Euzenius comma
| Ratio | 78125000/78121827 |
| Factorization | 23 × 3-13 × 510 × 7-2 |
| Monzo | [3 -13 10 -2⟩ |
| Size in cents | 0.07031446¢ |
| Name | euzenius comma |
| Color name | srry10-3, 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 (log2 nd) | 52.4385 |
| Weil height (log2 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.