3125edo: Difference between revisions

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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.

~~3125 = 55 , and as such it is the 5th edo of the form x^x. It hhas subset edos 5, 25, 125, and 625.~~

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

=== Prime harmonics ===

=== ~~Miscellaneous properties~~ ===

=== Subsets and supersets ===

~~The fact that~~ 3125 = 55 ~~makes curious notations possible based on~~ the ~~symmetric base 5 positional number system, by converting~~ the ~~number to base~~ 5 ~~with digits {-2, -1~~, 0, 1, 2}.

3125 = 55 , and as such it is the 5th edo of the form x^x. It hhas subset edos {{EDOs|5, 25, 125, and 625}}.

== Regular temperament properties ==

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 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.
-= 5<sup>5</sup> , and as such it is the 5th edo of the form x^x. It hhas subset edos 5, 25, 125, and 625.
+In the 2.5.11.13.19.23.29.31 subgroup, it supports a temperament called estates general, described as 1789 & 3125.
-In the 2.5.11.13.19.23.29.31 subgroup, it supports a temperament called estates general, described as 1789 & 3125.
 === Prime harmonics ===
 {{Harmonics in equal|3125|columns=11}}
-=== Miscellaneous properties ===
+=== Subsets and supersets ===
-The fact that 3125 = 5<sup>5</sup> makes curious notations possible based on the symmetric base 5 positional number system, by converting the number to base 5 with digits {-2, -1, 0, 1, 2}.
+= 5<sup>5</sup> , and as such it is the 5th edo of the form x^x. It hhas subset edos {{EDOs|5, 25, 125, and 625}}.
 == Regular temperament properties ==