Mercurial comma

Interval information

Ratio

557122275/556583944

Factorization

2^-3 × 3² × 5² × 7^-2 × 17^-5 × 19⁵

Monzo

[-3 2 2 -2 0 0 -5 5⟩

Size in cents

1.67365¢

Name(s)

missing^?

FJS name

[math]\displaystyle{ \text{ddd}{-3}^{5,5,19,19,19,19,19}_{7,7,17,17,17,17,17} }[/math]

Special properties

reduced

Tenney height (log₂ nd)

58.1054

Weil height (log₂ max(n, d))

58.1068

Wilson height (sopfr(nd))

216

Open this interval in xen-calc

557122275/556583944, or 1.673649 cents, is the amount by which five justly tuned 19/17's and two 15/14's exceeds an octave. As the ratio between these intervals is very close to phi, this is a strong harmonic entropy minimum in the golden meantone sequence, particularly well suited to stringed instruments that are normally tuned with slight octave stretches due to the inharmonicity of their partials.