40/21
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| Ratio | 40/21 |
| Factorization | 23 × 3-1 × 5 × 7-1 |
| Monzo | [3 -1 1 -1⟩ |
| Size in cents | 1115.5328¢ |
| 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 | |
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.