1612edo: Difference between revisions
Jump to navigation
Jump to search
No edit summary |
I have no idea why I made this mistake or why x31eq put out 1612df as tuning for silicon when it's not even divisible by 14 |
||
| Line 4: | Line 4: | ||
1612edo is a strong [[5-limit]] system, providing the tuning for [[quasithird]], [[aluminium]] and [[counterorson]] temperaments. | 1612edo is a strong [[5-limit]] system, providing the tuning for [[quasithird]], [[aluminium]] and [[counterorson]] temperaments. | ||
While it is only consistent up to 5-limit, there are higher-limit mappings to be considered | While it is only consistent up to 5-limit, there are higher-limit mappings to be considered. The patent val is a strong 2.3.5.13.17.23.29.31 subgroup tuning. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{harmonics in equal|1612}} | {{harmonics in equal|1612}} | ||
Revision as of 14:06, 21 October 2023
| ← 1611edo | 1612edo | 1613edo → |
1612edo is a strong 5-limit system, providing the tuning for quasithird, aluminium and counterorson temperaments.
While it is only consistent up to 5-limit, there are higher-limit mappings to be considered. The patent val is a strong 2.3.5.13.17.23.29.31 subgroup tuning.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.030 | +0.039 | -0.340 | +0.295 | -0.081 | +0.007 | +0.254 | +0.013 | -0.049 | -0.122 |
| Relative (%) | +0.0 | +4.0 | +5.2 | -45.6 | +39.6 | -10.9 | +1.0 | +34.1 | +1.8 | -6.5 | -16.4 | |
| Steps (reduced) |
1612 (0) |
2555 (943) |
3743 (519) |
4525 (1301) |
5577 (741) |
5965 (1129) |
6589 (141) |
6848 (400) |
7292 (844) |
7831 (1383) |
7986 (1538) | |
Subsets and supersets
3224edo, which doubles 1612edo, corrects mapping for 7 and 11.