21L 1s - Revision history

ArrowHead294 at 14:20, 5 May 2025

2025-05-05T14:20:42Z

← Older revision		Revision as of 14:20, 5 May 2025
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	[[Eliora]] proposes the name '''escapist''' for this pattern, referencing the [[escapade]] temperament which is supported by both [[21edo]] and [[22edo]], thus covering the entire tuning spectrum; [[User:Lériendil\|Lériendil]] proposes '''noletic''' for similar reasons, as 9 generators reach a diatonic [[4/3]], supporting the scale [[9ed4/3]] known also as "noleta".		[[Eliora]] proposes the name '''escapist''' for this pattern, referencing the [[escapade]] temperament which is supported by both [[21edo]] and [[22edo]], thus covering the entire tuning spectrum; [[User:Lériendil\|Lériendil]] proposes '''noletic''' for similar reasons, as 9 generators reach a diatonic [[4/3]], supporting the scale [[9ed4/3]] known also as "noleta".

	[[User:Moremajorthanmajor\|Moremajorthanmajor]] proposes the name ''tricesimoprimal quartertonic'' for this pattern since its harmonic entropy minimum corresponds to tempering out the unnamed comma 961/~~960 - the~~ tricesimoprimal quartertones being equated with each other. In addition, both [[21edo]] and [[22edo]], extreme ranges of the MOS do not temper out this comma, while EDOs up to 100-200 which have this scale do.		[[User:Moremajorthanmajor\|Moremajorthanmajor]] proposes the name ''tricesimoprimal quartertonic'' for this pattern since its harmonic entropy minimum corresponds to tempering out the unnamed comma 961/960—the tricesimoprimal quartertones being equated with each other. In addition, both [[21edo]] and [[22edo]], extreme ranges of the MOS do not temper out this comma, while EDOs up to 100-200 which have this scale do.

	== Tuning ranges ==		== Tuning ranges ==
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	== Scale properties ==		== Scale properties ==
	{{TAMNAMS use}}		{{TAMNAMS use}}
	{{MOS ~~data~~}}
			=== Intervals ===
			{{MOS intervals}}

			=== Generator chain ===
			{{MOS genchain}}

			=== Modes ===
			{{MOS mode degrees}}

	== Proposed mode names ===		== Proposed mode names ===

Lériendil at 11:47, 16 March 2025

2025-03-16T11:47:48Z

← Older revision		Revision as of 11:47, 16 March 2025
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	}}		}}
	{{MOS intro}}		{{MOS intro}}
	[[Eliora]] proposes the name '''escapist''' for this pattern, referencing the [[escapade]] temperament which is supported by both [[21edo]] and [[22edo]], thus covering the entire tuning spectrum.		[[Eliora]] proposes the name '''escapist''' for this pattern, referencing the [[escapade]] temperament which is supported by both [[21edo]] and [[22edo]], thus covering the entire tuning spectrum; [[User:Lériendil\|Lériendil]] proposes '''noletic''' for similar reasons, as 9 generators reach a diatonic [[4/3]], supporting the scale [[9ed4/3]] known also as "noleta".

	[[User:Moremajorthanmajor\|Moremajorthanmajor]] proposes the name ''tricesimoprimal quartertonic'' for this pattern since its harmonic entropy minimum corresponds to tempering out the unnamed comma 961/960 - the tricesimoprimal quartertones being equated with each other. In addition, both [[21edo]] and [[22edo]], extreme ranges of the MOS do not temper out this comma, while EDOs up to 100-200 which have this scale do.		[[User:Moremajorthanmajor\|Moremajorthanmajor]] proposes the name ''tricesimoprimal quartertonic'' for this pattern since its harmonic entropy minimum corresponds to tempering out the unnamed comma 961/960 - the tricesimoprimal quartertones being equated with each other. In addition, both [[21edo]] and [[22edo]], extreme ranges of the MOS do not temper out this comma, while EDOs up to 100-200 which have this scale do.

