125edo: Difference between revisions
Omg pls don't creep up the limit of the harmonics table. This entire paragraph of readability hell has no place in the theory section, either. |
m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" |
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=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|125 | {{Harmonics in equal|125}} | ||
{{Harmonics in equal|125|columns=9|start= | {{Harmonics in equal|125|columns=9|start=12|collapsed=true|title=Approximation of prime harmonics in 125edo (continued)}} | ||
=== Octave stretch === | === Octave stretch === | ||
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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 == | |||
* [[Catakleismic]][7]: 7 26 7 26 7 26 26 | |||
* Catakleismic[11]: 7 19 7 7 19 7 7 19 7 19 7 | |||
* Catakleismic[15]: 7 12 7 7 7 12 7 7 7 12 7 7 7 12 7 | |||
* Catakleismic[19]: 7 7 5 7 7 7 7 5 7 7 7 5 7 7 7 7 5 7 7 | |||
* Catakleismic[34]: 5 2 5 2 5 2 5 2 5 5 2 5 2 5 2 5 2 5 5 2 5 2 5 2 5 5 2 5 2 5 2 5 2 5 | |||
* Catakleismic[53]: 2 3 2 2 3 2 3 2 2 3 2 2 3 2 2 3 2 2 3 2 3 2 2 3 2 2 3 2 2 3 2 2 3 2 3 2 2 3 2 2 3 2 2 3 2 2 3 2 3 2 2 3 | |||
; Catakleismic[34] subsets | |||
{{Idiosyncratic terms|Meta-tropolis and its subsets named by [[Budjarn Lambeth]]}} | |||
* 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-midday scale: 40 19 14 14 14 24 | |||
** City-at-dusk scale: 40 19 14 28 12 12 | |||
** City-at-midnight scale: 40 19 14 14 26 12 | |||
** Port-at-dawn scale: 26 33 14 19 9 24 | |||
** Port-at-midday scale: 40 19 14 19 9 24 | |||
** Port-at-dusk scale: 40 19 14 28 10 14 | |||
** Port-at-midnight scale: 40 19 14 19 19 14 | |||
* Pseudo-minor blues: 21 12 26 14 33 19 | |||
* Pseudo-whole tone scale 19 21 21 19 26 19 | |||
== Music == | == Music == | ||