4L 3s - Revision history

Overthink: /* Scale tree */ add this

2026-05-30T20:06:33Z

Scale tree: add this

← Older revision		Revision as of 20:06, 30 May 2026
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	\| 6/5 = [[Amity]]/[[hitchcock]] ↑		\| 6/5 = [[Amity]]/[[hitchcock]] ↑
	\| 5/4 = [[Sixix]]		\| 5/4 = [[Sixix]]
			\| 4/3 = [[Supramin]]
	\| 13/8 = Golden 4L 3s (868.3282{{c}})		\| 13/8 = Golden 4L 3s (868.3282{{c}})
	\| 12/5 = [[Hyperkleismic]]		\| 12/5 = [[Hyperkleismic]]

Overthink: - redundant parameters

2026-05-06T23:52:22Z

- redundant parameters

← Older revision		Revision as of 23:52, 6 May 2026
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	\|ja=4L 3s		\|ja=4L 3s
	}}		}}
	{{Infobox MOS		{{Infobox MOS}}
	~~\| Name = smitonic~~
	~~\| Periods = 1~~
	~~\| nLargeSteps = 4~~
	~~\| nSmallSteps = 3~~
	~~\| Equalized = 5~~
	~~\| Collapsed = 3~~
	~~\| Pattern = LLsLsLs~~
	}}

	{{MOS intro}}		{{MOS intro}}

Furcht968 at 18:36, 3 April 2026

2026-04-03T18:36:14Z

← Older revision		Revision as of 18:36, 3 April 2026
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			{{Interwiki
			\|en=4L 3s
			\|es=
			\|de=
			\|ja=4L 3s
			}}
	{{Infobox MOS		{{Infobox MOS
	\| Name = smitonic		\| Name = smitonic

ArrowHead294 at 19:00, 3 March 2025

2025-03-03T19:00:31Z

← Older revision		Revision as of 19:00, 3 March 2025
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	== Scale properties ==		== Scale properties ==
	{{TAMNAMS use}}		{{TAMNAMS use}}
	{{MOS ~~scale properties~~}}
			=== Intervals ===
			{{MOS intervals}}

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

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

	==== Proposed names ====		==== Proposed names ====

ArrowHead294: /* Proposed names */

2025-02-28T18:03:40Z

Proposed names

← Older revision		Revision as of 18:03, 28 February 2025
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	==== Proposed names ====		==== Proposed names ====
	Alexandru Ianu ([[User:Ayceman\|Ayceman]])<ref>Description of ''Sylvian Moon Dance'' mentioning the naming proposal https://musescore.com/user/36772625/scores/6700443 – The theme relates to the mystical nature of the Tribunal and TES lore, which fits smitonic.</ref> has proposed the following mode names relating to the Almsivi in Morrowind (TES):		Alexandru Ianu ([[User:Ayceman\|Ayceman]])<ref>Description of ''Sylvian Moon Dance'' mentioning the naming proposal https://musescore.com/user/36772625/scores/6700443 – The theme relates to the mystical nature of the Tribunal and TES lore, which fits smitonic.</ref> has proposed the following mode names relating to the Almsivi in Morrowind (TES):
	{{MOS modes\|Mode Names=Nerevarine; Vivecan; Lorkhanic; Sothic; Kagrenacan; Almalexian; Dagothic}}		{{MOS modes
			\| Mode Names=Nerevarine $
			Vivecan $
			Lorkhanic $
			Sothic $
			Kagrenacan $
			Almalexian $
			Dagothic $
			}}

	== Theory ==		== Theory ==

ArrowHead294 at 18:03, 28 February 2025

2025-02-28T18:03:07Z

← Older revision		Revision as of 18:03, 28 February 2025
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	4L 3s can be seen as a [[Warped diatonic\|warped diatonic scale]], where one large step of diatonic ([[5L 2s]]) is replaced with a small step.		4L 3s can be seen as a [[Warped diatonic\|warped diatonic scale]], where one large step of diatonic ([[5L 2s]]) is replaced with a small step.

