32/27

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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]\text{m3}[/math]
Special properties reduced
Tenney height (log2 nd) 9.75489
Weil height (log2 max(n, d)) 10
Wilson height (sopfr (nd)) 19
Harmonic entropy
(Shannon, [math]\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, whos best approximation of a perfect 5th is the 800 cent interval that wraps around to the octave again after only three iterations. If it is used as a generator instead, it produces Gariberttet.

See also