125edo - Revision history

FloraC: 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"

2026-03-13T13:31:34Z

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"

← Older revision		Revision as of 13:31, 13 March 2026
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	\| [[Thunderclysmic]]		\| [[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 ==		== Scales ==

Overthink: /* Subsets and supersets */ mark idiosyncratic term

2026-02-10T00:24:43Z

Subsets and supersets: mark idiosyncratic term

← Older revision		Revision as of 00:24, 10 February 2026
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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]].

BudjarnLambeth: /* Scales */

2026-02-04T08:12:18Z

Scales

← Older revision		Revision as of 08:12, 4 February 2026
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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

BudjarnLambeth: /* Scales */

2026-02-04T08:10:19Z

Scales

← Older revision		Revision as of 08:10, 4 February 2026
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	; Catakleismic[34] subsets		; Catakleismic[34] subsets
	{{Idiosyncratic terms}}		{{Idiosyncratic terms\|Meta-tropolis and its subsets named by [[Budjarn Lambeth]]}}
	* City-at-dawn scale: 21 38 14 14 14 24		* Meta-tropolis scale: 14 7 5 14 19 14 14 5 9 10 2 12
	* City-at-midday scale: 40 19 14 14 14 24		** City-at-dawn scale: 21 38 14 14 14 24
	* City-at-dusk scale: 40 19 14 28 12 12		** City-at-midday scale: 40 19 14 14 14 24
	* City-at-midnight scale: 40 19 14 14 26 12		** City-at-dusk scale: 40 19 14 28 12 12
	* Port-at-dawn scale: 26 33 14 19 9 24		** City-at-midnight scale: 40 19 14 14 26 12
	* Port-at-midday scale: 40 19 14 19 9 24		** Port-at-dawn scale: 26 33 14 19 9 24
	* Port-at-dusk scale: 40 19 14 28 10 14		** Port-at-midday scale: 40 19 14 19 9 24
	* Port-at-midnight scale: 40 19 14 19 19 14		** 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-minor blues: 21 12 26 14 33 19
	* Pseudo-whole tone scale 19 21 21 19 26 19		* Pseudo-whole tone scale 19 21 21 19 26 19

BudjarnLambeth: /* Scales */

2026-02-04T08:04:12Z

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
 * 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
 == Music ==

BudjarnLambeth: /* Scales */ add 3

2026-02-04T07:36:07Z

Scales: add 3

← Older revision		Revision as of 07:36, 4 February 2026
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	* 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[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		** Subsets
	*** 21 ~~31 21~~ 14 14 24 (''~~canopy~~{{idio}}~~, approximated from [[16afdo]]~~'')		*** 21 38 14 14 14 24 (''city-at-dawn scale''{{idio}})
			*** 40 19 14 14 14 24 (''city-at-midday scale''{{idio}})
			*** 40 19 14 28 12 12 (''city-at-dusk scale''{{idio}})
			*** 40 19 14 14 26 12 (''city-at-midnight scale''{{idio}})
	*** 21 12 26 14 33 19 (''resembles [[antipental blues]]'')		*** 21 12 26 14 33 19 (''resembles [[antipental blues]]'')
	*** 19 21 21 19 26 19 (''resembles whole tone scale, [[6edo]]'')		*** 19 21 21 19 26 19 (''resembles whole tone scale, [[6edo]]'')

BudjarnLambeth: /* Scales */

2026-02-04T07:12:36Z

Scales

← Older revision		Revision as of 07:12, 4 February 2026
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	* 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[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		** Subsets
	*** 21 31 21 14 14 24 (''canopy{{idio}} (approximated from [[16afdo]])'')		*** 21 31 21 14 14 24 (''canopy{{idio}}, approximated from [[16afdo]]'')
	*** 21 12 26 14 33 19 (''resembles [[antipental blues]]'')		*** 21 12 26 14 33 19 (''resembles [[antipental blues]]'')
	*** 19 21 21 19 26 19 (''resembles whole tone scale, [[6edo]]'')		*** 19 21 21 19 26 19 (''resembles whole tone scale, [[6edo]]'')

BudjarnLambeth: /* Scales */ add 3

2026-02-04T07:12:22Z

Scales: add 3

← Older revision		Revision as of 07:12, 4 February 2026
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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[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[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		** 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

	== Music ==		== Music ==

BudjarnLambeth: /* Music */ add scales section

2026-02-03T07:08:14Z

Music: add scales section

← Older revision		Revision as of 07:08, 3 February 2026
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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

			== 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

	== Music ==		== Music ==

FloraC: Undo revision 217456 by Overthink (talk). Was never wrong in the first place

2025-11-22T14:52:27Z

Undo revision 217456 by Overthink (talk). Was never wrong in the first place

← Older revision		Revision as of 14:52, 22 November 2025
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	=== Octave stretch ===		=== 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 ===		=== Subsets and supersets ===