	== Name==		== Name ==
	{{TAMNAMS name}}		{{TAMNAMS name}}

	== Scale properties ==		== Scale properties ==
			{{TAMNAMS use}}
	{{MOS scale properties}}		{{MOS scale properties}}

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	== Scale tree==		== Scale tree==
	{{~~Scale tree~~\|~~4L 3s\|Comments=~~6/5: [[Amity]]/[[hitchcock]]↑;		{{MOS tuning spectrum
	5/4: [[Sixix]];		\| 6/5 = [[Amity]]/[[hitchcock]] ↑
	13/8: Golden 4L 3s (868.~~3282¢~~);		\| 5/4 = [[Sixix]]
	12/5: [[Hyperkleismic]];		\| 13/8 = Golden 4L 3s (868.3282{{c}})
	5/2 [[Orgone]];		\| 12/5 = [[Hyperkleismic]]
	13/5: Golden superkleismic;		\| 5/2 = [[Orgone]]
	8/3: [[Superkleismic]];		\| 13/5 = Golden superkleismic
	11/3: [[Hanson]]/[[keemun]];		\| 8/3 = [[Superkleismic]]
	6/1: [[Oolong]]/[[myna]]↓}}		\| 11/3 = [[Hanson]]/[[keemun]]
			\| 6/1 = [[Oolong]]/[[myna]] ↓
			}}

	== Music ==		== Music ==

ArrowHead294 at 05:40, 25 February 2025

2025-02-25T05:40:37Z

← Older revision		Revision as of 05:40, 25 February 2025
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	{{MOS intro}}		{{MOS intro}}
	4L 3s can be seen as a [[Warped diatonic\|warped diatonic scale]], where one large step of diatonic ([[5L 2s]]) is replaced with a small step.		4L 3s can be seen as a [[Warped diatonic\|warped diatonic scale]], where one large step of diatonic ([[5L 2s]]) is replaced with a small step.

	== Name==		== Name==
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	=== Temperament interpretations ===		=== Temperament interpretations ===
	{{main\|4L 3s/Temperaments}}		{{main\|4L 3s/Temperaments}}
	4L 3s has the following temperament interpretations:		4L 3s has the following temperament interpretations:
	* [[Sixix]], with generators around 338.6{{c}}.		* [[Sixix]], with generators around 338.6{{c}}.
	* [[Orgone]], with generators around 323.4{{c}}.		* [[Orgone]], with generators around 323.4{{c}}.

ArrowHead294 at 15:38, 24 February 2025

2025-02-24T15:38:59Z

← Older revision		Revision as of 15:38, 24 February 2025
Line 10:		Line 10:

	{{MOS intro}}		{{MOS intro}}
	4L 3s can be seen as a [[Warped diatonic\|warped diatonic scale]], where one large step of diatonic ([[5L 2s]]) is replaced with a small step.		4L 3s can be seen as a [[Warped diatonic\|warped diatonic scale]], where one large step of diatonic ([[5L 2s]]) is replaced with a small step.

	== Name==		== Name==
	{{TAMNAMS name}}		{{TAMNAMS name}}
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	== Scale properties ==		== Scale properties ==
	{{MOS scale properties}}		{{MOS scale properties}}


	==== Proposed names ====		==== Proposed names ====
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	{{MOS modes\|Mode Names=Nerevarine; Vivecan; Lorkhanic; Sothic; Kagrenacan; Almalexian; Dagothic}}		{{MOS modes\|Mode Names=Nerevarine; Vivecan; Lorkhanic; Sothic; Kagrenacan; Almalexian; Dagothic}}

