# 1024edo

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Prime factorization
2
Step size
1.17188¢
Fifth
599\1024 (701.953¢)
Semitones (A1:m2)
97:77 (113.7¢ : 90.23¢)
Consistency limit
9
Distinct consistency limit
9

← 1023edo | 1024edo | 1025edo → |

^{10}**1024 equal divisions of the octave** (abbreviated **1024edo** or **1024ed2**), also called **1024-tone equal temperament** (**1024tet**) or **1024 equal temperament** (**1024et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1024 equal parts of about 1.17 ¢ each. Each step represents a frequency ratio of 2^{1/1024}, or the 1024th root of 2.

## Theory

1024edo has a near-perfect 3/2, and, as the 10th power of two EDO, offers some much-needed correction for the flaws of 512edo.

It is consistent in the 9-odd-limit. It is great for the 2.3.5.7.13.19.23 subgroup.

### Prime harmonics

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

Error | Absolute (¢) | +0.000 | -0.002 | +0.405 | +0.315 | -0.537 | -0.293 | +0.513 | +0.143 | -0.149 | +0.501 | -0.114 |

Relative (%) | +0.0 | -0.2 | +34.6 | +26.9 | -45.8 | -25.0 | +43.8 | +12.2 | -12.7 | +42.7 | -9.7 | |

Steps (reduced) |
1024 (0) |
1623 (599) |
2378 (330) |
2875 (827) |
3542 (470) |
3789 (717) |
4186 (90) |
4350 (254) |
4632 (536) |
4975 (879) |
5073 (977) |