User:BudjarnLambeth/42ed257/128 - Revision history

Fredg999: Fix infobox ET parameters

2025-07-29T19:12:24Z

Fix infobox ET parameters

← Older revision		Revision as of 19:12, 29 July 2025
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	{{Infobox ET}}		{{Infobox ET\|42ed257/128}}
	'''42ed257/128''' is the [[Ed257/128\|equal division of the interval 257/128]] into forty-two parts of 28.73 [[cents]] each, corresponding to ~41.77[[edo]].		'''42ed257/128''' is the [[Ed257/128\|equal division of the interval 257/128]] into forty-two parts of 28.73 [[cents]] each, corresponding to ~41.77[[edo]].

BudjarnLambeth: BudjarnLambeth moved page 42ed257/128 to User:BudjarnLambeth/42ed257/128

2025-05-18T13:11:58Z

BudjarnLambeth moved page 42ed257/128 to User:BudjarnLambeth/42ed257/128

← Older revision	Revision as of 13:11, 18 May 2025
(No difference)

BudjarnLambeth: /* Scales */

2024-12-13T06:59:42Z

Scales

← Older revision		Revision as of 06:59, 13 December 2024
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	; [[Tonality diamond]]s		; [[Tonality diamond]]s
	These take advantage of 42ed257/128’s improved approximations of the full 47-limit compared to 42edo, especially its improved 3/1 and 5/1.		These take advantage of 42ed257/128’s improved approximations of the full 7-limit compared to 42edo, especially its improved 3/1 and 5/1.
	* [[Diamond7]]: '''8 1 2 2 4 3 2 2 4 3 2 2 8'''		* [[Diamond7]]: '''8 1 2 2 4 3 2 2 4 3 2 2 8'''
	* [[Diamond9]]: '''6 1 1 1 2 2 2 2 3 2 2 3 1 3 1 2 1 1 6'''		* [[Diamond9]]: '''6 1 1 1 2 2 2 2 3 2 2 3 1 3 1 2 1 1 6'''

BudjarnLambeth: /* Harmonics */

2024-12-12T22:53:58Z

Harmonics

← Older revision		Revision as of 22:53, 12 December 2024
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	=== Harmonics ===		=== Harmonics ===
	~~''See also:~~ [[~~Table of stretched 42edo tunings~~]]''		42ed257/128 is a kind of opposite twin to the scale [[ed255/128#42ed255/128\|42ed255/128]], as they improve 42edo’s [[JI]] approximation by about the same amount, but in opposite directions (those harmonics which are slightly sharp in one are slightly flat in the other).

	42ed257/~~128~~ is ~~a kind~~ of ~~opposite twin to the scale~~ [[~~191zpi~~]]~~. 191zpi makes~~ [[~~42edo~~]] ~~into a better 2.3.5.11.13 tuning, while 42ed257/128 makes 42edo into a better 2.3.5.7.17 tuning. They both improve 42edo but in opposite directions~~.		42ed257/128’s step size is very close to that of [[1ed28.7c\|APS720jot]] and [[zpi\|189zpi]].

	~~42ed257/128 is very similar to~~ [[~~1ed28.7c\|APS720jot~~]]~~, which achieves many of the same aims. The difference is that 42ed257/128 has better harmonics 3, 5 and 7, while APS720jot has better harmonics 2, 11 and 13~~.		See [[Table of stretched 42edo tunings]] for more.

	{{Harmonics in equal\|42\|257\|128\|intervals=prime}}		{{Harmonics in equal\|42\|257\|128\|intervals=prime}}

