3125edo: Difference between revisions

{{ED intro}}

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.

{{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 }}.

3125et is the first equal temperament past [[171edo|171]] with a lower [[Tenney–Euclidean temperament measures #TE simple badness|relative error]].  

! Generator*

! Cents*

! Associated<br>ratio*

<nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct

; [[Eliora]]

* [https://www.youtube.com/watch?v=mnTF1vBexBg ''Etude for Gamelan in Estates General and Pentonismic''] (2023)