	==Tuning ranges==		== Tuning ranges ==
	The scale's approach to standard harmony can be considered based on the mode.		The scale's approach to standard harmony can be considered based on the mode.

ArrowHead294 at 17:02, 3 March 2025

2025-03-03T17:02:17Z

← Older revision		Revision as of 17:02, 3 March 2025
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	{{MOS intervals}}		{{MOS intervals}}

	==Scale tree==		== Scale tree ==
	{{~~Scale tree~~}}		{{MOS tuning spectrum}}

	==See also==		== See also ==
	*[[32/31]]		* [[32/31]]
	*[[31/30]]		* [[31/30]]
	*[[Escapade]]		* [[Escapade]]

ArrowHead294 at 16:57, 3 March 2025

2025-03-03T16:57:54Z

← Older revision		Revision as of 16:57, 3 March 2025
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	=== Brighter modes ===		=== Brighter modes ===

	==== Diatonic fifth and 65edo (Ultrasoft and supersoft) ====		==== Diatonic fifth and 65edo (Ultrasoft and supersoft) ====
	Between 3\65 and 1\22, 13 steps amount to a diatonic fifth, which corresponds to the ultrasoft step ratio range. In [[65edo]], the fifth produced by 13 steps of the tricesimoprimal quartertonic scale is the same as 3 steps of [[5edo]], and thus is the exact boundary between a fifth proper and a fifth-sixth.		Between 3\65 and 1\22, 13 steps amount to a diatonic fifth, which corresponds to the ultrasoft step ratio range. In [[65edo]], the fifth produced by 13 steps of the tricesimoprimal quartertonic scale is the same as 3 steps of [[5edo]], and thus is the exact boundary between a fifth proper and a fifth-sixth.
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	2 steps act as a pseudo-16/15, and when they actually act as 16/15, 961/960 is tempered out.		2 steps act as a pseudo-16/15, and when they actually act as 16/15, 961/960 is tempered out.

	==~~Modes~~==		== Scale properties ==
			{{TAMNAMS use}}
			{{MOS data}}

			== Proposed mode names ===
	The author proposes naming the modes after Tarot Major Arcana adjectivals based on how many generators down there is since there are 22 of them.		The author proposes naming the modes after Tarot Major Arcana adjectivals based on how many generators down there is since there are 22 of them.

	{\| class="wikitable"		{\| class="wikitable"
	\|+
	~~!Mode~~
	~~!Name~~
	\|-		\|-
	\|~~<nowiki>~~21\|0~~</nowiki>~~		! Mode
	\|Foolish		! Name
			\|-
			\| 21{{pipe}}0
			\| Foolish
	\|-		\|-
	\|~~<nowiki>~~20\|1~~</nowiki>~~		\| 20{{pipe}}1
	\|Magical		\| Magical
	\|-		\|-
	\|~~<nowiki>~~19\|2~~</nowiki>~~		\| 19{{pipe}}2
	\|High Priestess's		\| High Priestess's
	\|-		\|-
	\|~~<nowiki>~~18\|3~~</nowiki>~~		\| 18{{pipe}}3
	\|Empress's		\| Empress's
	\|-		\|-
	\|~~...~~		\| …
	\|~~...~~		\| …
	\|-		\|-
	\|~~<nowiki>~~3\|19~~</nowiki>~~		\| 3{{pipe}}19
	\|Lunar		\| Lunar
	\|-		\|-
	\|~~<nowiki>~~2\|19~~</nowiki>~~		\| 2{{pipe}}19
	\|Solar		\| Solar
	\|-		\|-
	\|~~<nowiki>~~1\|20~~</nowiki>~~		\| 1{{pipe}}20
	\|Judgemental		\| Judgemental
	\|-		\|-
	\|~~<nowiki>~~0\|21~~</nowiki>~~		\| 0{{pipe}}21
	\|Worldwide		\| Worldwide
	\|}		\|}

BudjarnLambeth: == Intervals == {{MOS intervals}}

2024-12-15T08:36:33Z

== Intervals == {{MOS intervals}}

← Older revision		Revision as of 08:36, 15 December 2024
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	\|Worldwide		\|Worldwide
	\|}		\|}