	==Theory ==		== Theory ==
	===Low harmonic entropy scales===		=== Low harmonic entropy scales ===
	There are two notable harmonic entropy minima:		There are two notable harmonic entropy minima:
	*[[Kleismic family\|Kleismic temperament]], in which the generator is 6/5 and 6 of them make a 3/1.		* [[Kleismic family\|Kleismic temperament]], in which the generator is 6/5 and 6 of them make a 3/1.
	*[[myna\|Myna temperament]], in which the generator is also 6/5 but it takes 10 of them to make a 6/1, meaning that a larger MOS than 4L 3s is required to reach 3/2 or 4/3.		* [[myna\|Myna temperament]], in which the generator is also 6/5 but it takes 10 of them to make a 6/1, meaning that a larger MOS than 4L 3s is required to reach 3/2 or 4/3.
	===Temperament interpretations===
	~~:''Main article: [[~~4L 3s/Temperaments~~]]''~~		=== Temperament interpretations ===
			{{main\|4L 3s/Temperaments}}
	4L 3s has the following temperament interpretations:		4L 3s has the following temperament interpretations:
	*[[Sixix]], with generators around 338.6¢.		* [[Sixix]], with generators around 338.6{{c}}.
	*[[Orgone]], with generators around 323.4¢.		* [[Orgone]], with generators around 323.4{{c}}.
	*[[Kleismic]], with generators around ~~317¢~~.		* [[Kleismic]], with generators around 317{{c}}.

	Other temperaments, such as [[amity]] and [[myna]], require more than 7 pitches to contain the concordant chords optimized by these temperaments. If restricted to a rank-2 approach, a [[MODMOS]] or a larger MOS gamut is necessary to access these pitches.		Other temperaments, such as [[amity]] and [[myna]], require more than 7 pitches to contain the concordant chords optimized by these temperaments. If restricted to a rank-2 approach, a [[MODMOS]] or a larger MOS gamut is necessary to access these pitches.
	==Tuning ranges==
			== Tuning ranges ==
	{{Todo\|Populate\|comment=Populate with JI ratios from prior edits of this page.\|inline=1}}		{{Todo\|Populate\|comment=Populate with JI ratios from prior edits of this page.\|inline=1}}

	===Simple tunings===		=== Simple tunings ===
	The simplest tunings are those with step ratios 2:1, 3:1, and 3:2, producing 11edo, 15edo, and 18edo, respectively.		The simplest tunings are those with step ratios 2:1, 3:1, and 3:2, producing 11edo, 15edo, and 18edo, respectively.
	{{MOS tunings}}		{{MOS tunings}}

	===Parasoft tunings===		=== Parasoft tunings ===
	Parasoft smitonic tunings can be considered "meantone smitonic" since it has the following features of [[meantone]] diatonic tunings:		Parasoft smitonic tunings can be considered "meantone smitonic" since it has the following features of [[meantone]] diatonic tunings:

	*The major 1-mosstep, or large step, is around [[10/9]] to [[9/8]], thus making it a "meantone".		* The major 1-mosstep, or large step, is around [[10/9]] to [[9/8]], thus making it a "meantone".
	*The augmented 2-mosstep is around the size of a meantone-sized major 3rd and can be used as a stand-in for such.		* The augmented 2-mosstep is around the size of a meantone-sized major 3rd and can be used as a stand-in for such.

	These tunings have a major 4-mosstep and minor 4-mosstep that are about equally off a just 3/2 (~~702¢~~), and they have otherwise fairly convincing versions of both diatonic structure and tertian harmony, provided you frequently modify using the comma-like chromas. For this reason, parasoft might be the most accessible smitonic tuning range.		These tunings have a major 4-mosstep and minor 4-mosstep that are about equally off a just 3/2 (702{{c}}), and they have otherwise fairly convincing versions of both diatonic structure and tertian harmony, provided you frequently modify using the comma-like chromas. For this reason, parasoft might be the most accessible smitonic tuning range.

	Edos include [[18edo]], [[25edo]], and [[43edo]]. Some key considerations include:		Edos include [[18edo]], [[25edo]], and [[43edo]]. Some key considerations include:

