1783edo

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← 1782edo1783edo1784edo →
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.