5/3: Difference between revisions

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| Monzo = 0 -1 1
| Monzo = 0 -1 1
| Cents = 884.35871
| Cents = 884.35871
| Name = major sixth
| Name = classic major sixth
| Color name = y6, yo 6th
| FJS name = M6<sup>5</sup>
| Sound = jid_5_3_pluck_adu_dr220.mp3
| Sound = jid_5_3_pluck_adu_dr220.mp3
| Color name = y6, yo 6th
}}
}}


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 [[OverToneSeries|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 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.


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.


See: [[Gallery of Just Intervals]]
== See also ==
* [[6/5]] – its [[octave complement]]
* [[Gallery of Just Intervals]]
* [[Wikipedia:Major sixth|Major sixth - Wikipedia]]


[[Category:5-limit]]
[[Category:5-limit]]
[[Category:interval]]
[[Category:Interval]]
[[Category:just_interval]]
[[Category:Just interval]]
[[Category:ratio]]
[[Category:Ratio]]
[[Category:Sixth]]
[[Category:Sixth]]
[[Category:Major sixth]]
[[Category:Over-3]]
[[Category:Over-3]]

Revision as of 11:35, 19 September 2020

Interval information
Ratio 5/3
Factorization 3-1 × 5
Monzo [0 -1 1
Size in cents 884.3587¢
Name classic major sixth
Color name y6, yo 6th
FJS name [math]\displaystyle{ \text{M6}^{5} }[/math]
Special properties reduced
Tenney norm (log2 nd) 3.90689
Weil norm (log2 max(n, d)) 4.64386
Wilson norm (sopfr(nd)) 8

[sound info]
Open this interval in xen-calc

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.

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

See also