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, sinaic
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]
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14/13, the 2/3-tone or trienthird (one-third third), nicknamed the sinaic (after Ibn Sina who used it in one of his scales), is a somewhat exotic 13-limit interval measuring about 128.3¢, which is almost exactly 1/3 of a 5/4 major third- a stack of three trienthirds falling short of a 5/4 major third by a cantonisma.

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). Thus intervals close in size to it have been called sinaics.

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