32/27
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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,
reduced subharmonic
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
| Interval information |
reduced subharmonic
(Shannon, [math]\sqrt{nd}[/math])
[sound info]
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.