13/12: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Name = (lesser) tridecimal neutral second

~~| Ratio = 13/12~~

~~| Monzo = -2 -1 0 0 0 1~~

~~| Cents = 138.57266~~

| Name = ~~tredecimal~~ neutral second

| Color name = 3o2, tho 2nd

| Sound = jid_13_12_pluck_adu_dr220.mp3

}}

In [[13-limit]] [[Just Intonation]], '''13/12''' is a '''neutral second''' of about 138.6¢. It is a [[superparticular]] interval, as it is found in the harmonic series between the 13th and the 12th overtone (between [[13/8]] and [[3/2]] in the octave). It is flat of the [[11-limit]] lesser neutral second of [[12/11]] by [[144/143]] (about 12.1¢), and sharp of the 13-limit large semitone of [[14/13]] by [[169/168]] (about 10.3¢).

~~The neutral second in~~ [[~~17edo~~]] is about ~~141.2¢, about 2~~.6¢ ~~sharp of 13/12~~. ~~Thus~~, ~~if 10\17~~ (~~ten degrees of 17edo) is taken to approximate~~ 3/2 ~~and~~ 12~~\17 taken to approximate 13~~/8, ~~you can generate a~~ 13-limit ~~harmonic triad that approximates an 8:12:13 chord with a good~~ 13/12.

In [[13-limit]] [[just intonation]], '''13/12''' is the '''(lesser) tridecimal neutral second''' of about 138.6¢. It is a [[superparticular]] interval, as it is found in the harmonic series between the 13th and the 12th harmonics (between [[13/8]] and [[3/2]] in the octave). It is flat of the [[11-limit]] lesser neutral second of [[12/11]] by [[144/143]] (about 12.1¢), and sharp of the 13-limit large semitone of [[14/13]] by [[169/168]] (about 10.3¢).

~~:''See also [[Gallery of Just Intervals]]''~~

== Temperaments ==

[[~~Category:~~13~~-limit~~]]

== Approximation ==

[[~~Category:Interval~~]]

It is approximated to within about 0.11 [[cents]] by the 3-step interval of [[26edo]].

[[Category:~~Just interval~~]]

== See also ==

* [[24/13]] – its [[octave complement]]

* [[18/13]] – its [[fifth complement]]

* [[Gallery of just intervals]]

* [[List of superparticular intervals]]

[[Category:Second]]

[[Category:Neutral second]]

~~[[Category:Ratio]]~~

~~[[Category:Second]]~~

~~[[Category:Superparticular]]~~

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
+| Name = (lesser) tridecimal neutral second
-| Ratio = 13/12
-| Monzo = -2 -1 0 0 0 1
-| Cents = 138.57266
-| Name = tredecimal neutral second
 | Color name = 3o2, tho 2nd
 | Sound = jid_13_12_pluck_adu_dr220.mp3
 }}
-In [[13-limit]] [[Just Intonation]], '''13/12''' is a '''neutral second''' of about 138.6¢. It is a [[superparticular]] interval, as it is found in the harmonic series between the 13th and the 12th overtone (between [[13/8]] and [[3/2]] in the octave). It is flat of the [[11-limit]] lesser neutral second of [[12/11]] by [[144/143]] (about 12.1¢), and sharp of the 13-limit large semitone of [[14/13]] by [[169/168]] (about 10.3¢).
-The neutral second in [[17edo]] is about 141.2¢, about 2.6¢ sharp of 13/12. Thus, if 10\17 (ten degrees of 17edo) is taken to approximate 3/2 and 12\17 taken to approximate 13/8, you can generate a 13-limit harmonic triad that approximates an 8:12:13 chord with a good 13/12.
+In [[13-limit]] [[just intonation]], '''13/12''' is the '''(lesser) tridecimal neutral second''' of about 138.6¢. It is a [[superparticular]] interval, as it is found in the harmonic series between the 13th and the 12th harmonics (between [[13/8]] and [[3/2]] in the octave). It is flat of the [[11-limit]] lesser neutral second of [[12/11]] by [[144/143]] (about 12.1¢), and sharp of the 13-limit large semitone of [[14/13]] by [[169/168]] (about 10.3¢).
-:''See also [[Gallery of Just Intervals]]''
+== Temperaments ==
+{{Todo|expand|inline=1}}
-[[Category:13-limit]]
+== Approximation ==
-[[Category:Interval]]
+It is approximated to within about 0.11 [[cents]] by the 3-step interval of [[26edo]].
-[[Category:Just interval]]
+== See also ==
+* [[24/13]] – its [[octave complement]]
+* [[18/13]] – its [[fifth complement]]
+* [[Gallery of just intervals]]
+* [[List of superparticular intervals]]
+[[Category:Second]]
 [[Category:Neutral second]]
-[[Category:Ratio]]
-[[Category:Second]]
-[[Category:Superparticular]]