			== Intervals ==
			{{MOS intervals}}

	==Scale tree==		==Scale tree==

Eliora: /* Scale tree */

2024-03-03T00:27:42Z

Scale tree

@@ Line 72: / Line 72: @@
 ==Scale tree==
-{| class="wikitable center-all"
+{{Scale tree}}
-! colspan="6" |Generator
 ==See also==
 *[[32/31]]
 *[[31/30]]
 *[[Escapade]]

Eliora: adopt mos intro

2023-12-11T17:10:12Z

adopt mos intro

← Older revision		Revision as of 17:10, 11 December 2023
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	\| Other names = escapist,<br> tricesimoprimal quartertonic		\| Other names = escapist,<br> tricesimoprimal quartertonic
	}}		}}
	~~21L 1s is the scale which has a generator step between one step of [[21edo]] and one step of [[22edo]].~~		{{MOS intro}}

	[[Eliora]] proposes the name '''escapist''' for this pattern, referencing the [[escapade]] temperament which is supported by both [[21edo]] and [[22edo]], thus covering the entire tuning spectrum.		[[Eliora]] proposes the name '''escapist''' for this pattern, referencing the [[escapade]] temperament which is supported by both [[21edo]] and [[22edo]], thus covering the entire tuning spectrum.

Eliora at 17:05, 11 December 2023

2023-12-11T17:05:25Z

← Older revision		Revision as of 17:05, 11 December 2023
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	==Tuning ranges==		==Tuning ranges==
			The scale's approach to standard harmony can be considered based on the mode.

	=== Diatonic fifth and 65edo (Ultrasoft and supersoft) ===		=== Brighter modes ===

			==== Diatonic fifth and 65edo (Ultrasoft and supersoft) ====
	Between 3\65 and 1\22, 13 steps amount to a diatonic fifth, which corresponds to the ultrasoft step ratio range. In [[65edo]], the fifth produced by 13 steps of the tricesimoprimal quartertonic scale is the same as 3 steps of [[5edo]], and thus is the exact boundary between a fifth proper and a fifth-sixth.		Between 3\65 and 1\22, 13 steps amount to a diatonic fifth, which corresponds to the ultrasoft step ratio range. In [[65edo]], the fifth produced by 13 steps of the tricesimoprimal quartertonic scale is the same as 3 steps of [[5edo]], and thus is the exact boundary between a fifth proper and a fifth-sixth.

	If the pure 32/31 is used as a generator, the resulting fifth is 714.53756 cents, which puts it in the category around Ultrapyth.		If the pure 32/31 is used as a generator, the resulting fifth is 714.53756 cents, which puts it in the category around Ultrapyth.

	=== Fifth-sixth (hard of supersoft) ===		==== Fifth-sixth (hard of supersoft) ====
	From 1\21 to 3\65, 13 steps amount to a fifth-sixth.		From 1\21 to 3\65, 13 steps amount to a fifth-sixth.

	If the pure 31/30 is used as a generator, the resulting fifth-sixth is 737.96915 cents, which puts it in the category around father/petritri/aurora.		If the pure 31/30 is used as a generator, the resulting fifth-sixth is 737.96915 cents, which puts it in the category around father/petritri/aurora.

			=== Darker modes ===
			If instead the small step is stacked down, this enables the scale to approximate the standard 4:5:6 and 10:12:15 triads, as the [[escapade]] temperament does.

			The escapade temperament reaches 4/3 in 9 gensteps, meaning that modes from Hermit (12\|9) onward support a perfect fifth from the tonic. This also enables the modes from Hermit through Temperance (7\|14) to support the major triad, 4:5:6, and from Devil (6\|15) onward to support the minor triad, 10:12:15. The 700 cent fifth is supported in [[108edo]], stacking steps of 5\108 downward.

