40/21
40/21, the septimal acute major seventh, is a 7-limit interval measuring about 1115.5 cents.
| Interval information |
small septimal diminished octave
[sound info]
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 |