6/5
| Interval information |
reduced
[sound info]
In 5-limit just intonation, 6/5 is the classic or just minor third, measuring about 315.6¢. It is sharp of the Pythagorean minor third of 32/27 (about 294.1¢) as well as the 300¢ minor third of 4edo, 12edo and all other 4n-edos. It arises in the harmonic series between the 5th and 6th harmonics and appears in the 5-limit otonal triad of 4:5:6. A 5-limit minor triad in just intonation can be written 10:12:15, with 6/5 falling between 10 and 12, 5/4 falling between 12 and 15, and 3/2 falling between 10 and 15.
In higher-limit JI, 6/5 is only one of many minor thirds. A popular one in the 7-limit is 7/6 (about 266.9¢), the septimal subminor third, which is 36/35 (about 48.8¢) flat of 6/5. Another in the 13-limit is 13/11 (about 289.2¢), which is 66/65 (about 26.4¢) flat of 6/5. Both of these are more complex intervals than 6/5 and have their own character to them.
Approximation by EDOs
It is very accurately approximated by 19edo (5\19), and hence the enneadecal temperament.
The following EDOs (up to 200) contain good approximations[1] of the interval 6/5. Errors are given by magnitude, the arrows in the table show if the EDO representation is sharp (↑) or flat (↓).
| EDO | deg\edo | Absolute error (¢) |
Relative error (r¢) |
↕ | Equally acceptable multiples [2] |
|---|---|---|---|---|---|
| 15 | 4\15 | 4.3587 | 5.4484 | ↑ | |
| 19 | 5\19 | 0.1482 | 0.2346 | ↑ |
10\38, 15\57, 20\76, 25\95, 30\114, 35\133, 40\152, 45\171, 50\190 |
| 23 | 6\23 | 2.5978 | 4.9791 | ↓ | |
| 34 | 9\34 | 2.0058 | 5.683 | ↑ | |
| 42 | 11\42 | 1.3556 | 4.7445 | ↓ | |
| 53 | 14\53 | 1.3398 | 5.9176 | ↑ | |
| 61 | 16\61 | 0.8872 | 4.5099 | ↓ | |
| 72 | 19\72 | 1.0254 | 6.1523 | ↑ | |
| 80 | 21\80 | 0.6413 | 4.2752 | ↓ | |
| 91 | 24\91 | 0.8422 | 6.3869 | ↑ | |
| 99 | 26\99 | 0.4898 | 4.0406 | ↓ | |
| 110 | 29\110 | 0.7223 | 6.6215 | ↑ | |
| 118 | 31\118 | 0.387 | 3.806 | ↓ | |
| 129 | 34\129 | 0.6378 | 6.8562 | ↑ | |
| 137 | 36\137 | 0.3128 | 3.5714 | ↓ | |
| 156 | 41\156 | 0.2567 | 3.3367 | ↓ | |
| 175 | 46\175 | 0.2127 | 3.1021 | ↓ | |
| 194 | 51\194 | 0.1774 | 2.8675 | ↓ |
See also
- 5/3 – its octave complement
- 5/4 – its fifth complement
- 10/9 – its fourth complement
- Gallery of just intervals
- List of superparticular intervals
- File:Ji-6-5-csound-foscil-220hz.mp3 – another sound example