User:BudjarnLambeth/1ed28.7c - Revision history

BudjarnLambeth at 00:16, 2 August 2025

2025-08-02T00:16:47Z

← Older revision		Revision as of 00:16, 2 August 2025
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	{{todo\|merge articles\|inline=1\|text=Do not merge until discussion is complete. See [[User talk:BudjarnLambeth/1ed28.7c]]. Merge into [[42edo]]? (in a section titled "[[stretched and compressed tuning]]s", most likely, focusing on the most important aspects)}}		{{todo\|merge articles\|inline=1\|text='''Do not merge until discussion is complete. See [[User talk:BudjarnLambeth/1ed28.7c]]'''. Merge into [[42edo]]? (in a section titled "[[stretched and compressed tuning]]s", most likely, focusing on the most important aspects)}}
	{{Editable user page}}		{{Editable user page}}
	{{Infobox ET\|1ed31444/30927}}		{{Infobox ET\|1ed31444/30927}}

BudjarnLambeth at 00:16, 2 August 2025

2025-08-02T00:16:23Z

← Older revision		Revision as of 00:16, 2 August 2025
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	{{todo\|merge articles\|inline=1\|text=Merge into [[42edo]]? (in a section titled "[[stretched and compressed tuning]]s", most likely, focusing on the most important aspects)}}		{{todo\|merge articles\|inline=1\|text=Do not merge until discussion is complete. See [[User talk:BudjarnLambeth/1ed28.7c]]. Merge into [[42edo]]? (in a section titled "[[stretched and compressed tuning]]s", most likely, focusing on the most important aspects)}}
			{{Editable user page}}
	{{Infobox ET\|1ed31444/30927}}		{{Infobox ET\|1ed31444/30927}}
	'''Arithmetic pitch sequence of 720jot''' ('''APS720jot'''), also known as '''1 equal division of 720jot''' ('''1ed720jot''') or '''720-jot equal temperament''' ('''720jot-et'''), is an [[Equal-step tuning\|equal-step]] scale with steps of 720 [[30103edo\|jots]] (~28.7015 [[cents]]), or each 720th step of [[30103edo]].		'''Arithmetic pitch sequence of 720jot''' ('''APS720jot'''), also known as '''1 equal division of 720jot''' ('''1ed720jot''') or '''720-jot equal temperament''' ('''720jot-et'''), is an [[Equal-step tuning\|equal-step]] scale with steps of 720 [[30103edo\|jots]] (~28.7015 [[cents]]), or each 720th step of [[30103edo]].

Fredg999: Propose merge (similar tunings)

2025-08-01T04:20:14Z

Propose merge (similar tunings)

← Older revision		Revision as of 04:20, 1 August 2025
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			{{todo\|merge articles\|inline=1\|text=Merge into [[42edo]]? (in a section titled "[[stretched and compressed tuning]]s", most likely, focusing on the most important aspects)}}
	{{Infobox ET\|1ed31444/30927}}		{{Infobox ET\|1ed31444/30927}}
	'''Arithmetic pitch sequence of 720jot''' ('''APS720jot'''), also known as '''1 equal division of 720jot''' ('''1ed720jot''') or '''720-jot equal temperament''' ('''720jot-et'''), is an [[Equal-step tuning\|equal-step]] scale with steps of 720 [[30103edo\|jots]] (~28.7015 [[cents]]), or each 720th step of [[30103edo]].		'''Arithmetic pitch sequence of 720jot''' ('''APS720jot'''), also known as '''1 equal division of 720jot''' ('''1ed720jot''') or '''720-jot equal temperament''' ('''720jot-et'''), is an [[Equal-step tuning\|equal-step]] scale with steps of 720 [[30103edo\|jots]] (~28.7015 [[cents]]), or each 720th step of [[30103edo]].

BudjarnLambeth: BudjarnLambeth moved page 1ed28.7c to User:BudjarnLambeth/1ed28.7c

2025-05-18T13:12:33Z

BudjarnLambeth moved page 1ed28.7c to User:BudjarnLambeth/1ed28.7c

← Older revision	Revision as of 13:12, 18 May 2025
(No difference)

BudjarnLambeth: /* Theory */

2024-12-12T23:03:17Z

Theory

← Older revision		Revision as of 23:03, 12 December 2024
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	It is a kind of opposite twin to the scale [[1ed28.5c\|APS715jot]], 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).		It is a kind of opposite twin to the scale [[1ed28.5c\|APS715jot]], 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’s step size is very close to that of [[42ed257/128]] and [[~~191zpi~~]].		42ed257/128’s step size is very close to that of [[42ed257/128]] and [[zpi\|189zpi]].

	See [[Table of stretched 42edo tunings]] for more.		See [[Table of stretched 42edo tunings]] for more.

BudjarnLambeth: /* Theory */

2024-12-12T22:56:15Z

Theory

← Older revision		Revision as of 22:56, 12 December 2024
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	==Theory==		==Theory==
	~~''See also:~~ [[~~Table~~ of ~~stretched 42edo tunings~~]]''		APS720jot divides [[2/1]] into ~41.8097 equal parts, making it close to [[42edo]], but with [[pseudo-octave\|impure octaves]] and better approximations of harmonics [[3/1]] and [[5/1]].

	~~APS720jot divides~~ [[~~2/1~~]] ~~into ~41.8097 equal parts~~, ~~making it close to~~ [[~~42edo~~]], but ~~with [[pseudo-octave\|impure octaves]] and better approximations of~~ harmonics ~~[[3/1]] and [[5/1]]~~.		It is a kind of opposite twin to the scale [[1ed28.5c\|APS715jot]], 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).

