184edo

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← 183edo184edo185edo →
Prime factorization 23 × 23
Step size 6.52174¢ 
Fifth 108\184 (704.348¢) (→27\46)
Semitones (A1:m2) 20:12 (130.4¢ : 78.26¢)
Dual sharp fifth 108\184 (704.348¢) (→27\46)
Dual flat fifth 107\184 (697.826¢)
Dual major 2nd 31\184 (202.174¢)
Consistency limit 3
Distinct consistency limit 3

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 21/184, 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

Approximation of odd harmonics in 184edo
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 23 × 23, 184edo has subset edos 2, 4, 8, 23, 46, and 92.