11/8
In 11-limit just intonation, 11/8 is an undecimal superfourth of about 551.3¢. Falling about halfway between 12edo's perfect fourth and tritone, it is very xenharmonic. It is the simplest superfourth in JI. As an octave-reduced overtone, it is a basis of consonance in 11-limit JI, alongside the lower odd numbers 9, 7, 5 and 3. It can be found in harmonic series chords such as 4:5:6:7:8:9:10:11:12, sitting somewhere between the much stronger and more familiar consonances of 10 (prime 5) and 12 (prime 3). It is very well-represented in 24edo, making that system especially good for approximations of JI chords involving primes 3 and 11 such as 8:9:11:12.
| Interval information |
major fourth
reduced harmonic
[sound info]
Approximations by EDOs
Following EDOs (up to 200) contain good approximations[1] of the interval 11/8. 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] |
|---|---|---|---|---|---|
| 11 | 5\11 | 5.8634 | 5.3748 | ↓ | |
| 13 | 6\13 | 2.5282 | 2.7389 | ↑ | 12\26 |
| 24 | 11\24 | 1.3179 | 2.6359 | ↓ | 22\48 |
| 37 | 17\37 | 0.0334 | 0.1030 | ↑ | 34\74, 51\111, 68\148, 85\185 |
| 50 | 23\50 | 0.6821 | 2.8419 | ↑ | 46\100 |
| 61 | 28\61 | 0.4983 | 2.5329 | ↓ | 56\122 |
| 63 | 29\63 | 1.0630 | 5.5808 | ↑ | |
| 85 | 39\85 | 0.7297 | 5.1688 | ↓ | |
| 87 | 40\87 | 0.4062 | 2.9449 | ↑ | 80\174 |
| 98 | 45\98 | 0.2975 | 2.4299 | ↓ | 90\196 |
| 124 | 57\124 | 0.2950 | 3.0479 | ↑ | |
| 135 | 62\135 | 0.2068 | 2.3269 | ↓ | |
| 137 | 63\137 | 0.5069 | 5.7868 | ↑ | |
| 159 | 73\159 | 0.3745 | 4.9627 | ↓ | |
| 161 | 74\161 | 0.2349 | 3.1509 | ↑ | |
| 172 | 79\172 | 0.1552 | 2.2238 | ↓ | |
| 198 | 91\198 | 0.1972 | 3.2540 | ↑ |