27/20
| Interval information |
classic acute fourth
[sound info]
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.
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 7 | 3\7 | 514.29 | -5.27 | -3.07 |
| 14 | 6\14 | 514.29 | -5.27 | -6.14 |
| 16 | 7\16 | 525.00 | +5.45 | +7.26 |
| 21 | 9\21 | 514.29 | -5.27 | -9.21 |
| 23 | 10\23 | 521.74 | +2.19 | +4.19 |
| 30 | 13\30 | 520.00 | +0.45 | +1.12 |
| 37 | 16\37 | 518.92 | -0.63 | -1.95 |
| 44 | 19\44 | 518.18 | -1.37 | -5.02 |
| 46 | 20\46 | 521.74 | +2.19 | +8.39 |
| 51 | 22\51 | 517.65 | -1.90 | -8.09 |
| 53 | 23\53 | 520.75 | +1.20 | +5.32 |
| 60 | 26\60 | 520.00 | +0.45 | +2.24 |
| 67 | 29\67 | 519.40 | -0.15 | -0.83 |
| 74 | 32\74 | 518.92 | -0.63 | -3.90 |
| 76 | 33\76 | 521.05 | +1.50 | +9.51 |
Trivia
This ratio is the difference between two common record speeds (45rpm and "33"rpm). As such, alterations by this interval often occur when a record is played at the wrong speed.