2912edo: Difference between revisions
Jump to navigation
Jump to search
note that it's not just any tuning but a member of optimal et sequence close to pote |
fix subgroup |
||
| Line 4: | Line 4: | ||
2912edo is [[consistent]] to the [[7-odd-limit]], but the error on [[3/2|3]] and [[5/4|5]] is quite large, commending it to a [[dual-fifth]] interpretation. As a dual-fifth system, its sharp and flat approximations to 3/2 come from two notable systems - [[364edo]] and [[224edo]] (see the template to the right). | 2912edo is [[consistent]] to the [[7-odd-limit]], but the error on [[3/2|3]] and [[5/4|5]] is quite large, commending it to a [[dual-fifth]] interpretation. As a dual-fifth system, its sharp and flat approximations to 3/2 come from two notable systems - [[364edo]] and [[224edo]] (see the template to the right). | ||
Aside from the patent val, there is a number of mappings to be considered. 2912dd val provides a tuning close to [[POTE]] tuning for the [[tokko]] temperament, and 2912e val tunes [[skadi]]. 2912edo can be used with 2 | Aside from the patent val, there is a number of mappings to be considered. 2912dd val provides a tuning close to [[POTE]] tuning for the [[tokko]] temperament, and 2912e val tunes [[skadi]]. 2912edo can be used with 2.7.9.11.15.19 subgroup. | ||
=== Odd harmonics === | === Odd harmonics === | ||
{{Harmonics in equal|2912}} | {{Harmonics in equal|2912}} | ||
Revision as of 21:25, 18 February 2024
| ← 2911edo | 2912edo | 2913edo → |
2912edo is consistent to the 7-odd-limit, but the error on 3 and 5 is quite large, commending it to a dual-fifth interpretation. As a dual-fifth system, its sharp and flat approximations to 3/2 come from two notable systems - 364edo and 224edo (see the template to the right).
Aside from the patent val, there is a number of mappings to be considered. 2912dd val provides a tuning close to POTE tuning for the tokko temperament, and 2912e val tunes skadi. 2912edo can be used with 2.7.9.11.15.19 subgroup.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.169 | -0.187 | -0.007 | +0.074 | +0.056 | +0.132 | +0.055 | +0.127 | +0.014 | -0.177 | +0.160 |
| Relative (%) | -41.1 | -45.5 | -1.8 | +17.8 | +13.5 | +32.0 | +13.5 | +30.8 | +3.5 | -42.8 | +38.8 | |
| Steps (reduced) |
4615 (1703) |
6761 (937) |
8175 (2351) |
9231 (495) |
10074 (1338) |
10776 (2040) |
11377 (2641) |
11903 (255) |
12370 (722) |
12790 (1142) |
13173 (1525) | |
Subsets and supersets
Since 2912 factors as 25 × 7 × 13, 2912edo has subset edos 1, 2, 4, 7, 8, 13, 14, 16, 26, 28, 32, 52, 56, 91, 104, 112, 182, 208, 224, 364, 416, 728, 1456.