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 | [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{n\cdot d}[/math]) |
~4.38602 bits |
[sound info] | |
| open this interval in xen-calc | |
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.