Mercurial comma: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Icon =
| Ratio = 557122275/556583944
| Ratio = 557122275/556583944
| Monzo = -3 2 2 -2 0 0 -5 5
| Monzo = -3 2 2 -2 0 0 -5 5
| Cents = 1.673649
| Cents = 1.673649
| Name = Mercurial Comma
| Name = mercurial comma
| Color name =
| Color name =
| FJS name =
| Sound =
| Sound =
}}
}}


'''557122275/556583944''', or the '''mercurial comma''', has a value of 1.673649 [[cent|cents]], and is the amount by which five justly tuned [[19/17]]s and two [[15/14]]s 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|golden meantone]] sequence, particularly well suited to stringed instruments that are normally tuned with slight octave stretches due to the inharmonicity of their partials.
'''557122275/556583944''', or the '''mercurial comma''', has a value of 1.673649 [[cent]]s, and is the amount by which five justly tuned [[19/17]]s and two [[15/14]]s 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.


[[Category:19-limit]]
[[Category:19-limit]]
[[Category:Interval]]
[[Category:Unnoticeable comma]]
[[Category:Ratio]]
[[Category:Unnoticeable_comma]]
[[Category:Just interval]]
[[Category:Meantone]]
[[Category:Meantone]]
[[Category:Mercurial]]
[[Category:Mercurial]]

Revision as of 05:26, 22 January 2022

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 norm (log2 nd) 58.1054
Weil norm (log2 max(n, d)) 58.1068
Wilson norm (sopfr(nd)) 216
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.