40/21

Interval information

Ratio

40/21

Factorization

2³ × 3^-1 × 5 × 7^-1

[3 -1 1 -1⟩

Size in cents

1115.533¢

Names

septimal acute major seventh,
small septimal diminished octave

ry7, ruyo 7th

[math]\text{M7}^{5}_{7}[/math]

Special properties

9.71425

Weil height (log₂ max(n, d))

10.6439

21

Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])

~4.25066 bits

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.