# 1643edo

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**1643 equal divisions of the octave** (**1643edo**), or **1643-tone equal temperament** (**1643tet**), **1643 equal temperament** (**1643et**) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 1643 equal parts of about 0.73 ¢ each.

## Theory

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

Error | absolute (¢) | -0.068 | +0.053 | -0.354 | -0.136 | +0.112 | +0.130 | -0.016 | +0.218 | -0.252 | +0.309 |

relative (%) | -9 | +7 | -48 | -19 | +15 | +18 | -2 | +30 | -34 | +42 | |

Steps (reduced) |
2604 (961) |
3815 (529) |
4612 (1326) |
5208 (279) |
5684 (755) |
6080 (1151) |
6419 (1490) |
6716 (144) |
6979 (407) |
7217 (645) |

1643edo is the multiple of two very famous EDOs: 31edo and 53edo.

The best subgroup for it is the 2.3.5.9.11.13.15 subgroup. Nonetheless, it provides the optimal patent val for the 13-limit version of iodine temperament, which tempers out the Mercator's comma and has a basis 6656/6655, 34398/34375, 43904/43875, 59535/59488.