BudjarnLambeth: /* Scales */

2024-12-09T06:45:50Z

Scales

← Older revision		Revision as of 06:45, 9 December 2024
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	''(Names used are [[Template:Idiosyncratic\|idiosyncratic]].)''		''(Names used are [[Template:Idiosyncratic\|idiosyncratic]].)''
	* Eugene/Tritikleismic[9]		* Eugene/Tritikleismic[9]
	** Groovy aeolian pentatonic: 11 6 8 3 14		** Groovy aeolian pentatonic: '''11 6 8 3 14'''
	** [[Otonal]] mixolydian pentatonic: 14 3 8 11 6		** [[Otonal]] mixolydian pentatonic: '''14 3 8 11 6'''
	** Pseudo-[[equipentatonic]]: 11 6 8 6 11		** Pseudo-[[equipentatonic]]: '''11 6 8 6 11'''
	** Septimal melodic minor pentatonic: 8 3 14 14 3		** Septimal melodic minor pentatonic: '''8 3 14 14 3'''
	** Septimal Picardy pentatonic: 8 6 11 3 14		** Septimal Picardy pentatonic: '''8 6 11 3 14'''
	** Undecimal lydian-aeolian pentatonic: 8 14 3 11 6		** Undecimal lydian-aeolian pentatonic: '''8 14 3 11 6'''
	** Yokai pentatonic: 3 14 8 3 14		** Yokai pentatonic: '''3 14 8 3 14'''

BudjarnLambeth: /* Scales */ able to import these now that they're in the generic format

2024-12-09T06:45:20Z

Scales: able to import these now that they're in the generic format

← Older revision		Revision as of 06:45, 9 December 2024
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	* Qeema/Skateboard[19]: '''2 2 3 2 2 2 2 3 2 2 2 3 2 2 2 2 3 2 2'''		* Qeema/Skateboard[19]: '''2 2 3 2 2 2 2 3 2 2 2 3 2 2 2 2 3 2 2'''
	* ''Seville/Sevond is not available because it is generated by 42edo’s sharp fifth, and 42ed257/128 is designed to improve 42edo’s flat fifth instead''		* ''Seville/Sevond is not available because it is generated by 42edo’s sharp fifth, and 42ed257/128 is designed to improve 42edo’s flat fifth instead''


			; Subsets of MOS scales
			''(Names used are [[Template:Idiosyncratic\|idiosyncratic]].)''
			* Eugene/Tritikleismic[9]
			** Groovy aeolian pentatonic: 11 6 8 3 14
			** [[Otonal]] mixolydian pentatonic: 14 3 8 11 6
			** Pseudo-[[equipentatonic]]: 11 6 8 6 11
			** Septimal melodic minor pentatonic: 8 3 14 14 3
			** Septimal Picardy pentatonic: 8 6 11 3 14
			** Undecimal lydian-aeolian pentatonic: 8 14 3 11 6
			** Yokai pentatonic: 3 14 8 3 14

BudjarnLambeth: /* Scales */ Added to the wrong page

2024-12-09T06:17:50Z

Scales: Added to the wrong page

@@ Line 76: / Line 76: @@
 == Scales ==
 ; [[MOS scale]]s
 * Eugene/Tritikleismic[9]: '''3 8 3 3 8 3 3 8 3'''
@@ Line 86: / Line 83: @@
 * Qeema/Skateboard[19]: '''2 2 3 2 2 2 2 3 2 2 2 3 2 2 2 2 3 2 2'''
 * ''Seville/Sevond is not available because it is generated by 42edo’s sharp fifth, and 42ed257/128 is designed to improve 42edo’s flat fifth instead''

BudjarnLambeth: /* Scales */

2024-12-09T06:10:00Z

Scales

← Older revision		Revision as of 06:10, 9 December 2024
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	''(Names used are [[Template:Idiosyncratic\|idiosyncratic]]. Cent values rounded to 1 dec pl.)''		''(Names used are [[Template:Idiosyncratic\|idiosyncratic]]. Cent values rounded to 1 dec pl.)''
	* Eugene/Tritikleismic[9]		* Eugene/Tritikleismic[9]
	** Yokai pentatonic: 86.1, 487.9, 717.5, 803.6, 1205.5
	** Septimal Picardy pentatonic: 229.6, 401.8, 717.5, 803.6, 1205.5
	** Groovy aeolian pentatonic: 315.7, 487.9, 717.5, 803.6, 1205.5		** Groovy aeolian pentatonic: 315.7, 487.9, 717.5, 803.6, 1205.5
			** Major pseudo-[[pelog]]: 401.8, 487.9, 717.5, 1119.4, 1205.5
	** Pseudo-[[equipentatonic]]: 315.7, 487.9, 717.5, 889.7, 1205.5		** Pseudo-[[equipentatonic]]: 315.7, 487.9, 717.5, 889.7, 1205.5
			** Septimal melodic minor pentatonic: 229.6, 315.7, 717.5, 1119.4, 1205.5
			** Septimal Picardy pentatonic: 229.6, 401.8, 717.5, 803.6, 1205.5
	** Undecimal lydian-aeolian pentatonic: 229.6, 631.4, 1033.3, 1205.5		** Undecimal lydian-aeolian pentatonic: 229.6, 631.4, 1033.3, 1205.5
	** ~~Septimal melodic minor~~ pentatonic: ~~229~~.~~6, 315.7, 717.5, 1119.4, 1205.5~~		** Yokai pentatonic: 86.1, 487.9, 717.5, 803.6, 1205.5
	** Major pseudo-[[pelog]]: 401.8, 487.9, 717.5, ~~1119~~.4, 1205.5

