16/13: Difference between revisions

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~~'''16/13'''~~

{{Infobox Interval

|~~4 0 0 0 0~~ -~~1>~~

| Name = (greater) tridecimal neutral third, octave-reduced 13th subharmonic

| Color name = 3u3, thu 3rd

| Sound = jid_16_13_pluck_adu_dr220.mp3

}}

359.~~47234 cents~~

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.

[[~~File:jid_16_13_pluck_adu_dr220.mp3~~]] [[:~~File~~:~~jid_16_13_pluck_adu_dr220~~.~~mp3|sound sample~~]]

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]].

~~In [[13-limit|13-limit]] [[Just_intonation|Just Intonation]],~~ 16/13 is a ~~tridecimal (13-based) neutral third measuring about 359.5¢. It is the inversion~~ of ~~[[13/8|13/8]], the 13th harmonic. It differs from [[5/4|5/4]] by [[65/64|65/64]], about 26.8¢. It differs~~ from the ~~undecimal neutral third [[11/9|11/9]] by [[144/143|144/143]], about 12¢. 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|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 overtone~~ of ~~the [[OverToneSeries|harmonic series]]~~.

16/13 is a fraction of a cent away from the neutral third found in the 10''n'' family of edos.

~~See:~~ [[~~Gallery_of_Just_Intervals|Gallery of Just Intervals~~]] [[~~Category:~~13~~-limit~~]]

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]].

[[~~Category:interval~~]]

[[~~Category:just_interval~~]]

== See also ==

[[~~Category:neutral_3rd~~]]

* [[13/8]] – its [[octave complement]]

[[~~Category:ratio~~]]

* [[39/32]] – its [[fifth complement]]

[[Category:~~third~~]]

* [[Gallery of Just Intervals]]

[[Category:~~tridecimal~~]]

[[Category:Third]]

[[Category:Neutral third]]

@@ Line 1: / Line 1: @@
-'''16/13'''
+{{Infobox Interval
-|4 0 0 0 0 -1&gt;
+| Name = (greater) tridecimal neutral third, octave-reduced 13th subharmonic
+| Color name = 3u3, thu 3rd
+| Sound = jid_16_13_pluck_adu_dr220.mp3
+}}
-.47234 cents
+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.
-[[File:jid_16_13_pluck_adu_dr220.mp3]] [[:File:jid_16_13_pluck_adu_dr220.mp3|sound sample]]
+/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]].
-In [[13-limit|13-limit]] [[Just_intonation|Just Intonation]], 16/13 is a tridecimal (13-based) neutral third measuring about 359.5¢. It is the inversion of [[13/8|13/8]], the 13th harmonic. It differs from [[5/4|5/4]] by [[65/64|65/64]], about 26.8¢. It differs from the undecimal neutral third [[11/9|11/9]] by [[144/143|144/143]], about 12¢. 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|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 overtone of the [[OverToneSeries|harmonic series]].
+/13 is a fraction of a cent away from the neutral third found in the 10''n'' family of edos.
-See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]      [[Category:13-limit]]
+/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]].
-[[Category:interval]]
-[[Category:just_interval]]
+== See also ==
-[[Category:neutral_3rd]]
+* [[13/8]] – its [[octave complement]]
-[[Category:ratio]]
+* [[39/32]] – its [[fifth complement]]
-[[Category:third]]
+* [[Gallery of Just Intervals]]
-[[Category:tridecimal]]
+[[Category:Third]]
+[[Category:Neutral third]]