125edo: Difference between revisions
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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]]. | 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{{Idio}} 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]]. | 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]]. | ||
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| [[Thunderclysmic]] | | [[Thunderclysmic]] | ||
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<nowiki/>* [[Normal | <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 | ||
== Scales == | == Scales == | ||
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; Catakleismic[34] subsets | ; Catakleismic[34] subsets | ||
{{Idiosyncratic terms|Meta-tropolis and its subsets named by [[Budjarn Lambeth]]}} | {{Idiosyncratic terms|Meta-tropolis and its subsets named by [[Budjarn Lambeth]]}} | ||
* Meta-tropolis scale: 14 7 5 14 19 14 14 5 9 10 2 12 | * Meta-tropolis scale (12-tone): 14 7 5 14 19 14 14 5 9 10 2 12 | ||
** City-at-dawn scale: 21 38 14 14 14 24 | ** City-at-dawn scale: 21 38 14 14 14 24 | ||
** City-at-midday scale: 40 19 14 14 14 24 | ** City-at-midday scale: 40 19 14 14 14 24 | ||