32/27
Jump to navigation
Jump to search
| 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 | |
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.