# 1643edo

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Prime factorization
31 × 53
Step size
0.730371¢
Fifth
961\1643 (701.887¢) (→31\53)
Semitones (A1:m2)
155:124 (113.2¢ : 90.57¢)
Consistency limit
5
Distinct consistency limit
5

← 1642edo | 1643edo | 1644edo → |

**1643 equal divisions of the octave** (abbreviated **1643edo**), or **1643-tone equal temperament** (**1643tet**), **1643 equal temperament** (**1643et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1643 equal parts of about 0.73 ¢ each. Each step of 1643edo represents a frequency ratio of 2^{1/1643}, or the 1643rd root of 2.

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

The best subgroup for it is the 2.3.5.11.13 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.

### Odd harmonics

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

Error | absolute (¢) | -0.068 | +0.053 | -0.354 | -0.136 | +0.112 | +0.130 | -0.016 | +0.218 | -0.252 | +0.309 | -0.155 |

relative (%) | -9 | +7 | -48 | -19 | +15 | +18 | -2 | +30 | -34 | +42 | -21 | |

Steps (reduced) |
2604 (961) |
3815 (529) |
4612 (1326) |
5208 (279) |
5684 (755) |
6080 (1151) |
6419 (1490) |
6716 (144) |
6979 (407) |
7217 (645) |
7432 (860) |