5/3

Interval information

Ratio	5/3
Factorization	3-1 × 5
Monzo	[0 -1 1⟩
Size in cents	884.3587¢
Names	just major sixth, classic(al) major sixth, ptolemaic 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]
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Major sixth

In 5-limit just intonation, 5/3 is the just major sixth, classic(al) major sixth, or ptolemaic major sixth 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

• 6/5 – its octave complement
• 9/5 – its twelfth complement
• Gallery of just intervals
• ed5/3