# 1236edo

 ← 1235edo 1236edo 1237edo →
Prime factorization 22 × 3 × 103
Step size 0.970874¢
Fifth 723\1236 (701.942¢) (→241\412)
Semitones (A1:m2) 117:93 (113.6¢ : 90.29¢)
Consistency limit 17
Distinct consistency limit 17
Special properties

1236 equal divisions of the octave (abbreviated 1236edo or 1236ed2), also called 1236-tone equal temperament (1236tet) or 1236 equal temperament (1236et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1236 equal parts of about 0.971 ¢ each. Each step represents a frequency ratio of 21/1236, or the 1236th root of 2.

1236edo is a zeta peak edo, though not zeta integral nor zeta gap. It is a strong 17-limit system and distinctly consistent through the 17-odd-limit, with a 17-limit comma basis of {2601/2600, 4096/4095, 5832/5831, 6656/6655, 9801/9800, 105644/105625}.

### Prime harmonics

Approximation of prime harmonics in 1236edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 -0.013 +0.094 +0.106 +0.138 +0.249 -0.101 -0.426 -0.119 -0.451 -0.375
Relative (%) +0.0 -1.4 +9.7 +10.9 +14.3 +25.7 -10.4 -43.8 -12.3 -46.5 -38.7
Steps
(reduced)
1236
(0)
1959
(723)
2870
(398)
3470
(998)
4276
(568)
4574
(866)
5052
(108)
5250
(306)
5591
(647)
6004
(1060)
6123
(1179)

### Subsets and supersets

Since 1236 factors into 22 × 3 × 103, 1236edo has subset edos 2, 3, 6, 12, 103, 206, 309, and 618. It is divisible by 12, and is an atomic system.