# 5/3

 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 $\text{M6}^{5}$ 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, $\sqrt{nd}$) ~3.90657 bits https://en.xen.wiki/w/File:Jid_5_3_pluck_adu_dr220.mp3[sound info] open this interval in xen-calc
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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.