Mercurial comma: Difference between revisions

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Xenwolf (talk | contribs)
autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
8,705 edits
fixed https://www.wolframalpha.com/input/?i=557122275%2F556583944&assumption=%22ClashPrefs%22+-%3E+%7B%22Math%22%7D
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{{Infobox Interval
{{Infobox Interval
| Icon =  
| Icon =  
| Ratio = 557122275/556583994
| 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
Line 9: Line 9:
}}
}}


557122275/556583994, or 1.673649 cents, 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 in 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 1.673649 cents, 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 in 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.


[[Category:19-limit]]
[[Category:19-limit]]

Revision as of 14:05, 25 September 2020

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(s) missing ? 
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 1.673649 cents, 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 in 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.

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