1166edo
| ← 1165edo | 1166edo | 1167edo → |
1166 equal divisions of the octave (abbreviated 1166edo or 1166ed2), also called 1166-tone equal temperament (1166tet) or 1166 equal temperament (1166et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1166 equal parts of about 1.03 ¢ each. Each step represents a frequency ratio of 21/1166, or the 1166th root of 2.
1166edo is consistent in the 9-odd-limit.
In the 5-limit, 1166edo naturally lends itself to interpretation as a superset of 22edo and 53edo. It inherits the mapping for 3/2 from 53edo, tempering out the 53rd-octave Mercator's comma, [-84 53⟩, as well as the 22nd-octave major arcana comma, [-193 154 -22⟩. In the 7-limit, it tempers out 2401/2400, 65625/65536, and [36 -50 15 3⟩, providing a tuning for the tertiaseptal temperament.
In higher limits, it is a strong 2.3.17.19.41.43 subgroup tuning. Alternatively, 2.3.7/5.13/11.17.19 is also a strong subgroup choice.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.000 | -0.068 | -0.379 | -0.387 | +0.312 | +0.296 | +0.019 | -0.086 | -0.487 | -0.418 | +0.419 |
| relative (%) | +0 | -7 | -37 | -38 | +30 | +29 | +2 | -8 | -47 | -41 | +41 | |
| Steps (reduced) |
1166 (0) |
1848 (682) |
2707 (375) |
3273 (941) |
4034 (536) |
4315 (817) |
4766 (102) |
4953 (289) |
5274 (610) |
5664 (1000) |
5777 (1113) | |
Subsets and supersets
1166edo factors as 2 × 11 × 53, with subset edos 1, 2, 11, 22, 53, 106, 583, of which 22edo and 53edo are particularly notable. See above.