40/21
(Redirected from 40 21)
| Interval information |
small septimal diminished octave
[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.
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 13 | 12\13 | 1107.69 | -7.84 | -8.49 |
| 14 | 13\14 | 1114.29 | -1.25 | -1.45 |
| 15 | 14\15 | 1120.00 | +4.47 | +5.58 |
| 27 | 25\27 | 1111.11 | -4.42 | -9.95 |
| 28 | 26\28 | 1114.29 | -1.25 | -2.91 |
| 29 | 27\29 | 1117.24 | +1.71 | +4.13 |
| 42 | 39\42 | 1114.29 | -1.25 | -4.36 |
| 43 | 40\43 | 1116.28 | +0.75 | +2.67 |
| 44 | 41\44 | 1118.18 | +2.65 | +9.71 |
| 56 | 52\56 | 1114.29 | -1.25 | -5.82 |
| 57 | 53\57 | 1115.79 | +0.26 | +1.22 |
| 58 | 54\58 | 1117.24 | +1.71 | +8.26 |
| 70 | 65\70 | 1114.29 | -1.25 | -7.27 |
| 71 | 66\71 | 1115.49 | -0.04 | -0.24 |
| 72 | 67\72 | 1116.67 | +1.13 | +6.80 |