1152edo

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← 1151edo1152edo1153edo →
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 1.042 ¢ 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 +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.