14/13

Interval information

Ratio	14/13
Factorization	2 × 7 × 13-1
Monzo	[1 0 0 1 0 -1⟩
Size in cents	128.2982¢
Names	tridecimal 2/3-tone, trienthird
FJS name	[math]\displaystyle{ \text{M2}^{7}_{13} }[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	7.50779
Weil height (log2 max(n, d))	7.61471
Wilson height (sopfr(nd))	22
[sound info]
Open this interval in xen-calc

14/13, the 2/3-tone or trienthird (one-third third) interval is a somewhat exotic 13-limit interval which, measuring about 128.3¢, is almost exactly 1/3 of a major third of 5/4. The cantonisma – (5/4)/(14/13)³ = 10985/10976 – is tempered out in such notable EDOs as 46, 84, 94, 103, 111, 121, 130, 159, 224, 270, 494 and 764, leading to a variety of temperaments in which three trienthirds make up a major third.

The trienthird was a favorite interval of Avicenna (Ibn Sina) for his scale constructions, and may be considered a smaller size of neutral second (a second between major and minor).

In 13-limit Just Intonation, 14/13 represents the difference in size between the tridecimal minor third of 13/11 and undecimal major third of 14/11. It is also the difference between 13/10 and 7/5; 13/12 and 7/6; 13/9 and 14/9, and of course 13/8 and 7/4 and the inversions of the above. As it combines the primes 7 and 13, it appears in JI subgroup tunings involving those primes.

See also

• 13/7 – its octave complement
• Gallery of just intervals