# 382edo

← 381edo | 382edo | 383edo → |

**382 equal divisions of the octave** (abbreviated **382edo** or **382ed2**), also called **382-tone equal temperament** (**382tet**) or **382 equal temperament** (**382et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 382 equal parts of about 3.14 ¢ each. Each step represents a frequency ratio of 2^{1/382}, or the 382nd root of 2.

## Theory

382edo is consistent to the 7-odd-limit, but harmonics 3 and 7 are about halfway between its steps. It is also bad at approximating 11, 13, 15, and 17, though its 5, 9, 19, 21, and 23 are good, making it suitable for a 2.9.5.21.19.23 subgroup interpretation.

Using the patent val nonetheless, the equal temperament tempers out 65625/65536 in the 7-limit; 540/539, 4000/3993, and 9801/9800 in the 11-limit. It supports bastille.

### Odd harmonics

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

Error | Absolute (¢) | -1.43 | +0.07 | -1.29 | +0.28 | +1.56 | +1.36 | -1.36 | -1.29 | +0.92 | +0.42 | -0.00 |

Relative (%) | -45.6 | +2.3 | -41.0 | +8.9 | +49.7 | +43.2 | -43.2 | -41.1 | +29.2 | +13.5 | -0.1 | |

Steps (reduced) |
605 (223) |
887 (123) |
1072 (308) |
1211 (65) |
1322 (176) |
1414 (268) |
1492 (346) |
1561 (33) |
1623 (95) |
1678 (150) |
1728 (200) |

### Subsets and supersets

382 factors into 2 × 191 with 2edo and 191edo as its subset edos. 764edo, which doubles it, gives a good correction to the harmonics 3, 7, 11, 13, and 17.

## Regular temperament properties

Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
---|---|---|---|---|---|

Absolute (¢) | Relative (%) | ||||

2.9 | [1211 -382⟩ | [⟨382 1211]] | -0.0439 | 0.0439 | 1.40 |

2.9.5 | [38 -1 -15⟩, [25 -24 22⟩ | [⟨382 1211 887]] | -0.0399 | 0.0363 | 1.16 |

2.9.5.21 | 4375/4374, 52734375/52706752, [31 0 -2 -6⟩ | [⟨382 1211 887 1678]] | -0.0552 | 0.0412 | 1.31 |