1643edo

From Xenharmonic Wiki
Jump to navigation Jump to search

1643 equal divisions of the octave (1643edo), or 1643-tone equal temperament (1643tet), 1643 equal temperament (1643et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 1643 equal parts of about 0.73 ¢ each.

Theory

Approximation of odd harmonics in 1643edo
Harmonic 3 5 7 9 11 13 15 17 19 21
Error absolute (¢) -0.068 +0.053 -0.354 -0.136 +0.112 +0.130 -0.016 +0.218 -0.252 +0.309
relative (%) -9 +7 -48 -19 +15 +18 -2 +30 -34 +42
Steps
(reduced)
2604
(961)
3815
(529)
4612
(1326)
5208
(279)
5684
(755)
6080
(1151)
6419
(1490)
6716
(144)
6979
(407)
7217
(645)

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.