# 1152edo

← 1151edo | 1152edo | 1153edo → |

^{7}× 3^{2}**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 2^{1/1152}, 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 (%) | +0.0 | +12.3 | +13.9 | -7.3 | -26.5 | +9.3 | +24.3 | +38.8 | -14.3 | -39.4 | -23.4 | |

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 2^{7} × 3^{2}, 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.