14/13
Ratio | 14/13 |
Factorization | 2 × 7 × 13^{-1} |
Monzo | [1 0 0 1 0 -1⟩ |
Size in cents | 128.29824¢ |
Names | tridecimal 2/3-tone, trienthird, tridecimal supraminor second, sinaic |
Color name | 3uz2, thuzo 2nd |
FJS name | [math]\text{M2}^{7}_{13}[/math] |
Special properties | superparticular, reduced |
Tenney height (log_{2} n⋅d) | 7.50779 |
Weil height (max(n, d)) | 14 |
Benedetti height (n⋅d) | 182 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~4.61268 bits |
[sound info] | |
open this interval in xen-calc |
14/13, the tridecimal 2/3-tone or trienthird (one-third third) 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 by Zhea Erose. It may be called the tridecimal supraminor second as well, analogous to 21/13 being the tridecimal supraminor sixth.
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.