	It is ~~a kind~~ of ~~opposite twin to the scale~~ [[~~191zpi~~]]~~. 191zpi makes~~ [[~~42edo~~]] ~~into a better 2.3.5.11.13 tuning, while APS720jot 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 [[42ed257/128]] and [[191zpi]].

	~~APS720jot is very similar to~~ [[~~42ed257/128~~]]~~, 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===		===Harmonics===

BudjarnLambeth: add music

2024-12-09T07:59:41Z

add music

← Older revision		Revision as of 07:59, 9 December 2024
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	* [[Lumatone]]		* [[Lumatone]]
	** APS720jot can use most types of [[Lumatone mapping for 42edo]]		** APS720jot can use most types of [[Lumatone mapping for 42edo]]

			== Music ==
			* ''[https://www.youtube.com/watch?v=vdjhC9i5KF4 Four Short Experiments in Octave Stretched 42edo (Dec 2024)]'' - [[Budjarn Lambeth]]

	== See also ==		== See also ==

BudjarnLambeth: /* Scales */

2024-12-09T06:46:09Z

Scales

← Older revision		Revision as of 06:46, 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 */ convert new scales to same format as old scales

2024-12-09T06:44:36Z

Scales: convert new scales to same format as old scales

← Older revision		Revision as of 06:44, 9 December 2024
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	; Subsets of MOS scales		; Subsets of MOS scales
	''(Names used are [[Template:Idiosyncratic\|idiosyncratic]]~~. Cent values rounded to 1 dec pl~~.)''		''(Names used are [[Template:Idiosyncratic\|idiosyncratic]].)''
	* Eugene/Tritikleismic[9]		* Eugene/Tritikleismic[9]
	** Groovy aeolian pentatonic: ~~315.7, 487.9, 717.5, 803.~~6~~, 1205.5~~		** Groovy aeolian pentatonic: 11 6 8 3 14
	** ~~Major pseudo-~~[[~~pelog~~]]: ~~401.~~8~~, 487.9, 717.5, 1119.4, 1205.5~~		** [[Otonal]] mixolydian pentatonic: 14 3 8 11 6
	** Pseudo-[[equipentatonic]]: ~~315.7, 487.9, 717.5, 889.7, 1205.5~~		** Pseudo-[[equipentatonic]]: 11 6 8 6 11
	** Septimal melodic minor pentatonic: ~~229.6, 315.7, 717.5, 1119.4, 1205.5~~		** Septimal melodic minor pentatonic: 8 3 14 14 3
	** Septimal Picardy pentatonic: ~~229.6, 401.~~8~~, 717.5, 803.~~6~~, 1205.5~~		** Septimal Picardy pentatonic: 8 6 11 3 14
	** Undecimal lydian-aeolian pentatonic: ~~229.~~6~~, 631.4, 1033.3, 1205.5~~		** Undecimal lydian-aeolian pentatonic: 8 14 3 11 6
	** Yokai pentatonic: ~~86.1, 487.9, 717.5, 803.6, 1205.5~~		** Yokai pentatonic: 3 14 8 3 14

BudjarnLambeth: /* Scales */

2024-12-09T06:18:54Z

Scales

← Older revision		Revision as of 06:18, 9 December 2024
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	; Subsets of [[MOS ~~scale]]s~~		; Subsets of MOS scales
	''(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]

← Older revision		Revision as of 00:16, 2 August 2025
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	{{todo\|merge articles\|inline=1\|text=Merge into [[42edo]]? (in a section titled "[[stretched and compressed tuning]]s", most likely, focusing on the most important aspects)}}		{{todo\|merge articles\|inline=1\|text=Do not merge until discussion is complete. See [[User talk:BudjarnLambeth/1ed28.7c]]. Merge into [[42edo]]? (in a section titled "[[stretched and compressed tuning]]s", most likely, focusing on the most important aspects)}}
			{{Editable user page}}
	{{Infobox ET\|1ed31444/30927}}		{{Infobox ET\|1ed31444/30927}}
	'''Arithmetic pitch sequence of 720jot''' ('''APS720jot'''), also known as '''1 equal division of 720jot''' ('''1ed720jot''') or '''720-jot equal temperament''' ('''720jot-et'''), is an [[Equal-step tuning\|equal-step]] scale with steps of 720 [[30103edo\|jots]] (~28.7015 [[cents]]), or each 720th step of [[30103edo]].		'''Arithmetic pitch sequence of 720jot''' ('''APS720jot'''), also known as '''1 equal division of 720jot''' ('''1ed720jot''') or '''720-jot equal temperament''' ('''720jot-et'''), is an [[Equal-step tuning\|equal-step]] scale with steps of 720 [[30103edo\|jots]] (~28.7015 [[cents]]), or each 720th step of [[30103edo]].

← Older revision		Revision as of 04:20, 1 August 2025
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			{{todo\|merge articles\|inline=1\|text=Merge into [[42edo]]? (in a section titled "[[stretched and compressed tuning]]s", most likely, focusing on the most important aspects)}}
	{{Infobox ET\|1ed31444/30927}}		{{Infobox ET\|1ed31444/30927}}
	'''Arithmetic pitch sequence of 720jot''' ('''APS720jot'''), also known as '''1 equal division of 720jot''' ('''1ed720jot''') or '''720-jot equal temperament''' ('''720jot-et'''), is an [[Equal-step tuning\|equal-step]] scale with steps of 720 [[30103edo\|jots]] (~28.7015 [[cents]]), or each 720th step of [[30103edo]].		'''Arithmetic pitch sequence of 720jot''' ('''APS720jot'''), also known as '''1 equal division of 720jot''' ('''1ed720jot''') or '''720-jot equal temperament''' ('''720jot-et'''), is an [[Equal-step tuning\|equal-step]] scale with steps of 720 [[30103edo\|jots]] (~28.7015 [[cents]]), or each 720th step of [[30103edo]].