32/27
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Ratio | 32/27 |
Factorization | 2^{5} × 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 (log_{2} nd) | 9.75489 |
Weil height (log_{2} 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.