13/12: Difference between revisions

Line 1:

{{Infobox Interval

~~| Icon =~~

| Ratio = 13/12

| Monzo = -2 -1 0 0 0 1

Line 10:

Line 9:

}}

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¢).

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 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¢).

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.

Line 21:

Line 20:

[[Category:13-limit]]

[[Category:~~Interval]]~~

[[Category:Second]]

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

~~[[Category:Ratio~~]]

[[Category:Neutral second]]

~~[[Category:Second]]~~

[[Category:Superparticular]]

[[Category:Pages with internal sound examples]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
 | Ratio = 13/12
 | Monzo = -2 -1 0 0 0 1
@@ Line 10: / Line 9: @@
 }}
-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¢).
+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 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¢).
 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.
@@ Line 21: / Line 20: @@
 [[Category:13-limit]]
-[[Category:Interval]]
+[[Category:Second]]
-[[Category:Just interval]]
-[[Category:Ratio]]
 [[Category:Neutral second]]
-[[Category:Second]]
 [[Category:Superparticular]]
 [[Category:Pages with internal sound examples]]