# 1641edo

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Prime factorization
3 × 547
Step size
0.731261¢
Fifth
960\1641 (702.011¢) (→320\547)
Semitones (A1:m2)
156:123 (114.1¢ : 89.95¢)
Consistency limit
11
Distinct consistency limit
11

← 1640edo | 1641edo | 1642edo → |

**1641 equal divisions of the octave** (abbreviated **1641edo** or **1641ed2**), also called **1641-tone equal temperament** (**1641tet**) or **1641 equal temperament** (**1641et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1641 equal parts of about 0.731 ¢ each. Each step represents a frequency ratio of 2^{1/1641}, or the 1641st root of 2.

## Theory

This EDO corrects the mappings of 547edo for the 7-prime and the 11-prime, but is only consistent up to the 11-limit.

### Prime harmonics

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

Error | Absolute (¢) | +0.000 | +0.056 | -0.208 | +0.095 | +0.053 | -0.308 | +0.346 | +0.110 | -0.121 | +0.039 | +0.120 |

Relative (%) | +0.0 | +7.7 | -28.4 | +13.1 | +7.3 | -42.2 | +47.3 | +15.1 | -16.5 | +5.3 | +16.4 | |

Steps (reduced) |
1641 (0) |
2601 (960) |
3810 (528) |
4607 (1325) |
5677 (754) |
6072 (1149) |
6708 (144) |
6971 (407) |
7423 (859) |
7972 (1408) |
8130 (1566) |