40/27

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
Color name	y5, yo 5th
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 a syntonic comma (81/80) 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 dissonant sound in comparison to the perfect fifth, 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, its dark and active sound creates a kind of tension that, in classical-leaning or even medieval-leaning styles, can be arguably 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. Alternatively, a chord built around this grave fifth may be used in chord that acts as the final chord in an interrupted cadence with the effect of making such a cadence all the more powerful.

In Zarlino, it appears as the fifth of the ii chord.

See also

• 27/20 – its octave complement
• Gallery of just intervals