1783edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
'''1783edo''' divides the octave into 1783 equal parts of 0.673 cents each. It is a very strong 5-limit system, with a lower 5-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]] than anything until [[2513edo|2513]]. It tempers out the monzisma, | 54 -37 2 >; egads, | -36 -52 51 >; gross, | 144 -22 -47 >; and pirate, | -90 -15 49 >.
{{EDO intro|1783}}


{{Primes in edo|1783|prec=4}}
1783edo is a very strong 5-limit system, with a lower 5-limit [[Tenney-Euclidean temperament measures#TE simple badness|relative error]] than anything until [[2513edo|2513]]. It tempers out the [[monzisma]], {{monzo| 54 -37 2}}; egads, {{monzo| -36 -52 51 }}; gross, {{monzo| 144 -22 -47 }}; and pirate, {{monzo| -90 -15 49 }}.


[[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->
=== Prime harmonics ===
{{Harmonics in equal|1783|prec=4}}
 
=== Subsets and supersets ===
1783edo is the 276th [[prime edo]]. [[3566edo]], which doubles it, provides a good correction to the approximation of [[7/1|harmonic 7]].

Revision as of 14:43, 15 October 2023

← 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

Template:EDO intro

1783edo is a very strong 5-limit system, with a lower 5-limit relative error than anything until 2513. It tempers out the monzisma, [54 -37 2; egads, [-36 -52 51; gross, [144 -22 -47; and pirate, [-90 -15 49.

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.