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
Color name	19o517u5rryy-3, quinnosu-abiruyo negative 3rd
FJS name	[math]\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
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.22439 bits
Comma size	unnoticeable
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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 19/17s and two 15/14s exceed 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.

Etymology

It is named after the chemical element mercury due to its adjacency to gold, since mercury meantone is adjacent to golden meantone.

It is unrelated to the 80th-octave temperament by the same name.