5/3: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Undo revision 66326 by Xenwolf (talk)
Tag: Undo
m Name
Line 3: Line 3:
| Monzo = 0 -1 1
| Monzo = 0 -1 1
| Cents = 884.35871
| Cents = 884.35871
| Name = classic major sixth
| Name = classic/just major sixth
| Color name = y6, yo 6th
| Color name = y6, yo 6th
| FJS name = M6<sup>5</sup>
| FJS name = M6<sup>5</sup>
Line 13: Line 13:
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 ==
It is very accurately approximated by [[19edo]] (14\19), and hence the [[enneadecal]] temperament.  
It 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]]
* [[Wikipedia: Major sixth]]
* [[Wikipedia: Major sixth]]



Revision as of 13:47, 9 September 2021

Interval information
Ratio 5/3
Factorization 3-1 × 5
Monzo [0 -1 1
Size in cents 884.3587¢
Name classic/just 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.

Approximation

It is very accurately approximated by 19edo (14\19), and hence the enneadecal temperament.

See also