81/70

From Xenharmonic Wiki
Revision as of 20:13, 27 September 2020 by Xenwolf (talk | contribs) (See also: added link to 5th compl.)
Jump to navigation Jump to search
Interval information
Ratio 81/70
Factorization 2-1 × 34 × 5-1 × 7-1
Monzo [-1 4 -1 -1
Size in cents 252.6804¢
Names septimal semiaugmented second,
septimal ultramajor second
Color name rg2, rugu 2nd
FJS name [math]\displaystyle{ \text{M2}_{5,7} }[/math]
Special properties reduced
Tenney norm (log2 nd) 12.4691
Weil norm (log2 max(n, d)) 12.6797
Wilson norm (sopfr(nd)) 26
Open this interval in xen-calc

81/70, the septimal semiaugmented second or septimal ultramajor second is a 7-limit interseptimal ratio of about 253 cents. It is sharp of a subminor third 7/6 by a sensamagic comma 245/243, and sharp of a major second 16/9 by a septimal quartertone 36/35.

It is also sharp of a minor third 6/5 by a subminor second 28/27. For this fact it is useful in the Canovian chord and provides the function of a voice leading up to the minor third.

The interval is so perfectly approximated by 19-edo, with an error of 0.05 cents. There are a number of edos that do this equally well, 171-edo to name one. The first edo that does this better than 19-edo with patent val is 660-edo.

See also