# 8745edo

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Prime factorization
3 × 5 × 11 × 53
Step size
0.137221¢
Fifth
5115\8745 (701.887¢) (→31\53)
Semitones (A1:m2)
825:660 (113.2¢ : 90.57¢)
Dual sharp fifth
5116\8745 (702.024¢)
Dual flat fifth
5115\8745 (701.887¢) (→31\53)
Dual major 2nd
1486\8745 (203.911¢)
Consistency limit
7
Distinct consistency limit
7

← 8744edo | 8745edo | 8746edo → |

**8745 equal divisions of the octave** (abbreviated **8745edo**), or **8745-tone equal temperament** (**8745tet**), **8745 equal temperament** (**8745et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 8745 equal parts of about 0.137 ¢ each. Each step of 8745edo represents a frequency ratio of 2^{1/8745}, or the 8745th root of 2. This dual-fifths system is the largest number EDO which tempers out Mercator's comma.

### Prime harmonics

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

Error | absolute (¢) | -0.0682 | -0.0358 | -0.0437 | +0.0008 | +0.0371 | -0.0474 | +0.0332 | +0.0189 | -0.0173 | +0.0253 | +0.0618 |

relative (%) | -50 | -26 | -32 | +1 | +27 | -35 | +24 | +14 | -13 | +18 | +45 | |

Steps (reduced) |
13860 (5115) |
20305 (2815) |
24550 (7060) |
27721 (1486) |
30253 (4018) |
32360 (6125) |
34166 (7931) |
35745 (765) |
37148 (2168) |
38411 (3431) |
39559 (4579) |