5/3: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = classic | | Name = just major sixth, classic(al) major sixth, ptolemaic major sixth | ||
| Color name = y6, yo 6th | | Color name = y6, yo 6th | ||
| Sound = jid_5_3_pluck_adu_dr220.mp3 | | Sound = jid_5_3_pluck_adu_dr220.mp3 | ||
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{{Wikipedia|Major sixth}} | {{Wikipedia|Major sixth}} | ||
In [[5-limit]] [[just intonation]], '''5/3''' is | In [[5-limit]] [[just intonation]], '''5/3''' is the '''just''', '''classic(al)''', 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. | ||
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 relative smallness. | ||
== Approximation == | == Approximation == | ||
5/3 is very accurately approximated by [[19edo]] (14\19), and hence the [[enneadecal]] temperament. | |||
== See also == | == See also == | ||
* [[6/5]] – its [[octave complement]] | * [[6/5]] – its [[octave complement]] | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
== Notes == | |||
<references/> | |||
[[Category:Sixth]] | [[Category:Sixth]] | ||
[[Category:Major sixth]] | [[Category:Major sixth]] | ||
[[Category:Over-3]] | [[Category:Over-3]] | ||
Revision as of 12:26, 12 January 2023
| Interval information |
classic(al) major sixth,
ptolemaic major sixth
[sound info]
In 5-limit just intonation, 5/3 is the just, classic(al), or ptolemaic major sixth[1] of about 884.4¢. It represents the difference between the 5th and 3rd harmonics, 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.
Approximation
5/3 is very accurately approximated by 19edo (14\19), and hence the enneadecal temperament.