	== Relation to other equal divisions ==		== Relation to other equal divisions ==
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	\|-		\|-
	\| \|\| \|\| \|\|5\108\|\| \|\| \|\|5\|\|3\|\|1.667		\| \|\| \|\| \|\|5\108\|\| \|\| \|\|5\|\|3\|\|1.667
	\|		\|Inverting the scale yields a 700 cent fifth
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\|12\259\|\|12\|\|7\|\|1.714		\| \|\| \|\| \|\| \|\| \|\|12\259\|\|12\|\|7\|\|1.714

Eliora: not super sure what to do with the mode names and everything given how the page is written off 22L 1s but I see the valuability of this MOS in the context of an escapade-like temperament

2023-02-19T13:09:23Z

not super sure what to do with the mode names and everything given how the page is written off 22L 1s but I see the valuability of this MOS in the context of an escapade-like temperament

← Older revision		Revision as of 13:09, 19 February 2023
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	21L 1s is the scale which has a generator step between one step of [[21edo]] and one step of [[22edo]].		21L 1s is the scale which has a generator step between one step of [[21edo]] and one step of [[22edo]].

	[[Eliora]] proposes the name '''escapist''' for this pattern, referencing the escapade temperament which is supported by both [[21edo]] and [[22edo]], thus covering the entire tuning spectrum.		[[Eliora]] proposes the name '''escapist''' for this pattern, referencing the [[escapade]] temperament which is supported by both [[21edo]] and [[22edo]], thus covering the entire tuning spectrum.

	[[User:Moremajorthanmajor\|Moremajorthanmajor]] proposes the name ''tricesimoprimal quartertonic'' for this pattern since its harmonic entropy minimum corresponds to tempering out the unnamed comma 961/960 - the tricesimoprimal quartertones being equated with each other. In addition, both [[21edo]] and [[22edo]], extreme ranges of the MOS do not temper out this comma, while EDOs up to 100-200 which have this scale do.		[[User:Moremajorthanmajor\|Moremajorthanmajor]] proposes the name ''tricesimoprimal quartertonic'' for this pattern since its harmonic entropy minimum corresponds to tempering out the unnamed comma 961/960 - the tricesimoprimal quartertones being equated with each other. In addition, both [[21edo]] and [[22edo]], extreme ranges of the MOS do not temper out this comma, while EDOs up to 100-200 which have this scale do.
Line 129:		Line 129:
	\|-		\|-
	\| \|\|2\43\|\| \|\| \|\| \|\| \|\|2\|\|1\|\|2.000		\| \|\|2\43\|\| \|\| \|\| \|\| \|\|2\|\|1\|\|2.000
	\|Basic ~~tricesimoprimal quartertonic~~		\|Basic escapist
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\|9\193\|\|9\|\|4\|\|2.250		\| \|\| \|\| \|\| \|\| \|\|9\193\|\|9\|\|4\|\|2.250

Eliora: 31-limit is a bit too complex for scales of this size, refer to the escapade temperament

2023-02-19T13:05:52Z

31-limit is a bit too complex for scales of this size, refer to the escapade temperament

← Older revision		Revision as of 13:05, 19 February 2023
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	\| Collapsed = 1		\| Collapsed = 1
	\| Pattern = LLL...21x...LLLs		\| Pattern = LLL...21x...LLLs
	\| Other names = escapist, tricesimoprimal quartertonic		\| Other names = escapist,<br> tricesimoprimal quartertonic
	}}		}}
	21L 1s is the scale ~~that is most commonly produced by stacking the interval~~ of [[~~32/31~~]] or [[~~31/30~~]].		21L 1s is the scale which has a generator step between one step of [[21edo]] and one step of [[22edo]].

	[[Eliora]] proposes the name '''escapist''' for this pattern, referencing the escapade temperament which is supported by both [[21edo]] and [[22edo]], thus covering the entire tuning spectrum.		[[Eliora]] proposes the name '''escapist''' for this pattern, referencing the escapade temperament which is supported by both [[21edo]] and [[22edo]], thus covering the entire tuning spectrum.
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	*[[32/31]]		*[[32/31]]
	*[[31/30]]		*[[31/30]]
			*[[Escapade]]