16/13: Difference between revisions

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added the color name
Overthink (talk | contribs)
13/8 is the octave-reduced form of 13/1
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{{Infobox Interval
{{Infobox Interval
| Ratio = 16/13
| Name = (greater) tridecimal neutral third, octave-reduced 13th subharmonic
| Monzo = 4 0 0 0 0 -1
| Cents = 359.47234
| Name = (greater) tridecimal neutral third, <br>octave-reduced 13th subharmonic
| Color name = 3u3, thu 3rd
| Color name = 3u3, thu 3rd
| FJS name = M3<sub>13</sub>
| Sound = jid_16_13_pluck_adu_dr220.mp3
| Sound = jid_16_13_pluck_adu_dr220.mp3
}}
}}


In [[13-limit]] [[just intonation]], '''16/13''', the '''(greater) tridecimal neutral third''', is a 13-limit-based interval measuring about 359.5¢. It is the inversion of [[13/8]], the 13th harmonic.  
In [[13-limit]] [[just intonation]], '''16/13''', the '''(greater) tridecimal neutral third''', is a 13-limit-based interval measuring about 359.5¢. It is the inversion of [[13/8]], the [[octave reduction|octave-reduced]] 13th harmonic.  


16/13 differs from the Pythagorean major third [[81/64]] by [[1053/1024]], about 48¢, from the classic major third [[5/4]] by [[65/64]], about 27¢, from the undecimal neutral third [[11/9]] by [[144/143]], about 12¢, and from the rastmic neutral third [[27/22]] by [[352/351]], about 4.9¢. A [[List_of_root-3rd-P5_triads_in_JI|root-3rd-P5 triad]] featuring 16/13 is 26:32:39, which introduces another tridecimal neutral third, [[39/32]], which measures about 342.5¢. The interval between these two intervals is [[512/507]], about 17¢. While 16/13 is utonal, 39/32 is otonal, as it is the 39th harmonic of the [[harmonic series]].
16/13 differs from the Pythagorean major third [[81/64]] by [[1053/1024]], about 48¢, from the classic major third [[5/4]] by [[65/64]], about 27¢, from the undecimal neutral third [[11/9]] by [[144/143]], about 12¢, and from the rastmic neutral third [[27/22]] by [[352/351]], about 4.9¢. A [[List_of_root-3rd-P5_triads_in_JI|root-3rd-P5 triad]] featuring 16/13 is 26:32:39, which introduces another tridecimal neutral third, [[39/32]], which measures about 342.5¢. The interval between these two intervals is [[512/507]], about 17¢. While 16/13 is utonal, 39/32 is otonal, as it is the 39th harmonic of the [[harmonic series]].
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16/13 is a fraction of a cent away from the neutral third found in the 10''n'' family of edos.  
16/13 is a fraction of a cent away from the neutral third found in the 10''n'' family of edos.  


16/13 is near the border-region between neutral thirds and submajor thirds, so it has a bright edge to it compared to narrower neutral thirds, while still sounding slightly darker than a major third like [[5/4]].
== Approximation ==
{{Interval edo approximation|16/13}}
== See also ==
== See also ==
* [[13/8]] – its [[octave complement]]
* [[13/8]] – its [[octave complement]]
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* [[Gallery of Just Intervals]]       
* [[Gallery of Just Intervals]]       


[[Category:13-limit]]
[[Category:Third]]
[[Category:Third]]
[[Category:Neutral third]]
[[Category:Neutral third]]
[[Category:Octave-reduced subharmonics]]
[[Category:Pages with internal sound examples]]