11/7
In 11-limit just intonation, 11/7 is an undecimal minor sixth, specifically the pentacircle minor sixth, measuring about 782.5 cents. 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.
| Interval information |
pentacircle minor sixth
[sound info]
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. It functions as such in voicings of the harmonic eleventh chord, 4:5:6:7:9:11.
However, it is only flat of the Pythagorean minor sixth (about 792.2 ¢) by a pentacircle comma (896/891), which makes it function sometimes as a minor sixth, hence the names. For one thing, as it is 22/21 (about 80.5 ¢) above the perfect fifth, it can be resolved down by a step to the perfect fifth.
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.
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 3 | 2\3 | 800.00 | +17.51 | +4.38 |
| 6 | 4\6 | 800.00 | +17.51 | +8.75 |
| 17 | 11\17 | 776.47 | -6.02 | -8.53 |
| 20 | 13\20 | 780.00 | -2.49 | -4.15 |
| 23 | 15\23 | 782.61 | +0.12 | +0.22 |
| 26 | 17\26 | 784.62 | +2.12 | +4.60 |
| 29 | 19\29 | 786.21 | +3.71 | +8.98 |
| 40 | 26\40 | 780.00 | -2.49 | -8.31 |
| 43 | 28\43 | 781.40 | -1.10 | -3.93 |
| 46 | 30\46 | 782.61 | +0.12 | +0.45 |
| 49 | 32\49 | 783.67 | +1.18 | +4.82 |
| 52 | 34\52 | 784.62 | +2.12 | +9.20 |
| 63 | 41\63 | 780.95 | -1.54 | -8.08 |
| 66 | 43\66 | 781.82 | -0.67 | -3.71 |
| 69 | 45\69 | 782.61 | +0.12 | +0.67 |
| 72 | 47\72 | 783.33 | +0.84 | +5.05 |
| 75 | 49\75 | 784.00 | +1.51 | +9.42 |
Proximity with acoustic pi
22/7, one octave higher, is a fraction convergent to the continued fraction of acoustic pi. Such is the exactness, that 22/7π is an unnoticeable comma of only 0.7 cents.
See also
- 14/11 – its octave complement
- 21/11 – its twelfth complement
- Ed11/7
- Gallery of just intervals
- File:Ji-11-7-csound-foscil-220hz.mp3 – another sound example