1643edo

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← 1642edo1643edo1644edo →
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

1643 equal divisions of the octave (abbreviated 1643edo), or 1643-tone equal temperament (1643tet), 1643 equal temperament (1643et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1643 equal parts of about 0.73 ¢ each. Each step of 1643edo represents a frequency ratio of 21/1643, or the 1643rd root of 2.

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

The best subgroup for it is the 2.3.5.11.13 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.

Odd harmonics

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 +7 -48 -19 +15 +18 -2 +30 -34 +42 -21
Steps
(reduced)
2604
(961)
3815
(529)
4612
(1326)
5208
(279)
5684
(755)
6080
(1151)
6419
(1490)
6716
(144)
6979
(407)
7217
(645)
7432
(860)