# 184edo

← 183edo | 184edo | 185edo → |

^{3}× 23**184 equal divisions of the octave** (abbreviated **184edo** or **184ed2**), also called **184-tone equal temperament** (**184tet**) or **184 equal temperament** (**184et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 184 equal parts of about 6.52 ¢ each. Each step represents a frequency ratio of 2^{1/184}, or the 184th root of 2.

184edo is closely related to 46edo, but the patent vals differ on the mapping for 5. It is inconsistent to the 5-odd-limit and higher limits, with five mappings possible for the 11-limit: ⟨184 292 427 517 637] (patent val), ⟨184 **291** 427 **516** **636**] (184bde), ⟨184 292 **428** 517 637] (184c), ⟨184 292 427 **516** **636**] (184de), and ⟨184 292 427 517 **636**] (184e).

Using the patent val, it tempers out the tetracot comma, 20000/19683 and 286102294921875/281474976710656 in the 5-limit; 3125/3087, 10976/10935, and 65536/64827 in the 7-limit; 540/539, 896/891, 6875/6804, and 12005/11979 in the 11-limit; 352/351, 364/363, 640/637, and 676/675 in the 13-limit.

Using the 184bde val, it tempers out 129140163/125000000 and 553584375/536870912 in the 5-limit; 225/224, 50421/50000, and 38263752/37515625 in the 7-limit; 385/384, 540/539, 15309/15125, and 43923/43750 in the 11-limit; 351/350, 625/624, 1001/1000, 4455/4394, and 7203/7150 in the 13-limit. Using the 184bdef val, 1573/1568, 1575/1573, 1701/1690, 1716/1715, and 3042/3025 are tempered out in the 13-limit.

Using the 184c val, it tempers out the diaschisma, 2048/2025 and the sensipent comma, 78732/78125 in the 5-limit; 2401/2400 and 65536/64827 in the 7-limit; 176/175, 896/891, 3773/3750, and 14641/14580 in the 11-limit; 351/350, 352/351, 364/363, and 9295/9261 in the 13-limit.

Using the 184de val, it tempers out 1029/1024, 153664/151875, and 214375/209952 in the 7-limit; 896/891, 1331/1323, 2401/2376, and 3773/3750 in the 11-limit; 196/195, 676/675, 1001/1000, 3185/3168 in the 13-limit.

Using the 184e val, it tempers out 385/384, 3388/3375, 9801/9800, and 12100/11907 in the 11-limit; 275/273, 572/567, 640/637, and 847/845 in the 13-limit.

### Odd harmonics

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

Error | Absolute (¢) | +2.39 | -1.53 | +2.91 | -1.74 | +3.03 | +0.78 | +0.86 | -0.61 | +2.49 | -1.22 | -2.19 |

Relative (%) | +36.7 | -23.5 | +44.7 | -26.6 | +46.5 | +11.9 | +13.2 | -9.3 | +38.1 | -18.6 | -33.5 | |

Steps (reduced) |
292 (108) |
427 (59) |
517 (149) |
583 (31) |
637 (85) |
681 (129) |
719 (167) |
752 (16) |
782 (46) |
808 (72) |
832 (96) |

### Subsets and supersets

Since 184 factors into 2^{3} × 23, 184edo has subset edos 2, 4, 8, 23, 46, and 92.