5/3

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Interval information
Ratio 5/3
Factorization 3-1 × 5
Monzo [0 -1 1
Size in cents 884.35871¢
Names just major sixth,
classic(al) major sixth,
ptolemaic major sixth
Color name y6, yo 6th
FJS name [math]\text{M6}^{5}[/math]
Special properties reduced
Tenney height (log2 nd) 3.90689
Weil height (log2 max(n, d)) 4.64386
Wilson height (sopfr(nd)) 8
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~3.90657 bits

[sound info]
open this interval in xen-calc
English Wikipedia has an article on:

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.

See also

Notes

  1. For reference, see 5-limit.