39/32

Interval information

Ratio	39/32
Factorization	2-5 × 3 × 13
Monzo	[-5 1 0 0 0 1⟩
Size in cents	342.4827¢
Names	lesser tridecimal neutral third, octave-reduced 39th harmonic
Color name	3o3, tho 3rd
FJS name	[math]\displaystyle{ \text{m3}^{13} }[/math]
Special properties	reduced, reduced harmonic
Tenney norm (log2 nd)	10.2854
Weil norm (log2 max(n, d))	10.5708
Wilson norm (sopfr(nd))	26
[sound info]
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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.

Approximation

Edo approximations for 39/32 (342.48 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
7	2\7	342.86	+0.37	+0.22
14	4\14	342.86	+0.37	+0.44
21	6\21	342.86	+0.37	+0.66
28	8\28	342.86	+0.37	+0.87
35	10\35	342.86	+0.37	+1.09
42	12\42	342.86	+0.37	+1.31
49	14\49	342.86	+0.37	+1.53
56	16\56	342.86	+0.37	+1.75
63	18\63	342.86	+0.37	+1.97
70	20\70	342.86	+0.37	+2.18
77	22\77	342.86	+0.37	+2.40

See also

• 64/39 – its octave complement
• 16/13 – its fifth complement
• Gallery of just intervals