1984edo

Revision as of 15:48, 1 November 2023 by Eliora (talk | contribs) (Created page with "{{Infobox ET}} {{EDO intro|1984}} 1984edo is consistent in the 7-odd-limit and it is a mostly sharp system, with 3, 5, 7, 11, and 17 all tuned sharp. Though, the harmonic...")
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← 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

Template:EDO intro

1984edo is consistent in the 7-odd-limit and it is a mostly sharp system, with 3, 5, 7, 11, and 17 all tuned sharp. Though, the harmonics 9 and 15 are tuned flat and are one step off their combined steps, which limits the edo's consistency. In higher limit, 1984edo approximates well the 2.9.19.31.33 subgroup.

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


Approximation of odd harmonics in 1984edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41
Error Absolute (¢) +0.263 +0.178 +0.126 -0.079 +0.295 +0.198 -0.164 +0.287 +0.068 -0.216 +0.153 -0.248 +0.183 -0.142 -0.076 -0.047 -0.301 +0.269 -0.144 -0.232
Relative (%) +43.4 +29.5 +20.8 -13.1 +48.8 +32.8 -27.1 +47.4 +11.2 -35.8 +25.3 -41.1 +30.3 -23.4 -12.5 -7.8 -49.8 +44.5 -23.8 -38.3
Steps
(reduced)
3145
(1161)
4607
(639)
5570
(1602)
6289
(337)
6864
(912)
7342
(1390)
7751
(1799)
8110
(174)
8428
(492)
8714
(778)
8975
(1039)
9213
(1277)
9434
(1498)
9638
(1702)
9829
(1893)
10008
(88)
10176
(256)
10336
(416)
10486
(566)
10629
(709)