# 1783edo

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 ← 1782edo 1783edo 1784edo →
Prime factorization 1783 (prime)
Step size 0.673023¢
Fifth 1043\1783 (701.963¢)
Semitones (A1:m2) 169:134 (113.7¢ : 90.19¢)
Consistency limit 9
Distinct consistency limit 9

1783 equal divisions of the octave (abbreviated 1783edo or 1783ed2), also called 1783-tone equal temperament (1783tet) or 1783 equal temperament (1783et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1783 equal parts of about 0.673 ¢ each. Each step represents a frequency ratio of 21/1783, or the 1783rd root of 2.

1783edo is a very strong 5-limit system, with a lower 5-limit relative error than anything until 2513. It is consistent to the 9-odd-limit, but there is a large relative delta for the harmonic 7. Together with decent approximations to 11, 13, 17, and 19, it makes for a good no-7 19-limit tuning.

In the 5-limit the equal temperament tempers out the monzisma, [54 -37 2; egads, [-36 -52 51; gross, [144 -22 -47; and pirate, [-90 -15 49.

Using the patent val, it tempers out 2460375/2458624 in the 7-limit; 3025/3024 and 180224/180075 in the 11-limit; 1716/1715 and 4096/4095 in the 13-limit. The alternative 1783d val tempers out 4375/4374 in the 7-limit; 41503/41472 and 160083/160000 in the 11-limit; 10648/10647 in the 13-limit.

### Prime harmonics

Approximation of prime harmonics in 1783edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.0000 +0.0080 +0.0015 +0.3272 -0.1121 +0.0781 +0.0362 -0.0369 +0.3291 +0.1480 -0.2235
Relative (%) +0.0 +1.2 +0.2 +48.6 -16.7 +11.6 +5.4 -5.5 +48.9 +22.0 -33.2
Steps
(reduced)
1783
(0)
2826
(1043)
4140
(574)
5006
(1440)
6168
(819)
6598
(1249)
7288
(156)
7574
(442)
8066
(934)
8662
(1530)
8833
(1701)

### Subsets and supersets

1783edo is the 276th prime edo. 3566edo, which doubles it, provides a good correction to the approximation of harmonic 7.