11/7
| Ratio | 11/7 |
| Factorization | 7-1 × 11 |
| Monzo | [0 0 0 -1 1⟩ |
| Size in cents | 782.49204¢ |
| Names | undecimal minor sixth, undecimal augmented fifth |
| Color name | 1or5, loru 5th |
| FJS name | [math]\text{P5}^{11}_{7}[/math] |
| Special properties | reduced |
| Tenney height (log2 nd) | 6.26679 |
| Weil height (log2 max(n, d)) | 6.91886 |
| Wilson height (sopfr (nd)) | 18 |
| Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~4.57449 bits |
[sound info] | |
| open this interval in xen-calc | |
In 11-limit just intonation, 11/7 is an undecimal minor sixth, measuring about 782.5¢. It is the inversion of 14/11, the undecimal major third.
11/7 is flat of the Pythagorean minor sixth of 128/81 (about 792.2¢) by a pentacircle comma, 896/891. 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.
11/7 is 22/21 (about 80.5¢) above the 3/2 perfect fifth, allowing the possibility of a resolution 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
- Gallery of just intervals
- File:Ji-11-7-csound-foscil-220hz.mp3 – another sound example