# 1236edo

← 1235edo | 1236edo | 1237edo → |

^{2}× 3 × 103**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 2^{1/1236}, 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

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 2^{2} × 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.