11/7
| Interval information |
pentacircle minor sixth
(Shannon, [math]\sqrt{nd}[/math])
[sound info]
In 11-limit just intonation, 11/7 is an undecimal minor sixth, specifically the pentacircle minor sixth, measuring about 782.5¢. It is the inversion of 14/11, the pentacircle major third, and represents the difference between the 7th and 11th harmonics of the harmonic series.
In many notation systems (e.g. FJS, HEJI), it is an imperfect fifth, as it is a perfect fifth (3/2) plus an instance of 22/21, which is a stack consisting of an undecimal quartertone (33/32) and a septimal comma (64/63), neither of which changes the scale degree or quality. However, it is only flat of the Pythagorean (3-limit) minor sixth of 128/81 (about 792.2¢) by a pentacircle comma (896/891), which makes it function more often as a minor sixth, hence the names.
It is flat of the 5-limit minor sixth of 8/5 (about 813.7¢) by 56/55. It is sharp of the 7-limit subminor sixth of 14/9 (about 764.9¢) by a mothwellsma, 99/98. And finally, it is sharp of the classic augmented fifth of 25/16 (about 772.6¢) by a valinorsma, 176/175.
As 11/7 is 22/21 (about 80.5¢) above the perfect fifth, it can be resolved down by a step from 11/7 to 3/2.
Approximations by edos
Following edos (up to 200) contain good approximations[1] of the interval 11/7. Errors are given by magnitude, the arrows in the table show if the edo representation is sharp (↑) or flat (↓).
| Edo | deg\edo | Absolute error (¢) |
Relative error (r¢) |
↕ | Equally acceptable multiples [2] |
|---|---|---|---|---|---|
| 20 | 13\20 | 2.4920 | 4.1534 | ↓ | |
| 23 | 15\23 | 0.1167 | 0.2236 | ↑ | 30\46, 45\69, 60\92, 75\115, 90\138, 105\161, 120\184 |
| 26 | 17\26 | 2.1233 | 4.6006 | ↑ | |
| 43 | 28\43 | 1.0967 | 3.9298 | ↓ | |
| 49 | 32\49 | 1.1814 | 4.8242 | ↑ | |
| 66 | 43\66 | 0.6739 | 3.7062 | ↓ | |
| 72 | 47\72 | 0.8413 | 5.0478 | ↑ | |
| 89 | 58\89 | 0.4696 | 3.4826 | ↓ | 116\178 |
| 95 | 62\95 | 0.6659 | 5.2714 | ↑ | |
| 112 | 73\112 | 0.3492 | 3.2590 | ↓ | |
| 118 | 77\118 | 0.5588 | 5.4950 | ↑ | |
| 135 | 88\135 | 0.2698 | 3.0354 | ↓ | |
| 141 | 92\141 | 0.4867 | 5.7186 | ↑ | |
| 158 | 103\158 | 0.2136 | 2.8118 | ↓ | |
| 164 | 107\164 | 0.4348 | 5.9422 | ↑ | |
| 181 | 118\181 | 0.1716 | 2.5882 | ↓ | |
| 187 | 122\187 | 0.3957 | 6.1658 | ↑ |
Proximity with π/2
(11/7)/(π/2) = 22/7π is an unnoticeable comma of only 0.7 cents.
See also
- 14/11 – its octave complement
- Ed11/7
- Gallery of just intervals
- File:Ji-11-7-csound-foscil-220hz.mp3 – another sound example