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	septimal acute major seventh,; small septimal diminished octave
Color name	ry7, ruyo 7th
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
	https://en.xen.wiki/w/File:Jid_40_21_pluck_adu_dr220.mp3; [sound info]
	Open this interval in xen-calc

40/21, the septimal acute major seventh, is a 7-limit interval measuring about 1115.5 cents.

Terminology

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 just intonation notation systems such as Sagittal notation, Helmholtz-Ellis notation and Functional Just System, viewed as the Pythagorean major seventh (243/128) altered by 5120/5103.