1643edo: Difference between revisions

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Created page with "{{EDO intro|1643}} == Theory == {{Harmonics in equal|1643}} 1643edo is the multiple of two very famous EDOs: 31edo and 53edo. The best subgroup for it is the 2.3.5.9..."
 
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{{Infobox ET}}
{{EDO intro|1643}}
{{EDO intro|1643}}



Revision as of 15:37, 9 October 2022

← 1642edo 1643edo 1644edo →
Prime factorization 31 × 53
Step size 0.730371 ¢ 
Fifth 961\1643 (701.887 ¢) (→ 31\53)
Semitones (A1:m2) 155:124 (113.2 ¢ : 90.57 ¢)
Consistency limit 5
Distinct consistency limit 5

Template:EDO intro

Theory

Approximation of odd harmonics in 1643edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -0.068 +0.053 -0.354 -0.136 +0.112 +0.130 -0.016 +0.218 -0.252 +0.309 -0.155
Relative (%) -9.3 +7.2 -48.4 -18.7 +15.4 +17.8 -2.1 +29.9 -34.5 +42.2 -21.2
Steps
(reduced)
2604
(961)
3815
(529)
4612
(1326)
5208
(279)
5684
(755)
6080
(1151)
6419
(1490)
6716
(144)
6979
(407)
7217
(645)
7432
(860)

1643edo is the multiple of two very famous EDOs: 31edo and 53edo.

The best subgroup for it is the 2.3.5.9.11.13.15 subgroup. Nonetheless, it provides the optimal patent val for the 13-limit version of iodine temperament, which tempers out the Mercator's comma and has a basis 6656/6655, 34398/34375, 43904/43875, 59535/59488.