14/11

Interval information

Ratio	14/11
Factorization	2 × 7 × 11-1
Monzo	[1 0 0 1 -1⟩
Size in cents	417.508¢
Name	undecimal major third
Color name	1uz4, luzo 4th
FJS name	[math]\displaystyle{ \text{P4}^{7}_{11} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	7.26679
Weil norm (log2 max(n, d))	7.61471
Wilson norm (sopfr(nd))	20
[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