13/12: Difference between revisions

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~~'''13/12'''~~

{{Infobox Interval

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

| Name = (lesser) tridecimal neutral second

| Color name = 3o2, tho 2nd

| Sound = jid_13_12_pluck_adu_dr220.mp3

}}

138.~~57266 cents~~

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¢).

[[~~File:jid_13_12_pluck_adu_dr220.mp3~~]] [[~~:File:jid_13_12_pluck_adu_dr220~~.~~mp3~~|~~sound sample]]~~

== Approximation ==

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

{{Interval edo approximation|{{PAGENAME}}}}

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

== Temperaments ==

13/12 can be used to generate [[bleu]] temperament in the 2.3.7.11.13 subgroup, mapping [[3/2]] to +5 generators, [[7/4]] to +7 generators, [[11/8]] to +4 generators, and [[13/8]] to +6 generators.

~~The neutral second in~~ [[~~17edo|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~~.

A slightly sharp 13/12 generates [[glacier]] temperament, which equates 5 13/12's to 3/2 like bleu. This temperament has an extension to the 2.3.7.11.13.23.29 subgroup which is more complex but much more accurate than bleu.

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

== See also ==

[[~~Category:interval~~]]

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

[[~~Category:just_interval~~]]

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

[[~~Category:neutral_2nd~~]]

* [[Gallery of just intervals]]

[[Category:~~ratio~~]]

* [[List of superparticular intervals]]

[[Category:second]]

[[Category:Second]]

[[Category:Neutral second]]

@@ Line 1: / Line 1: @@
-'''13/12'''
+{{Infobox Interval
-|-2 -1 0 0 0 1&gt;
+| Name = (lesser) tridecimal neutral second
+| Color name = 3o2, tho 2nd
+| Sound = jid_13_12_pluck_adu_dr220.mp3
+}}
-.57266 cents
+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¢).
-[[File:jid_13_12_pluck_adu_dr220.mp3]] [[:File:jid_13_12_pluck_adu_dr220.mp3|sound sample]]
+== Approximation ==
+It is approximated to within about 0.11 [[cents]] by the 3-step interval of [[26edo]].
+{{Interval edo approximation|{{PAGENAME}}}}
-In [[13-limit|13-limit]] [[Just_intonation|Just Intonation]], 13/12 is a neutral second of about 138.6¢. It is a [[superparticular|superparticular]] interval, as it is found in the harmonic series between the 13th and the 12th overtone (between [[13/8|13/8]] and [[3/2|3/2]] in the octave). It is flat of the [[11-limit|11-limit]] lesser neutral second of [[12/11|12/11]] by [[144/143|144/143]] (about 12.1¢), and sharp of the 13-limit large semitone of [[14/13|14/13]] by [[169/168|169/168]] (about 10.3¢).
+== Temperaments ==
+/12 can be used to generate [[bleu]] temperament in the 2.3.7.11.13 subgroup, mapping [[3/2]] to +5 generators, [[7/4]] to +7 generators, [[11/8]] to +4 generators, and [[13/8]] to +6 generators.
-The neutral second in [[17edo|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.
+A slightly sharp 13/12 generates [[glacier]] temperament, which equates 5 13/12's to 3/2 like bleu. This temperament has an extension to the 2.3.7.11.13.23.29 subgroup which is more complex but much more accurate than bleu.
-See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]      [[Category:13-limit]]
+== See also ==
-[[Category:interval]]
+* [[24/13]] – its [[octave complement]]
-[[Category:just_interval]]
+* [[18/13]] – its [[fifth complement]]
-[[Category:neutral_2nd]]
+* [[Gallery of just intervals]]
-[[Category:ratio]]
+* [[List of superparticular intervals]]
-[[Category:second]]
+[[Category:Second]]
+[[Category:Neutral second]]