1152edo
| ← 1151edo | 1152edo | 1153edo → |
1152 equal divisions of the octave (abbreviated 1152edo or 1152ed2), also called 1152-tone equal temperament (1152tet) or 1152 equal temperament (1152et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1152 equal parts of about 1.04 ¢ each. Each step represents a frequency ratio of 21/1152, or the 1152nd root of 2.
1152edo is consistent in the 9-odd-limit, where it corrects the 576edo's mapping for 5. The equal temperament tempers out the ennealimma, [1 -27 18⟩, as well as [99 2 -44⟩, in the 5-limit, 2401/2400, 4375/4374, 250047/250000, 420175/419904, 40353607/40310784 (tritrizo), 78125000/78121827 (euzenius), as well as [94 -33 -24 5⟩ in the 7-limit. It supports the hemiennealimmal temperament and germanium temperament in the 11-limit despite not being consistent.
It is a strong 2.3.5.7.13.17.23 subgroup tuning, or alternatively a no-11, no-17, no-19 23-limit tuning. More so, if intervals containing 11, 17, and 19 are removed, 1152edo consistently represents the intervals of the 23-odd-limit and not just 23-prime-limit. A comma basis for the 2.3.5.7.13.17.23 subgroup is {3381/3380, 4375/4374, 4761/4760, 4914/4913, 8281/8280, 19136/19125}. It also tempers out the comma associating 70/69 to 1 step of 48edo.
The 1152deef val provides a tuning close to the POTE tuning of the stockhausenic temperament.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.000 | +0.128 | +0.145 | -0.076 | -0.276 | +0.097 | +0.253 | +0.404 | -0.149 | -0.411 | -0.244 |
| relative (%) | +0 | +12 | +14 | -7 | -27 | +9 | +24 | +39 | -14 | -39 | -23 | |
| Steps (reduced) |
1152 (0) |
1826 (674) |
2675 (371) |
3234 (930) |
3985 (529) |
4263 (807) |
4709 (101) |
4894 (286) |
5211 (603) |
5596 (988) |
5707 (1099) | |
Subsets and supersets
Since 1152 factors as 27 × 32, 1152edo has subset edos 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576.
1152edo is a highly factorable edo. Its abundancy index is around 1.87.