3776edo
| ← 3775edo | 3776edo | 3777edo → |
3776 equal divisions of the octave (abbreviated 3776edo or 3776ed2), also called 3776-tone equal temperament (3776tet) or 3776 equal temperament (3776et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 3776 equal parts of about 0.318 ¢ each. Each step represents a frequency ratio of 21/3776, or the 3776th root of 2.
Theory
3776edo is a good 2.3.11.13.19 subgroup system. It does not tune the 15-odd-limit consistently, though a reasonable represenation exists through the 19-limit patent val. There, it provides the optimal patent val for the oganesson temperament in the 7-, 11-, 13-, 17-, and the 19-limit.
It tempers out the quartisma in the 11-limit, and is a tuning for the rank-3 van gogh temperament.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.058 | +0.127 | +0.136 | +0.115 | +0.059 | +0.044 | -0.133 | -0.083 | -0.055 | -0.124 | +0.010 |
| relative (%) | +18 | +40 | +43 | +36 | +19 | +14 | -42 | -26 | -17 | -39 | +3 | |
| Steps (reduced) |
5985 (2209) |
8768 (1216) |
10601 (3049) |
11970 (642) |
13063 (1735) |
13973 (2645) |
14752 (3424) |
15434 (330) |
16040 (936) |
16585 (1481) |
17081 (1977) | |
Regular temperament properties
Rank-2 temperaments
| Periods per 8ve |
Generator (reduced) |
Cents (reduced) |
Associated ratio |
Temperaments |
|---|---|---|---|---|
| 118 | 1781\3776 (21\3776) |
565.995 (6.67) |
165/119 (?) |
Oganesson |