125edo: Difference between revisions
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→Subsets and supersets: Mention 13.888edo |
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 125 factors into primes as 5<sup>3</sup>, 125edo contains [[5edo]] and [[25edo]] as subset edos. Being the cube closest to division of the octave by the Germanic {{w|long hundred}}, 125edo has a unit step which is the cubic (fine) relative cent of [[1edo]]. Using every 9th step, | Since 125 factors into primes as 5<sup>3</sup>, 125edo contains [[5edo]] and [[25edo]] as subset edos. Being the cube closest to division of the octave by the Germanic {{w|long hundred}}, 125edo has a unit step which is the cubic (fine) relative cent of [[1edo]]. | ||
Using every 9th step of 125edo, '''86.4-cET''' (also known as '''1ed86.4{{cent}}''', and sometimes '''13.888edo''' by approximation) still encapsulates many of its best-tuned harmonics, such as the 3rd, 7th, 9th and 11th. It has been voted "monthly tuning" multiple times on the [[Monthly Tunings]] Facebook group. This subset is closely related to [[22edt]], another tuning that closely approximates [[42zpi]]. | |||
{{harmonics in cet|86.4|prec=1}} | |||
{{harmonics in cet|86.4|prec=1|start=11}} | |||
== Regular temperament properties == | == Regular temperament properties == | ||
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<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | <nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | ||
== Music == | |||
* ''[https://soundcloud.com/morphosyntax-1/the-butterflys-dream The Butterfly’s Dream]'' (in 86.4-cET) by [[Herman Miller]] (2022) | |||
[[Category:Catakleismic]] | [[Category:Catakleismic]] | ||