# 8192edo

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Prime factorization
2
Step size
0.146484¢
Fifth
4792\8192 (701.953¢) (→599\1024)
Semitones (A1:m2)
776:616 (113.7¢ : 90.23¢)
Consistency limit
9
Distinct consistency limit
9

← 8191edo | 8192edo | 8193edo → |

^{13}**8192 equal divisions of the octave** (abbreviated **8192edo** or **8192ed2**), also called **8192-tone equal temperament** (**8192tet**) or **8192 equal temperament** (**8192et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 8192 equal parts of about 0.146 ¢ each. Each step represents a frequency ratio of 2^{1/8192}, or the 8192nd root of 2.

## Theory

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

Error | Absolute (¢) | +0.0000 | -0.0019 | -0.0344 | +0.0217 | +0.0492 | -0.0003 | -0.0726 | -0.0033 | -0.0029 | +0.0615 | +0.0328 |

Relative (%) | +0.0 | -1.3 | -23.5 | +14.8 | +33.6 | -0.2 | -49.6 | -2.2 | -2.0 | +42.0 | +22.4 | |

Steps (reduced) |
8192 (0) |
12984 (4792) |
19021 (2637) |
22998 (6614) |
28340 (3764) |
30314 (5738) |
33484 (716) |
34799 (2031) |
37057 (4289) |
39797 (7029) |
40585 (7817) |

This is the 13th power of two EDO, but with a consistency limit of only 9, it's not as impressive as the one before it, though to be fair, its representations of harmonics 3, 13, 19, and 23 are very good.