14/11
Ratio | 14/11 |
Factorization | 2 × 7 × 11^{-1} |
Monzo | [1 0 0 1 -1⟩ |
Size in cents | 417.50796¢ |
Names | undecimal major third, pentacircle major third |
Color name | 1uz4, luzo 4th |
FJS name | [math]\text{P4}^{7}_{11}[/math] |
Special properties | reduced |
Tenney height (log_{2} nd) | 7.26679 |
Weil height (log_{2} max(n, d)) | 7.61471 |
Wilson height (sopfr (nd)) | 20 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.249 bits |
[sound info] | |
open this interval in xen-calc |
In 11-limit just intonation, 14/11 is an undecimal major third, specifically the pentacircle major third, a supermajor third of about 417.5¢. It represents the difference between the 11th and 14th harmonics of the harmonic series.
In many notation systems based on the 3-limit with commatic alterations (e.g. FJS, HEJI), it is an imperfect fourth, as it is a perfect fourth (4/3) minus 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 sharp of the Pythagorean (3-limit) major third of 81/64 (about 407.8¢) by a pentacircle comma (896/891), which makes it function more often as a major third, hence the names.
14/11 can 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¢. 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.
It also appears in chords such as 8:11:14, the principal triad of orgone temperament.
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