16/13: Difference between revisions

Line 5:

| Cents = 359.47234

| Name = neutral tridecimal third

| ~~Color~~ name =

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

| Sound = jid_16_13_pluck_adu_dr220.mp3

}}

In [[13-limit]] [[just intonation]], '''16/13''' is a tridecimal (13-based) neutral third measuring about 359.5¢. It is the inversion of [[13/8]], the 13th harmonic. It differs from [[5/4]] by [[65/64]], about ~~26.8¢. It differs~~ from the undecimal neutral third [[11/9]] by [[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]], 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''' is a tridecimal (13-based) neutral third 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]].

See: [[Gallery of Just Intervals]]

== See also ==

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

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

* [[Gallery of Just Intervals]]

[[Category:13-limit]]

@@ Line 5: / Line 5: @@
 | Cents = 359.47234
 | Name = neutral tridecimal third
-| Color name =
+| FJS name = M3<sub>13</sub>
 | Sound = jid_16_13_pluck_adu_dr220.mp3
 }}
-In [[13-limit]] [[just intonation]], '''16/13''' is a tridecimal (13-based) neutral third measuring about 359.5¢. It is the inversion of [[13/8]], the 13th harmonic. It differs from [[5/4]] by [[65/64]], about 26.8¢. It differs from the undecimal neutral third [[11/9]] by [[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]], 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''' is a tridecimal (13-based) neutral third 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]].
-See: [[Gallery of Just Intervals]]
+== See also ==
+* [[13/8]] - its [[octave complement]]
+* [[39/32]] - its fifth complement
+* [[Gallery of Just Intervals]]
 [[Category:13-limit]]