125edo: Difference between revisions

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=== 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]].

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| [[Thunderclysmic]]

|}

<nowiki/>* [[Normal ~~lists~~|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~|minimal form]] in parentheses if distinct

<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 ==

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* 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

** Subsets

*** 21 31 21 14 14 24 (''canopy{{idio}}, approximated from [[16afdo]]'')

*** 21 12 26 14 33 19 (''resembles [[antipental blues]]'')

*** 19 21 21 19 26 19 (''resembles whole tone scale, [[6edo]]'')

* 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 ==

@@ Line 13: / Line 13: @@
 === 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]].
@@ Line 143: / Line 143: @@
 | [[Thunderclysmic]]
 |}
-<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
+<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 ==
@@ Line 151: / Line 151: @@
 * 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
-** Subsets
-*** 21 31 21 14 14 24 (''canopy{{idio}}, approximated from [[16afdo]]'')
-*** 21 12 26 14 33 19 (''resembles [[antipental blues]]'')
-*** 19 21 21 19 26 19 (''resembles whole tone scale, [[6edo]]'')
 * 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 ==