14/11
| Ratio | 14/11 |
| Factorization | 2 × 7 × 11-1 |
| Monzo | [1 0 0 1 -1⟩ |
| Size in cents | 417.50796¢ |
| Name | undecimal major third |
| Color name | 1uz4, luzo 4th |
| FJS name | [math]\text{P4}^{7}_{11}[/math] |
| Special properties | reduced |
| Tenney height (log2 nd) | 7.26679 |
| Weil height (log2 max(n, d)) | 7.61471 |
| Wilson height (sopfr (nd)) | 20 |
| Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~4.57421 bits |
[sound info] | |
| open this interval in xen-calc | |
In 11-limit just intonation, 14/11 is the undecimal major third, a supermajor third of about 417.5¢. It represents the difference between the 11th and 14th overtones of the harmonic series and appears in chords such as 8:11:14, the principal triad of orgone temperament. 14/11 can also function as a neo-Gothic major third, as it falls between 5/4 and 9/7. Indeed, it is the mediant ratio between those simpler intervals, as it is (5+9)/(4+7), and is 56/55 sharp of 5/4, 99/98 flat of 9/7. Other relatively simple thirds in this region can be generated by taking the mediant between 5/4 and 14/11 (which is (5+14)/(4+11) = 19/15, about 409.2¢) and between 14/11 and 9/7 (which is (14+9)/(11+7) = 23/18, about 424.4¢. Also in this region is the Pythagorean (3-limit) major third of 81/64 (about 407.8¢), of which 14/11 is sharp by 896/891. The fact that this interval functions as a type of third is one of the reasons why 7/4, the octave reduced version of the 14th harmonic, can be argued to be a type of "sinth"- a cross between a sixth and a seventh- as opposed to merely a subminor seventh.
See also
- 11/7 – its octave complement
- 33/28 – its fifth complement
- Gallery of just intervals
- Gentle chords
- List of root-3rd-P5 triads in JI
External links
- The Noble Mediant by Margo Schulter and David Keenan