81/70

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
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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

• 140/81 – its octave complement
• 35/27 – its fifth complement
• Gallery of just intervals