3125edo: Difference between revisions

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== Theory ==

3125et is notable for being an extremely strong [[7-limit]] system. It is also [[consistent]] through the [[15-odd-limit]], and except for [[17/11]] ~~and~~ [[19/17]] and their [[octave complement]]s, it is consistent to the [[35-odd-limit]].

3125et is notable for being an extremely strong [[7-limit]] system. It is also [[consistent]] through the [[15-odd-limit]], and except for [[17/11]], [[19/17]] and their [[octave complement]]s, it is consistent to the [[35-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]] and 1399680/1399489 are all tempered out.

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]] 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 {{nowrap|1789 & 3125}}.~~

=== Prime harmonics ===

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=== Subsets and supersets ===

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

{{nowrap| 3125 {{=}} 55 }}, and as such 3125edo is the 5th edo of the form ''n''''n''. It has subset edos {{EDOs| 5, 25, 125, and 625 }}.

== Regular temperament properties ==

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 == Theory ==
-et is notable for being an extremely strong [[7-limit]] system. It is also [[consistent]] through the [[15-odd-limit]], and except for [[17/11]] and [[19/17]] and their [[octave complement]]s, it is consistent to the [[35-odd-limit]].
+et is notable for being an extremely strong [[7-limit]] system. It is also [[consistent]] through the [[15-odd-limit]], and except for [[17/11]], [[19/17]] and their [[octave complement]]s, it is consistent to the [[35-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]] and 1399680/1399489 are all tempered out.
+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]] 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 {{nowrap|1789 & 3125}}.
 === Prime harmonics ===
@@ Line 14: / Line 12: @@
 === Subsets and supersets ===
-= {{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 }}.
+{{nowrap| 3125 {{=}} 5<sup>5</sup> }}, and as such 3125edo is the 5th edo of the form ''n''<sup>''n''</sup>. It has subset edos {{EDOs| 5, 25, 125, and 625 }}.
 == Regular temperament properties ==