# 1984edo

 ← 1983edo 1984edo 1985edo →
Prime factorization 26 × 31
Step size 0.604839¢
Fifth 1161\1984 (702.218¢)
Semitones (A1:m2) 191:147 (115.5¢ : 88.91¢)
Dual sharp fifth 1161\1984 (702.218¢)
Dual flat fifth 1160\1984 (701.613¢) (→145\248)
Dual major 2nd 337\1984 (203.831¢)
Consistency limit 7
Distinct consistency limit 7

1984 equal divisions of the octave (abbreviated 1984edo or 1984ed2), also called 1984-tone equal temperament (1984tet) or 1984 equal temperament (1984et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1984 equal parts of about 0.605 ¢ each. Each step represents a frequency ratio of 21/1984, or the 1984th root of 2.

1984edo is consistent in the 7-odd-limit and is a mostly sharp system, with 3, 5, 7, 11, and 17 all tuned sharp. Harmonics 9 and 15, though, are tuned flat, which results in inconsistencies, that is, their direct approximations are not the same as the sum of their constituent odd harmonics' direct approximations: 9/1 is 6289 steps while 3/1 is 3145 steps (and 3145 + 3145 = 6290, ≠ 6289), and 15/1 is 7751 steps while 5/1 is 4607 steps (and 3145 + 4607 = 7752, ≠ 7751). 1984edo does, however, approximate the 2.9.19.31.33 subgroup well.

In the 7-limit the equal temperament tempers out the wizma (420175/419904), the garischisma (33554432/33480783), and the pessoalisma (2147483648/2144153025).

### Odd harmonics

Approximation of odd harmonics in 1984edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +0.263 +0.178 +0.126 -0.079 +0.295 +0.198 -0.164 +0.287 +0.068 -0.216 +0.153
Relative (%) +43.4 +29.5 +20.8 -13.1 +48.8 +32.8 -27.1 +47.4 +11.2 -35.8 +25.3
Steps
(reduced)
3145
(1161)
4607
(639)
5570
(1602)
6289
(337)
6864
(912)
7342
(1390)
7751
(1799)
8110
(174)
8428
(492)
8714
(778)
8975
(1039)

### Subsets and supersets

Since 1984 factors into 26 × 31, 1984edo has subset edos 2, 4, 8, 16, 31, 32, 62, 64, 124, 248, 496, and 992.