1749edo: Difference between revisions

(One intermediate revision by one other user not shown)

Line 3:

== Theory ==

1749edo is [[consistent]] in the 7-odd-limit with strong approximations, however the approximation to the 11th harmonic is poor. The most straightforward extension is the 2.3.5.7.13.17.31 subgroup.

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 ~~provides~~ the optimal ~~patent val~~ for the [[aemilic]] temperament in the [[7-limit]], as a multiple of [[159edo]].

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 ===

[[~~Category:Equal divisions of the octave|####~~]] 

=== 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]].

@@ Line 3: / Line 3: @@
 == Theory ==
-edo is [[consistent]] in the 7-odd-limit with strong approximations, however the approximation to the 11th harmonic is poor. The most straightforward extension is the 2.3.5.7.13.17.31 subgroup.
+edo 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 provides the optimal patent val for the [[aemilic]] temperament in the [[7-limit]], as a multiple of [[159edo]].
+It is part of the [[optimal ET sequence]] for the [[aemilic]] temperament in the [[7-limit]], as a multiple of [[159edo]].
 e 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}}
-[[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->
+=== 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]].