BudjarnLambeth: /* Scales */

2024-12-09T06:09:27Z

Scales

← Older revision		Revision as of 06:09, 9 December 2024
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	** Septimal Picardy pentatonic: 229.6, 401.8, 717.5, 803.6, 1205.5		** Septimal Picardy pentatonic: 229.6, 401.8, 717.5, 803.6, 1205.5
	** Groovy aeolian pentatonic: 315.7, 487.9, 717.5, 803.6, 1205.5		** Groovy aeolian pentatonic: 315.7, 487.9, 717.5, 803.6, 1205.5
	** Pseudo-[[~~equipentatoic~~]]: 315.7, 487.9, 717.5, 889.7, 1205.5		** Pseudo-[[equipentatonic]]: 315.7, 487.9, 717.5, 889.7, 1205.5
	** Undecimal lydian-aeolian pentatonic: 229.6, 631.4, 1033.3, 1205.5		** Undecimal lydian-aeolian pentatonic: 229.6, 631.4, 1033.3, 1205.5
	** Septimal melodic minor pentatonic: 229.6, 315.7, 717.5, 1119.4, 1205.5		** Septimal melodic minor pentatonic: 229.6, 315.7, 717.5, 1119.4, 1205.5

BudjarnLambeth: /* Scales */ Added subsets of tritikleismic9: will eventually change these to 1 2 1 2 format instead of 100.0 200.0 300.0 format but just getting them written down for now to start

2024-12-09T06:09:11Z

Scales: Added subsets of tritikleismic9: will eventually change these to 1 2 1 2 format instead of 100.0 200.0 300.0 format but just getting them written down for now to start

← Older revision		Revision as of 06:09, 9 December 2024
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	* Qeema/Skateboard[19]: '''2 2 3 2 2 2 2 3 2 2 2 3 2 2 2 2 3 2 2'''		* Qeema/Skateboard[19]: '''2 2 3 2 2 2 2 3 2 2 2 3 2 2 2 2 3 2 2'''
	* ''Seville/Sevond is not available because it is generated by 42edo’s sharp fifth, and 42ed257/128 is designed to improve 42edo’s flat fifth instead''		* ''Seville/Sevond is not available because it is generated by 42edo’s sharp fifth, and 42ed257/128 is designed to improve 42edo’s flat fifth instead''


			; Subsets of [[MOS scale]]s
			''(Names used are [[Template:Idiosyncratic\|idiosyncratic]]. Cent values rounded to 1 dec pl.)''
			* Eugene/Tritikleismic[9]
			** Yokai pentatonic: 86.1, 487.9, 717.5, 803.6, 1205.5
			** Septimal Picardy pentatonic: 229.6, 401.8, 717.5, 803.6, 1205.5
			** Groovy aeolian pentatonic: 315.7, 487.9, 717.5, 803.6, 1205.5
			** Pseudo-[[equipentatoic]]: 315.7, 487.9, 717.5, 889.7, 1205.5
			** Undecimal lydian-aeolian pentatonic: 229.6, 631.4, 1033.3, 1205.5
			** Septimal melodic minor pentatonic: 229.6, 315.7, 717.5, 1119.4, 1205.5
			** Major pseudo-[[pelog]]: 401.8, 487.9, 717.5, 1119.4, 1205.5