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Interval information
Ratio 39/32
Factorization 2-5 × 3 × 13
Monzo [-5 1 0 0 0 1
Size in cents 342.48266¢
Names lesser tridecimal neutral third,
octave-reduced 39th harmonic
Color name 3o3, tho 3rd
FJS name [math]\text{m3}^{13}[/math]
Special properties reduced
Tenney height (log2 nd) 10.2854
Weil height (log2 max(n, d)) 10.5708
Wilson height (sopfr (nd)) 26
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~4.2507 bits

[sound info]
open this interval in xen-calc

In 13-limit just intonation, 39/32, the (lesser) tridecimal neutral third, is the otonal combination of primes 13 and 3 octave-reduced. It is the fifth complement of 16/13, which measures about 359.5¢.

39/32 differs from the Pythagorean minor third 32/27 by 1053/1024, about 48¢, from the classic minor third 6/5 by 65/64, about 27¢, from the rastmic neutral third 27/22 by 144/143, about 12¢, and from the undecimal neutral third 11/9 by 352/351, about 4.9¢.

39/32 is a fraction of a cent away from the neutral third found in the 7n family of edos.

39/32 is near the border-region between neutral thirds and supraminor thirds, so it has a dark edge to it compared to wider neutral thirds, while still sounding slightly brighter than a minor third like 6/5.

See also