# 182edo

← 181edo | 182edo | 183edo → |

**182 equal divisions of the octave** (abbreviated **182edo** or **182ed2**), also called **182-tone equal temperament** (**182tet**) or **182 equal temperament** (**182et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 182 equal parts of about 6.593 ¢ each. Each step represents a frequency ratio of 2^{1/182}, or the 182nd root of 2.

## Theory

182edo is inconsistent to the 5-limit and higher limit, with three mappings suitable for the 11-limit: ⟨182 288 423 511 630] (patent val), ⟨182 289 423 511 630] (182b), and ⟨182 288 422 511 629] (182ce). It does have a potential as a 2.7.9.15.17.19 subgroup temperament.

182edo (182bef val) is a tuning for the shrutar temperament in the 19-limit and petrtri in the 2.11/5.13/5 subgroup.

### Odd harmonics

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

Error | absolute (¢) | -3.05 | +2.70 | +0.40 | +0.49 | +2.53 | -3.17 | -0.36 | +0.54 | -0.81 | -2.65 | -1.90 |

relative (%) | -46 | +41 | +6 | +7 | +38 | -48 | -5 | +8 | -12 | -40 | -29 | |

Steps (reduced) |
288 (106) |
423 (59) |
511 (147) |
577 (31) |
630 (84) |
673 (127) |
711 (165) |
744 (16) |
773 (45) |
799 (71) |
823 (95) |

## Regular temperament properties

### Commas

Using the patent val, it tempers out the quinbigu comma, 10077696/9765625 and 3486784401/3355443200 in the 5-limit; 126/125, 1728/1715, and 1937102445/1879048192 in the 7-limit; 2187/2156, 2835/2816, 5632/5625, and 14700/14641 in the 11-limit; 364/363, 676/675, 1287/1280, and 1701/1690 in the 13-limit.

Using the 182b val, it tempers out the diaschisma, 2048/2025 and [-4 -37 27⟩; in the 5-limit; 245/243, 6144/6125, and 9882516/9765625 in the 7-limit; 3025/3024, 3773/3750, and 4000/3993 in the 11-limit.

Using the 182bf val, 196/195, 325/324, 364/363, and 1001/1000 are tempered out in the 13-limit. Using the 182ce val, it tempers out the kleisma, 15625/15552 and the lalagu comma, 43046721/41943040 in the 5-limit; 2430/2401, 33075/32768, and 78125/76832 in the 7-limit; 243/242, 385/384, 2420/2401, and 6250/6237 in the 11-limit; 351/350, 1188/1183, 1287/1280, 1575/1573, and 1625/1617 in the 13-limit.

Using the 182f val, 144/143, 847/845, 1001/1000, and 1716/1715 are tempered out in the 13-limit.