3920edo
| ← 3919edo | 3920edo | 3921edo → |
3920 equal divisions of the octave (abbreviated 3920edo or 3920ed2), also called 3920-tone equal temperament (3920tet) or 3920 equal temperament (3920et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 3920 equal parts of about 0.306 ¢ each. Each step represents a frequency ratio of 21/3920, or the 3920th root of 2.
3920edo is consistent in the 21-odd-limit.
It is a tuning for a number of fractional-octave temperaments, such as barium, which identifies 81/80 with 1/56th of the octave. It also tunes the 80th-octave temperaments tetraicosic and octodeca, for both of which it provides the optimal patent val upwards to the 19-limit.
Besides that, it is a tuning for the 5-limit gross temperament and the laquinzo-aquadquadgu temperament, tempering out [-7 19 -16 5⟩ = 19534128475869/19531250000000.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.016 | +0.013 | +0.052 | +0.009 | +0.085 | +0.045 | +0.038 | -0.111 | -0.087 | -0.138 |
| Relative (%) | +0.0 | -5.3 | +4.2 | +16.9 | +2.8 | +27.6 | +14.6 | +12.4 | -36.3 | -28.6 | -45.0 | |
| Steps (reduced) |
3920 (0) |
6213 (2293) |
9102 (1262) |
11005 (3165) |
13561 (1801) |
14506 (2746) |
16023 (343) |
16652 (972) |
17732 (2052) |
19043 (3363) |
19420 (3740) | |
Subsets and supersets
3920edo has subset edos 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 49, 56, 70, 80, 98, 112, 140, 196, 245, 280, 392, 490, 560, 784, 980, 1960.