# 1152edo

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 ← 1151edo 1152edo 1153edo →
Prime factorization 27 × 32
Step size 1.04167¢
Fifth 674\1152 (702.083¢) (→337\576)
Semitones (A1:m2) 110:86 (114.6¢ : 89.58¢)
Consistency limit 9
Distinct consistency limit 9

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

Approximation of prime harmonics in 1152edo
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 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.