5/3: Difference between revisions

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In [[5-limit]] [[just intonation]], '''5/3''' is the '''just major sixth''', '''classic(al) major sixth''', or '''ptolemaic major sixth'''<ref>For reference, see [[5/4]]. </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.

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.

== Approximation ==

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

== See also ==

* [[6/5]] – its [[octave complement]]

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

* [[Ed5/3]]

* [[Gallery of just intervals]]

* [[ed5/3]]

== Notes ==

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[[Category:Sixth]]

[[Category:Major sixth]]

[[Category:Over-3]]

[[Category:Over-3 intervals]]

[[Category:Tritave-reduced harmonics]]

[[Category:Taxicab-2 intervals]]

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 {{Wikipedia|Major sixth}}
-In [[5-limit]] [[just intonation]], '''5/3''' is the '''just major sixth''', '''classic(al) major sixth''', or '''ptolemaic major sixth'''<ref>For reference, see [[5/4]]. </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.
+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.
 == 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]]
+* [[9/5]] – its [[twelfth complement]]
+* [[Ed5/3]]
 * [[Gallery of just intervals]]
-* [[ed5/3]]
 == Notes ==
@@ Line 23: / Line 25: @@
 [[Category:Sixth]]
 [[Category:Major sixth]]
-[[Category:Over-3]]
+[[Category:Over-3 intervals]]
 [[Category:Tritave-reduced harmonics]]
+[[Category:Taxicab-2 intervals]]