# 848edo

← 847edo | 848edo | 849edo → |

^{4}× 53**848 equal divisions of the octave** (abbreviated **848edo** or **848ed2**), also called **848-tone equal temperament** (**848tet**) or **848 equal temperament** (**848et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 848 equal parts of about 1.42 ¢ each. Each step represents a frequency ratio of 2^{1/848}, or the 848th root of 2.

848edo is consistent to the 15-odd-limit and contains the famous 53edo as a subset. In the 5-limit, it is a very strong system, which tempers out the Mercator's comma. It also tunes kwazy and provides the optimal patent val for the 5-limit geb temperament.

In higher limits, it is a strong 2.3.5.13.23 subgroup system, with optional additions of either 7 and 11 or 17 and 19. It provides the optimal patent val for sextantonic, the rank-4 temperament tempering out 2601/2600 in the 2.3.5.13.17 subgroup.

### Prime harmonics

Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Error | Absolute (¢) | +0.000 | -0.068 | +0.007 | +0.514 | +0.569 | +0.038 | -0.238 | -0.343 | +0.028 | +0.611 | -0.224 |

Relative (%) | +0.0 | -4.8 | +0.5 | +36.3 | +40.2 | +2.7 | -16.8 | -24.3 | +1.9 | +43.2 | -15.8 | |

Steps (reduced) |
848 (0) |
1344 (496) |
1969 (273) |
2381 (685) |
2934 (390) |
3138 (594) |
3466 (74) |
3602 (210) |
3836 (444) |
4120 (728) |
4201 (809) |

### Subsets and supersets

Since 848 factors into 2^{4} × 53, 848edo has subset edos 2, 4, 8, 16, 53, 106, 212, and 424.