5/3: Difference between revisions

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{| ~~class~~=~~"wikitable"~~

{{Infobox Interval

|-

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

| Color name = y6, yo 6th

|-

| Sound = jid_5_3_pluck_adu_dr220.mp3

~~| | JI Glyph of 5/3~~

}}

|}

'''5/3'''

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.

|0 -~~1 1>~~

~~884~~.~~35871 cents~~

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

[[~~File:jid_5_3_pluck_adu_dr220.mp3~~]] [[~~:File:jid_5_3_pluck_adu_dr220~~.~~mp3~~|~~sound sample]]~~

== Approximation ==

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

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

== See also ==

* [[6/5]] – its [[octave complement]]

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

* [[Ed5/3]]

* [[Gallery of just intervals]]

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

== Notes ==

~~See:~~ [[~~Gallery_of_Just_Intervals|Gallery of Just Intervals~~]] [[Category:~~5-limit~~]]

[[Category:Sixth]]

[[Category:~~interval~~]]

[[Category:Major sixth]]

[[Category:~~just_interval~~]]

[[Category:Over-3 intervals]]

[[Category:~~ratio~~]]

[[Category:Tritave-reduced harmonics]]

[[Category:Taxicab-2 intervals]]

@@ Line 1: / Line 1: @@
-{| class="wikitable"
+{{Infobox Interval
-|-
+| Name = just major sixth, classic(al) major sixth, ptolemaic major sixth
-| | [[File:glyph_5_3.png|alt=glyph 5 3.png|111x113px|glyph 5 3.png]]
+| Color name = y6, yo 6th
-|-
+| Sound = jid_5_3_pluck_adu_dr220.mp3
-| | JI Glyph of 5/3
+}}
-|}
+{{Wikipedia|Major sixth}}
-'''5/3'''
+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.
-|0 -1 1&gt;
-.35871 cents
+/3 has a more mellow sound than 27/16, owing to its simpler beating pattern as well as its smaller size.
-[[File:jid_5_3_pluck_adu_dr220.mp3]] [[:File:jid_5_3_pluck_adu_dr220.mp3|sound sample]]
+== Approximation ==
+/3 is very accurately approximated by [[19edo]] (14\19), and hence the [[enneadecal]] temperament.
+{{Interval edo approximation|5/3}}
-In [[5-limit|5-limit]] [[Just_intonation|Just Intonation]], 5/3 is a major sixth of about 884.4¢. It represents the difference between the 5th and 3rd overtones of the [[OverToneSeries|harmonic series]], and appears in just chords such as 3:4:5 (a 2nd inversion major triad). Its inversion is [[6/5|6/5]], the 5-limit minor third. It differs from the Pythagorean major sixth of [[27/16|27/16]] (about 905.9¢) by the syntonic comma of [[81/80|81/80]] (about 21.5¢). This means that in systems which temper out the syntonic comma, such as [[12edo|12edo]] and [[Meantone|meantone]] systems, 5/3 and 27/16 are conflated.
+== See also ==
+* [[6/5]] – its [[octave complement]]
+* [[9/5]] – its [[twelfth complement]]
+* [[Ed5/3]]
+* [[Gallery of just intervals]]
-/3 has a more mellow sound than 27/16, owing to its relative smallness.
+== Notes ==
+<references/>
-See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]      [[Category:5-limit]]
+[[Category:Sixth]]
-[[Category:interval]]
+[[Category:Major sixth]]
-[[Category:just_interval]]
+[[Category:Over-3 intervals]]
-[[Category:ratio]]
+[[Category:Tritave-reduced harmonics]]
+[[Category:Taxicab-2 intervals]]