# 1210edo

← 1209edo | 1210edo | 1211edo → |

^{2}**1210 equal divisions of the octave** (abbreviated **1210edo** or **1210ed2**), also called **1210-tone equal temperament** (**1210tet**) or **1210 equal temperament** (**1210et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1210 equal parts of about 0.992 ¢ each. Each step represents a frequency ratio of 2^{1/1210}, or the 1210th root of 2.

1210edo is consistent in the 13-odd-limit, though it is a sharp system with high errors and with all odd harmonics upwards to 23 except 15 tending sharp. As such, the tuning system would benefit from octave compression. It can also be used as a 2.3.7.11.17.19-subgroup system for best accuracy.

1210edo provides the optimal patent val for the titanium temperament in the 11- and the 13-limit. Aside from this, in the 11-limit it provides the optimal patent val for decoid, baffin, as well as the rank-3 temperament zisa.

### Odd harmonics

Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Error | Absolute (¢) | +0.194 | +0.463 | +0.100 | +0.388 | +0.087 | +0.464 | -0.335 | +0.169 | +0.008 | +0.293 | +0.486 |

Relative (%) | +19.5 | +46.7 | +10.1 | +39.1 | +8.8 | +46.8 | -33.8 | +17.0 | +0.8 | +29.6 | +49.0 | |

Steps (reduced) |
1918 (708) |
2810 (390) |
3397 (977) |
3836 (206) |
4186 (556) |
4478 (848) |
4727 (1097) |
4946 (106) |
5140 (300) |
5315 (475) |
5474 (634) |

### Subsets and supersets

Since 1210 factors as 2 × 5 × 11^{2}, 1210edo has subset edos 2, 5, 10, 11, 22, 55, 110, 121, 242, 605.