1053edo

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← 1052edo1053edo1054edo →
Prime factorization 34 × 13
Step size 1.1396¢
Fifth 616\1053 (701.994¢)
Semitones (A1:m2) 100:79 (114¢ : 90.03¢)
Consistency limit 11
Distinct consistency limit 11

1053 equal divisions of the octave (abbreviated 1053edo), or 1053-tone equal temperament (1053tet), 1053 equal temperament (1053et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1053 equal parts of about 1.14 ¢ each. Each step of 1053edo represents a frequency ratio of 21/1053, or the 1053rd root of 2.

1053edo is consistent in the 11-odd-limit. It is a very strong 5-limit tuning where it tempers out [1 -27 18 (ennealimma), [91 -12 -31 (astro comma), and [92 -39 -13 (aluminium comma). It supports and gives a good tuning for the quadraennealimmal temperament, as well as the 27th-octave trinealimmal.

Prime harmonics

Approximation of prime harmonics in 1053edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error absolute (¢) +0.000 +0.039 +0.011 -0.165 +0.249 +0.498 -0.112 -0.077 -0.354 -0.517 +0.264
relative (%) +0 +3 +1 -14 +22 +44 -10 -7 -31 -45 +23
Steps
(reduced)
1053
(0)
1669
(616)
2445
(339)
2956
(850)
3643
(484)
3897
(738)
4304
(92)
4473
(261)
4763
(551)
5115
(903)
5217
(1005)

Subsets and supersets

Since 1053 factors as 34 × 13, 1053edo has subset edos 3, 9, 13, 27, 39, 81, 117, 351.