39/32: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Ratio = 39/32
| Name = lesser tridecimal neutral third, octave-reduced 39th harmonic
| Monzo = -5 1 0 0 0 1
| Color name = 3o3, tho 3rd
| Cents = 342.48266
| Sound = Ji-39-32-csound-foscil-220hz.mp3
| Name = octave-reduced 39th harmonic
| Color name =  
| Sound =  
}}
}}


'''39/32''' is the combination of primes 13 and 3 octave-reduced. It is a fraction of a cent away from the neutral third found in the 7n family of edos.  
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¢.  


[[Category:Interval]]
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 7''n'' 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 ==
 
* [[64/39]] – its [[octave complement]]
* [[16/13]] – its [[fifth complement]]
* [[Gallery of just intervals]]
 
[[Category:Third]]
[[Category:Neutral third]]
[[Category:Neutral third]]
[[Category:Overtone]]
[[Category:Todo:expand]]

Latest revision as of 23:44, 8 March 2023

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 height (log2 nd) 10.2854
Weil height (log2 max(n, d)) 10.5708
Wilson height (sopfr(nd)) 26

[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