5/3: Difference between revisions

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{{Infobox Interval

~~| Ratio = 5/3~~

| Name = just major sixth, classic(al) major sixth, ptolemaic major sixth

~~| Monzo = 0 -1 1~~

~~| Cents = 884.35871~~

| Name = classic major sixth

| Color name = y6, yo 6th

~~| FJS name = M6<sup>5</sup>~~

| Sound = jid_5_3_pluck_adu_dr220.mp3

}}

In [[5-limit]] [[~~Just Intonation~~]], '''5/3''' is a '''major sixth''' of about 884.4¢. It represents the difference between the 5th and 3rd ~~overtones of the~~ [[harmonic ~~series~~]], and appears in just chords such as 3:4:5 (a 2nd inversion major triad). Its inversion is [[6/5]], the 5-limit minor third. It differs from the Pythagorean major sixth of [[27/16]] (about 905.9¢) by the syntonic comma of [[81/80]] (about 21.5¢). This means that in systems which temper out the syntonic comma, such as [[12edo]] and [[meantone]] systems, 5/3 and [[27/16]] are conflated.

In [[5-limit]] [[just intonation]], '''5/3''' is the '''just major sixth''', '''classic(al) major sixth''', or '''ptolemaic major sixth'''<ref>For reference, see [[5-limit]]. </ref> of about 884.4¢. It represents the difference between the 5th and 3rd [[harmonic]]s, and appears in just chords such as 3:4:5 (a 2nd inversion major triad). Its inversion is [[6/5]], the 5-limit minor third. It differs from the Pythagorean major sixth of [[27/16]] (about 905.9¢) by the syntonic comma of [[81/80]] (about 21.5¢). This means that in systems which temper out the syntonic comma, such as [[12edo]] and [[meantone]] systems, 5/3 and [[27/16]] are conflated.

5/3 has a more mellow sound than 27/16, owing to its ~~relative smallness~~.

5/3 has a more mellow sound than 27/16, owing to its simpler beating pattern as well as its smaller size.

It is very accurately approximated by [[19edo]] (14\19), and hence the [[enneadecal]] temperament.

== Approximation ==

5/3 is very accurately approximated by [[19edo]] (14\19), and hence the [[enneadecal]] temperament.

== See also ==

* [[6/5]] – its [[octave complement]]

* [[~~Gallery of Just Intervals~~]]

* [[9/5]] – its [[twelfth complement]]

* [[~~Wikipedia: Major sixth~~]]

* [[Ed5/3]]

* [[Gallery of just intervals]]

== Notes ==

~~[[Category:5-limit]]~~

~~[[Category:Interval]]~~

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

~~[[Category:Ratio]]~~

[[Category:Sixth]]

[[Category:Major sixth]]

[[Category:Over-3]]

[[Category:Over-3 intervals]]

[[Category:Tritave-reduced harmonics]]

[[Category:Taxicab-2 intervals]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Ratio = 5/3
+| Name = just major sixth, classic(al) major sixth, ptolemaic major sixth
-| Monzo = 0 -1 1
-| Cents = 884.35871
-| Name = classic major sixth
 | Color name = y6, yo 6th
-| FJS name = M6<sup>5</sup>
 | Sound = jid_5_3_pluck_adu_dr220.mp3
 }}
+{{Wikipedia|Major sixth}}
-In [[5-limit]] [[Just Intonation]], '''5/3''' is a '''major sixth''' of about 884.4¢. It represents the difference between the 5th and 3rd overtones of the [[harmonic series]], and appears in just chords such as 3:4:5 (a 2nd inversion major triad). Its inversion is [[6/5]], the 5-limit minor third. It differs from the Pythagorean major sixth of [[27/16]] (about 905.9¢) by the syntonic comma of [[81/80]] (about 21.5¢). This means that in systems which temper out the syntonic comma, such as [[12edo]] and [[meantone]] systems, 5/3 and [[27/16]] are conflated.
+In [[5-limit]] [[just intonation]], '''5/3''' is the '''just major sixth''', '''classic(al) major sixth''', or '''ptolemaic major sixth'''<ref>For reference, see [[5-limit]]. </ref> of about 884.4¢. It represents the difference between the 5th and 3rd [[harmonic]]s, and appears in just chords such as 3:4:5 (a 2nd inversion major triad). Its inversion is [[6/5]], the 5-limit minor third. It differs from the Pythagorean major sixth of [[27/16]] (about 905.9¢) by the syntonic comma of [[81/80]] (about 21.5¢). This means that in systems which temper out the syntonic comma, such as [[12edo]] and [[meantone]] systems, 5/3 and [[27/16]] are conflated.
-/3 has a more mellow sound than 27/16, owing to its relative smallness.
+/3 has a more mellow sound than 27/16, owing to its simpler beating pattern as well as its smaller size.
-It is very accurately approximated by [[19edo]] (14\19), and hence the [[enneadecal]] temperament.
+== Approximation ==
+/3 is very accurately approximated by [[19edo]] (14\19), and hence the [[enneadecal]] temperament.
+{{Interval edo approximation|5/3}}
 == See also ==
 * [[6/5]] – its [[octave complement]]
-* [[Gallery of Just Intervals]]
+* [[9/5]] – its [[twelfth complement]]
-* [[Wikipedia: Major sixth]]
+* [[Ed5/3]]
+* [[Gallery of just intervals]]
+== Notes ==
+<references/>
-[[Category:5-limit]]
-[[Category:Interval]]
-[[Category:Just interval]]
-[[Category:Ratio]]
 [[Category:Sixth]]
 [[Category:Major sixth]]
-[[Category:Over-3]]
+[[Category:Over-3 intervals]]
+[[Category:Tritave-reduced harmonics]]
+[[Category:Taxicab-2 intervals]]