40/21
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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]\text{M7}^{5}_{7}[/math]
Special properties
reduced
Tenney height (log2 nd)
9.71425
Weil height (log2 max(n, d))
10.6439
Wilson height (sopfr(nd))
21
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~4.25066 bits
[sound info]
open this interval in xen-calc
| Interval information |
small septimal diminished octave
(Shannon, [math]\sqrt{nd}[/math])
[sound info]
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.