Euzenius comma

Interval information

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 breedsma and a stack of two ragismas, 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.

See also

• Unnoticeable comma