16/13: Difference between revisions

Line 4:

| Monzo = 4 0 0 0 0 -1

| Cents = 359.47234

| Name = greater tridecimal neutral third, <br> octave-reduced 13th subharmonic

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

| FJS name = M3<sub>13</sub>

| 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. It differs from [[81/64]] by [[1053/1024]], about 48¢, from [[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 overtone of the [[harmonic series]].

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.

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 overtone of the [[harmonic series]].

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

== See also ==

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

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

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

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

* [[Gallery of Just Intervals]]

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[[Category:Interval]]

[[Category:Just interval]]

[[Category:Ratio]]

[[Category:Neutral third]]

~~[[Category:Ratio]]~~

[[Category:Third]]

~~[[Category:Tridecimal]]~~

[[Category:Subharmonic]]

@@ Line 4: / Line 4: @@
 | Monzo = 4 0 0 0 0 -1
 | Cents = 359.47234
-| Name = greater tridecimal neutral third, <br> octave-reduced 13th subharmonic
+| Name = (greater) tridecimal neutral third, <br>octave-reduced 13th subharmonic
 | FJS name = M3<sub>13</sub>
 | 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. It differs from [[81/64]] by [[1053/1024]], about 48¢, from [[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 overtone of the [[harmonic series]].
+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.
+/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 overtone of the [[harmonic series]].
 /13 is a fraction of a cent away from the neutral third found in the 10''n'' family of edos.
 == See also ==
-* [[13/8]] - its [[octave complement]]
+* [[13/8]] – its [[octave complement]]
-* [[39/32]] - its fifth complement
+* [[39/32]] – its [[fifth complement]]
 * [[Gallery of Just Intervals]]
@@ Line 21: / Line 23: @@
 [[Category:Interval]]
 [[Category:Just interval]]
+[[Category:Ratio]]
 [[Category:Neutral third]]
-[[Category:Ratio]]
 [[Category:Third]]
-[[Category:Tridecimal]]
 [[Category:Subharmonic]]