13/12: Difference between revisions

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

{{Infobox Interval

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

| Icon =

| 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¢).

~~138~~.~~57266 cents~~

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.

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

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

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¢).

[[Category:13-limit]]

[[Category:Interval]]

~~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.

[[Category:Just interval]]

[[Category:Neutral 2nd]]

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

[[Category:Neutral second]]

[[Category:~~interval~~]]

[[Category:Ratio]]

[[Category:~~just_interval~~]]

[[Category:Second]]

[[Category:~~neutral_2nd~~]]

[[Category:Superparticular]]

[[Category:~~ratio~~]]

[[Category:~~second~~]]

@@ Line 1: / Line 1: @@
-'''13/12'''
+{{Infobox Interval
-|-2 -1 0 0 0 1&gt;
+| Icon =
+| 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¢).
-.57266 cents
+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.
-[[File:jid_13_12_pluck_adu_dr220.mp3]] [[:File:jid_13_12_pluck_adu_dr220.mp3|sound sample]]
+:''See also [[Gallery of Just Intervals]]''
-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¢).
+[[Category:13-limit]]
+[[Category:Interval]]
-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.
+[[Category:Just interval]]
+[[Category:Neutral 2nd]]
-See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]      [[Category:13-limit]]
+[[Category:Neutral second]]
-[[Category:interval]]
+[[Category:Ratio]]
-[[Category:just_interval]]
+[[Category:Second]]
-[[Category:neutral_2nd]]
+[[Category:Superparticular]]
-[[Category:ratio]]
-[[Category:second]]