384edo
| ← 383edo | 384edo | 385edo → |
384 equal divisions of the octave (abbreviated 384edo or 384ed2), also called 384-tone equal temperament (384tet) or 384 equal temperament (384et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 384 equal parts of about 3.13 ¢ each. Each step represents a frequency ratio of 21/384, or the 384th root of 2.
Theory
384edo is consistent in the 7-odd-limit. The equal temperament tempers out the misty comma [26 -12 -3⟩, and the 5-limit tritriple comma [31 20 -27⟩ in the 5-limit, and 3136/3125, 5120/5103, 250047/250000, and the mistisma 458752/455625 in the 7-limit.
As a tuning standard
A step of 384edo is known as a pentamu (fifth MIDI-resolution unit, 5mu, 25 = 32 equal divisions of the 12edo semitone). The internal data structure of the 5mu requires one byte, with the first two bits reserved as flags, one to indicate the byte's status as data, and one to indicate the sign (+ or −) showing the direction of the pitch-bend up or down, and one other bit which is not used.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.00 | +1.17 | +1.19 | -0.08 | -1.32 | +0.10 | +1.29 | -0.64 | -0.15 | -1.45 | -1.29 |
| relative (%) | +0 | +37 | +38 | -2 | -42 | +3 | +41 | -20 | -5 | -46 | -41 | |
| Steps (reduced) |
384 (0) |
609 (225) |
892 (124) |
1078 (310) |
1328 (176) |
1421 (269) |
1570 (34) |
1631 (95) |
1737 (201) |
1865 (329) |
1902 (366) | |
Subsets and supersets
Since 384 factors into 27 × 3, 384edo has subset edos 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, and 192.
See also
- Equal multiplications of MIDI-resolution units