1643edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== | 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 [[Mercator family#Iodine|iodine]] temperament, which tempers out the [[Mercator's comma]] and has a basis 6656/6655, 34398/34375, 43904/43875, 59535/59488. | |||
=== Odd harmonics === | |||
{{Harmonics in equal|1643}} | {{Harmonics in equal|1643}} | ||
Latest revision as of 17:00, 20 February 2025
| ← 1642edo | 1643edo | 1644edo → |
1643 equal divisions of the octave (abbreviated 1643edo or 1643ed2), also called 1643-tone equal temperament (1643tet) or 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 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
| 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) | |