1749edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|1749}} == Theory == This EDO has a consistency level of only 9, nevertheless, it's well-behaved in the 2.3.5.7.13.17 subgroup. {{Harmonics in equa..." |
No edit summary |
||
| (4 intermediate revisions by 3 users not shown) | |||
| Line 1: | Line 1: | ||
{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
1749edo is [[consistent]] in the [[9-odd-limit]] with strong approximations; however the approximation to the [[11/1|11th harmonic]] is poor. The most straightforward extension is the 2.3.5.7.13.17.31 subgroup. | |||
It is part of the [[optimal ET sequence]] for the [[aemilic]] temperament in the [[7-limit]], as a multiple of [[159edo]]. | |||
1749e val is the most straightforward extension into the 11-limit, as it is better tuned than the patent val and strongly supports 11-limit [[aemilic]] extension. | |||
=== Prime harmonics === | |||
{{Harmonics in equal|1749}} | {{Harmonics in equal|1749}} | ||
[[ | === Subsets and supersets === | ||
Since 1749 factors as {{Factorization|1749}}, 1749edo has subset edos {{EDOs|1, 3, 11, 33, 53, 159, 583}}. | |||
[[3498edo]], which divides the step in two, improves on the harmonic 11 and is consistent in the [[25-odd-limit]]. | |||