27/20
| Ratio | 27/20 |
| Factorization | 2-2 × 33 × 5-1 |
| Monzo | [-2 3 -1⟩ |
| Size in cents | 519.55129¢ |
| Names | wolf fourth, classic acute fourth |
| Color name | g4, gu 4th |
| FJS name | [math]\text{P4}_{5}[/math] |
| Special properties | reduced |
| Tenney height (log2 nd) | 9.07682 |
| Weil height (log2 max(n, d)) | 9.50978 |
| Wilson height (sopfr (nd)) | 18 |
| Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~4.51694 bits |
[sound info] | |
| open this interval in xen-calc | |
In 5-limit just intonation, 27/20, the classic acute fourth, is an interval measuring about 519.6 ¢. It differs from the 4/3 perfect fourth by 81/80 (about 21.5 ¢), the syntonic comma. It arises naturally in JI as (for instance) the difference between a 5-limit major third and a stack of five 3/2 perfect fifths, or as the interval between 10/9 and 3/2. In 12edo and meantone systems, this interval would be no different from 4/3, as the syntonic comma is tempered out. 27/20 has been described as a "wolf" interval, implying that it "howls", as compared to simpler intervals within the 5-limit such as 5/4 and 9/8. Although in a 5-limit context it is traditionally avoided, it can be an essential interval in a harmonic context of higher complexity, where it may be admired for its bright and active character and its distinctness from 4/3.