32/27

Interval information

Ratio	32/27
Factorization	25 × 3-3
Monzo	[5 -3⟩
Size in cents	294.135¢
Name	Pythagorean minor third
Color name	w3, wa 3rd
FJS name	[math]\displaystyle{ \text{m3} }[/math]
Special properties	reduced, reduced subharmonic
Tenney height (log2 nd)	9.75489
Weil height (log2 max(n, d))	10
Wilson height (sopfr(nd))	19
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~4.22969 bits
[sound info]
Open this interval in xen-calc

The Pythagorean minor third of 32/27 is the interval between 9/8 and 4/3 which arises naturally in 3-limit just intonation. Compared to the more typical 6/5- with which it is conflated in meantone- this interval is more dissonant, with a harmonic entropy level roughly on par with that of 9/8.

It is 352/351 sharp of 13/11, and tempering 352/351 out equates it with 13/11 and leads to minthmic chords.

Temperaments

32/27 is treated as a comma in edos 3 & 6, where the best approximation of a perfect 5th is the 800 cent interval that wraps around to the octave again after only three iterations. Temperaments it can be interpreted as if used as a generator include Kleiboh or Gariberttet.

See also

• 27/16 – its octave complement
• 81/64 – its fifth complement
• 9/8 – its fourth complement
• Gallery of just intervals
• Pythagorean tuning