# 4380edo

← 4379edo | 4380edo | 4381edo → |

^{2}× 3 × 5 × 73**4380 equal divisions of the octave** (abbreviated **4380edo** or **4380ed2**), also called **4380-tone equal temperament** (**4380tet**) or **4380 equal temperament** (**4380et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 4380 equal parts of about 0.274 ¢ each. Each step represents a frequency ratio of 2^{1/4380}, or the 4380th root of 2.

4380edo is consistent in the 31-odd-limit and has the lowest relative error in the 47-limit, being only beaten by the 7361o val.

In light of having 60 as a divisor, 4380edo is a tuning for the neodymium temperament in the 17-limit. It is worth noting that 4380edo tempers out the magnetisma on its 43-limit patent val, and therefore tunes the extension neodymium magnet.

### Prime harmonics

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

Error | Absolute (¢) | +0.000 | -0.037 | -0.012 | -0.059 | -0.085 | +0.020 | -0.024 | +0.021 | -0.055 | +0.012 | -0.104 |

Relative (%) | +0.0 | -13.6 | -4.5 | -21.5 | -31.0 | +7.4 | -8.7 | +7.7 | -20.1 | +4.3 | -38.0 | |

Steps (reduced) |
4380 (0) |
6942 (2562) |
10170 (1410) |
12296 (3536) |
15152 (2012) |
16208 (3068) |
17903 (383) |
18606 (1086) |
19813 (2293) |
21278 (3758) |
21699 (4179) |

### Subsets and supersets

4380edo has subset edos 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 73, 146, 219, 292, 365, 438, 730, 876, 1095, 1460, 2190. One step of 4380edo is one sixth of a Woolhouse unit (1\730).