament where this comma is tempered out, as both the breedsma and the ragisma are tempered out. Another example of rank-2 temperament is given by fortune.