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

Mercurial Comma

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, the mercurial comma, 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 adjacent to 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.