40/21

Interval information

Ratio	40/21
Factorization	23 × 3-1 × 5 × 7-1
Monzo	[3 -1 1 -1⟩
Size in cents	1115.533¢
Names	acute major seventh, small septimal diminished octave
FJS name	[math]\displaystyle{ \text{M7}^{5}_{7} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	9.71425
Weil norm (log2 max(n, d))	10.6439
Wilson norm (sopfr(nd))	21
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40/21, the acute major seventh, is a 7-limit interval measuring about 1115.5 cents. Despite being approximated by the diminished octave in systems like septimal meantone, and even being called the "small septimal diminished octave" by some musicians due to analogy with 21/20 being called the "large septimal chroma", 40/21 is a major seventh in both Helmholtz-Ellis notation and Functional Just System because it is sharp of the Pythagorean major seventh (243/128) by 5120/5103.

See also

• 21/20 – its octave complement
• Gallery of just intervals