Mercurial comma
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Ratio | 557122275/556583944 |
Factorization | 2^{-3} × 3^{2} × 5^{2} × 7^{-2} × 17^{-5} × 19^{5} |
Monzo | [-3 2 2 -2 0 0 -5 5⟩ |
Size in cents | 1.6736497¢ |
Name | mercurial comma |
Color name | 19o^{5}17u^{5}rryy-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 (log_{2} nd) | 58.1054 |
Weil height (log_{2} max(n, d)) | 58.1068 |
Wilson height (sopfr (nd)) | 216 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.22439 bits |
Comma size | unnoticeable |
open this interval in xen-calc |
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.