1643edo: Difference between revisions
Jump to navigation
Jump to search
Added a category and moved the theory text |
No edit summary |
||
| Line 5: | Line 5: | ||
1643edo is the multiple of two very famous EDOs: [[31edo]] and [[53edo]]. | 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. | 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. | ||
{{Harmonics in equal|1643}} | {{Harmonics in equal|1643}} | ||
[[Category:Equal divisions of the octave|####]] <!-- 4-digit number --> | [[Category:Equal divisions of the octave|####]] <!-- 4-digit number --> | ||
Revision as of 10:12, 22 December 2022
| ← 1642edo | 1643edo | 1644edo → |
Theory
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.
| 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) | |