125edo: Difference between revisions

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=== Octave stretch ===

125edo's approximated harmonics 3, 5, and 11 can be improved, and moreover the approximated harmonic 13 can be brought to consistency, by slightly [[stretched and compressed tuning|stretching the octave]], though it comes at the expense of somewhat less accurate approximations of 7, 17, and 19. Tunings such as [[198edt]] and [[323ed6]] are great demonstrations of this.

125edo's approximated harmonics 3, 5, and 13 can be improved, and moreover the approximated harmonic 11 can be brought to consistency, by slightly [[stretched and compressed tuning|stretching the octave]], though it comes at the expense of somewhat less accurate approximations of 7, 17, and 19. Tunings such as [[198edt]] and [[323ed6]] are great demonstrations of this.

=== 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 ==

* [[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 ==

@@ Line 10: / Line 10: @@
 === Octave stretch ===
-edo's approximated harmonics 3, 5, and 11 can be improved, and moreover the approximated harmonic 13 can be brought to consistency, by slightly [[stretched and compressed tuning|stretching the octave]], though it comes at the expense of somewhat less accurate approximations of 7, 17, and 19. Tunings such as [[198edt]] and [[323ed6]] are great demonstrations of this.
+edo's approximated harmonics 3, 5, and 13 can be improved, and moreover the approximated harmonic 11 can be brought to consistency, by slightly [[stretched and compressed tuning|stretching the octave]], though it comes at the expense of somewhat less accurate approximations of 7, 17, and 19. Tunings such as [[198edt]] and [[323ed6]] are great demonstrations of this.
 === 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 ==
+* [[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 ==