3125edo: Difference between revisions

Line 3:

== Theory ==

3125edo is ~~distinctly~~ [[consistent]] through the [[15-odd-limit]]. A basis for its 7-limit commas is 78125000/78121827, 645700815/645657712 and 281484423828125/281474976710656. In the 11-limit, 151263/151250, 820125/819896, 21437500/21434787 and [[Quartisma|117440512/117406179]] are tempered out – it should be noted this edo is so far the only one [https://en.xen.wiki/index.php?title=3125edo&oldid=7860 known to have been confirmed] as tempering out 117440512/117406179 prior to the independent discovery of this comma's significance as the difference between a stack of five [[33/32]] quartertones and one [[7/6]] subminor third. In the 13-limit, 6656/6655, 123201/123200, 140625/140608, 151263/151250 and 1399680/1399489 are all tempered out.

3125edo is [[consistency|distinctly consistent]] through the [[15-odd-limit]]. A basis for its 7-limit commas is 78125000/78121827, 645700815/645657712 and 281484423828125/281474976710656. In the 11-limit, 151263/151250, 820125/819896, 21437500/21434787 and [[Quartisma|117440512/117406179]] are tempered out – it should be noted this edo is so far the only one [https://en.xen.wiki/index.php?title=3125edo&oldid=7860 known to have been confirmed] as tempering out 117440512/117406179 prior to the independent discovery of this comma's significance as the difference between a stack of five [[33/32]] quartertones and one [[7/6]] subminor third. In the 13-limit, 6656/6655, 123201/123200, 140625/140608, 151263/151250 and 1399680/1399489 are all tempered out.

In the 2.5.11.13.19.23.29.31 subgroup, it supports a temperament called estates general, described as 1789 & 3125.

Line 11:

=== Subsets and supersets ===

3125 = ~~5<sup>5</sup>~~ , and as such it is the 5th edo of the form ~~x^x~~. It has subset edos {{EDOs|5, 25, 125, and 625}}.

3125 = {{factorization|3125}}, and as such it is the 5th edo of the form ''n''<sup>''n''</sup>. It has subset edos {{EDOs| 5, 25, 125, and 625 }}.

== Regular temperament properties ==

@@ Line 3: / Line 3: @@
 == Theory ==
-edo is distinctly [[consistent]] through the [[15-odd-limit]]. A basis for its 7-limit commas is 78125000/78121827, 645700815/645657712 and 281484423828125/281474976710656. In the 11-limit, 151263/151250, 820125/819896, 21437500/21434787 and [[Quartisma|117440512/117406179]] are tempered out – it should be noted this edo is so far the only one [https://en.xen.wiki/index.php?title=3125edo&oldid=7860 known to have been confirmed] as tempering out 117440512/117406179 prior to the independent discovery of this comma's significance as the difference between a stack of five [[33/32]] quartertones and one [[7/6]] subminor third. In the 13-limit, 6656/6655, 123201/123200, 140625/140608, 151263/151250 and 1399680/1399489 are all tempered out.
+edo is [[consistency|distinctly consistent]] through the [[15-odd-limit]]. A basis for its 7-limit commas is 78125000/78121827, 645700815/645657712 and 281484423828125/281474976710656. In the 11-limit, 151263/151250, 820125/819896, 21437500/21434787 and [[Quartisma|117440512/117406179]] are tempered out – it should be noted this edo is so far the only one [https://en.xen.wiki/index.php?title=3125edo&oldid=7860 known to have been confirmed] as tempering out 117440512/117406179 prior to the independent discovery of this comma's significance as the difference between a stack of five [[33/32]] quartertones and one [[7/6]] subminor third. In the 13-limit, 6656/6655, 123201/123200, 140625/140608, 151263/151250 and 1399680/1399489 are all tempered out.
 In the 2.5.11.13.19.23.29.31 subgroup, it supports a temperament called estates general, described as 1789 & 3125.
@@ Line 11: / Line 11: @@
 === Subsets and supersets ===
-= 5<sup>5</sup> , and as such it is the 5th edo of the form x^x. It has subset edos {{EDOs|5, 25, 125, and 625}}.
+= {{factorization|3125}}, and as such it is the 5th edo of the form ''n''<sup>''n''</sup>. It has subset edos {{EDOs| 5, 25, 125, and 625 }}.
 == Regular temperament properties ==