40/27

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Revision as of 16:42, 13 July 2021 by Aura (talk | contribs)
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Interval information
Ratio 40/27
Factorization 23 × 3-3 × 5
Monzo [3 -3 1
Size in cents 680.4487¢
Names wolf fifth,
classic grave fifth
FJS name [math]\displaystyle{ \text{P5}^{5} }[/math]
Special properties reduced
Tenney height (log2 nd) 10.0768
Weil height (log2 max(n, d)) 10.6439
Wilson height (sopfr(nd)) 20

[sound info]
Open this interval in xen-calc

The classic grave fifth of 40/27 is the interval between 9/8 and 5/3. It is 81/80, a syntonic comma, flat of 3/2. In some contexts it may be considered a wolf fifth. In meantone, of course, it is equated with a perfect fifth. Although often underappreciated and even avoided on account of its rather dirty sound, it can nevertheless prove useful in the hands of the right composer. Specifically, when used as an interval in its own right, or as the interval spanning the difference between the root and the fifth of a chord, it creates a subtle tension that, according to Aura, is best followed up either by a chord containing a 64/45 tritone for an increase in tension, or by a chord with a perfect fifth between the root and the fifth for a decrease in tension- at least in classical-leaning styles. Alternatively, a chord built around this grave fifth may be used in chord that acts as the final chord in a deceptive cadence with the effect of making such a cadence all the more powerful.

See also