18/13: Difference between revisions

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~~'''18/13'''~~

{{Infobox Interval

|~~1 2 0 0 0 -1>~~

| Name = tridecimal augmented fourth, low tritone

| Color name = 3u4, thu 4th

| Sound = jid_18_13_pluck_adu_dr220.mp3

}}

563.~~3823 cents~~

In [[13-limit]] [[just intonation]], '''18/13''', the '''tridecimal augmented fourth''' is a '''low [[tritone]]''' measuring about 563.4¢. It represents the interval between the 13th and 18th harmonics of the [[overtone scales|harmonic series]].

[[~~File:jid_18_13_pluck_adu_dr220~~.~~mp3~~]] [[~~:File:jid_18_13_pluck_adu_dr220.mp3|sound sample~~]]

The low tritone in [[17edo]] approximates 18/13 quite well, while 17edo's approximations of [[13/8]] and [[9/8]] are both a little sharp. The inversion of 18/13 is [[13/9]], a high tritone measuring about 636.6¢; the interval between these two tridecimal (13-based) tritones is [[169/162]], approximately 73.2¢.

In [[13-limit|13-limit]] [[Just_intonation|Just Intonation]], '''18/13''' is a low [[tritone|tritone]] measuring about 563.4¢. It represents the interval between the 13th and 18th overtones of the [[overtone_scales|harmonic series]]. The low tritone in [[17edo|17edo]] approximates 18/13 quite well, while 17edo's approximations of [[13/8|13/8]] and [[9/8|9/8]] are both a little sharp. The inversion of 18/13 is [[13/9|13/9]], a high tritone measuring about 636.6¢; the interval between these two tridecimal (13-based) tritones is 169/162, approximately 73.2¢.

== See also ==

~~Other just tritones include~~ [[7/~~5|7/5~~]], [[~~10/7|10/7~~]], [[~~45/32|45/32]], [[64/45|64/45]], [[24/17|24/17]], [[17/12|17~~/12]], [[~~23/16|23/16~~]], [[~~32/23|32/23~~]]~~, and, of course, infinitely many more intervals.~~

* [[13/9]] – its [[octave complement]]

* [[13/12]] – its [[fifth complement]]

* [[Gallery of just intervals]]

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

[[Category:Tritone]]

~~[[Category:15-limit]]~~

~~[[Category:interval]]~~

~~[[Category:just_interval]]~~

~~[[Category:ratio]]~~

[[Category:~~tritone~~]]

@@ Line 1: / Line 1: @@
-'''18/13'''
+{{Infobox Interval
-|1 2 0 0 0 -1&gt;
+| Name = tridecimal augmented fourth, low tritone
+| Color name = 3u4, thu 4th
+| Sound = jid_18_13_pluck_adu_dr220.mp3
+}}
-.3823 cents
+In [[13-limit]] [[just intonation]], '''18/13''', the '''tridecimal augmented fourth''' is a '''low [[tritone]]''' measuring about 563.4¢. It represents the interval between the 13th and 18th harmonics of the [[overtone scales|harmonic series]].
-[[File:jid_18_13_pluck_adu_dr220.mp3]] [[:File:jid_18_13_pluck_adu_dr220.mp3|sound sample]]
+The low tritone in [[17edo]] approximates 18/13 quite well, while 17edo's approximations of [[13/8]] and [[9/8]] are both a little sharp. The inversion of 18/13 is [[13/9]], a high tritone measuring about 636.6¢; the interval between these two tridecimal (13-based) tritones is [[169/162]], approximately 73.2¢.
-In [[13-limit|13-limit]] [[Just_intonation|Just Intonation]], '''18/13''' is a low [[tritone|tritone]] measuring about 563.4¢. It represents the interval between the 13th and 18th overtones of the [[overtone_scales|harmonic series]]. The low tritone in [[17edo|17edo]] approximates 18/13 quite well, while 17edo's approximations of [[13/8|13/8]] and [[9/8|9/8]] are both a little sharp. The inversion of 18/13 is [[13/9|13/9]], a high tritone measuring about 636.6¢; the interval between these two tridecimal (13-based) tritones is 169/162, approximately 73.2¢.
+== See also ==
-Other just tritones include [[7/5|7/5]], [[10/7|10/7]], [[45/32|45/32]], [[64/45|64/45]], [[24/17|24/17]], [[17/12|17/12]], [[23/16|23/16]], [[32/23|32/23]], and, of course, infinitely many more intervals.
+* [[13/9]] – its [[octave complement]]
+* [[13/12]] – its [[fifth complement]]
+* [[Gallery of just intervals]]
-See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]      [[Category:13-limit]]
+[[Category:Tritone]]
-[[Category:15-limit]]
-[[Category:interval]]
-[[Category:just_interval]]
-[[Category:ratio]]
-[[Category:tritone]]