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 [[5/4]]. </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 | 5/3 has a more mellow sound than 27/16, owing to its simpler beating pattern as well as its smaller size. | ||
== Approximation == | == Approximation == | ||
Revision as of 09:09, 15 August 2023
| Interval information |
classic(al) major sixth,
ptolemaic major sixth
[sound info]
In 5-limit just intonation, 5/3 is the just major sixth, classic(al) major sixth, 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 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.