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
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557122275/556583944, or the mercurial comma, has a value of 1.673649 cents, and 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.