	*18edo can be used to make the large and small steps more distinct, or can be considered a distorted 19edo diatonic.		* 18edo can be used to make the large and small steps more distinct, or can be considered a distorted 19edo diatonic.
	**18edo has a major 1-mosstep that is close to 9/8 (~~203¢~~).		** 18edo has a major 1-mosstep that is close to 9/8 (203{{c}}).
	**18edo's major and minor 4-mossteps are both equally off from 12edo's diatonic perfect 5th (~~700¢~~) by 33.3¢.		** 18edo's major and minor 4-mossteps are both equally off from 12edo's diatonic perfect 5th (700{{c}}) by 33.3{{c}}.
	**18edo is also more suited for conventionally jazz styles due to its 6-fold symmetry.		** 18edo is also more suited for conventionally jazz styles due to its 6-fold symmetry.
	*The augmented 2-mosstep of 25edo is very close to 5/4 (~~386¢~~).		* The augmented 2-mosstep of 25edo is very close to 5/4 (386{{c}}).
	{{MOS tunings\|Step Ratios=3/2; 7/5; 4/3}}		{{MOS tunings\|Step Ratios=3/2; 7/5; 4/3}}

	===Hyposoft tunings===		=== Hyposoft tunings ===
	Hyposoft smitonic tunings (3:2 to 2:1) are characterized by generators that are a supraminor 3rd, between ~~327¢~~ and ~~333¢~~. By analogy of parasoft tunings being called "meantone smitonic", these tunings can be considered "[[Gentle region\|neogothic]] smitonic" or "[[archy]] smitonic".		Hyposoft smitonic tunings (3:2 to 2:1) are characterized by generators that are a supraminor 3rd, between 327{{c}} and 333{{c}}. By analogy of parasoft tunings being called "meantone smitonic", these tunings can be considered "[[Gentle region\|neogothic]] smitonic" or "[[archy]] smitonic".

	Edos include [[11edo]] (not shown), [[18edo]], and [[29edo]].		Edos include [[11edo]] (not shown), [[18edo]], and [[29edo]].
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	=== Hypohard tunings===		=== Hypohard tunings===
	Hypohard smitonic tunings (2:1 to 3:1) have generators between ~~320¢~~ and ~~327¢~~. The major 1-mosstep, or large step, tends to approximate [[8/7]] (~~231¢~~) and the major 3-mosstep tends to approximate [[11/8]] (~~551¢~~). [[26edo]] approximates these two intervals very well. These JI approximations are associated with [[orgone]] temperament.		Hypohard smitonic tunings (2:1 to 3:1) have generators between 320{{c}} and 327{{c}}. The major 1-mosstep, or large step, tends to approximate [[8/7]] (231{{c}}) and the major 3-mosstep tends to approximate [[11/8]] (551{{c}}). [[26edo]] approximates these two intervals very well. These JI approximations are associated with [[orgone]] temperament.

	Other hypohard edos include [[11edo]] (not shown), [[15edo]] and [[37edo]].		Other hypohard edos include [[11edo]] (not shown), [[15edo]] and [[37edo]].
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	{{MOS tunings\|Step Ratios=3/1; 5/2; 7/3}}		{{MOS tunings\|Step Ratios=3/1; 5/2; 7/3}}

	===Parahard tunings===		=== Parahard tunings ===
	Parahard smitonic tunings (3:1 to 4:1) have generators between 315.9¢ and ~~320¢~~, putting it close to a pure 6/5 (~~316¢~~). Stacking six generators and octave-reducing approximates 3/2 (~~702¢~~), a diatonic perfect 5th, represented by the diminished 5-mosstep.		Parahard smitonic tunings (3:1 to 4:1) have generators between 315.9{{c}} and 320{{c}}, putting it close to a pure 6/5 (316{{c}}). Stacking six generators and octave-reducing approximates 3/2 (702{{c}}), a diatonic perfect 5th, represented by the diminished 5-mosstep.

	This range contains very accurate edos such as [[53edo]] and [[72edo]], and has very accurate approximations to many [[low-overtone JI]] intervals, namely basic [[5-limit]] ratios and some ratios involving 13. However, 4L 3s only has one interval of 3/2, so it's suggested to use a larger MOS, such as [[4L 7s]], to achieve 5-limit harmony.		This range contains very accurate edos such as [[53edo]] and [[72edo]], and has very accurate approximations to many [[low-overtone JI]] intervals, namely basic [[5-limit]] ratios and some ratios involving 13. However, 4L 3s only has one interval of 3/2, so it's suggested to use a larger MOS, such as [[4L 7s]], to achieve 5-limit harmony.
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	{{MOS tunings\|Step Ratios=4/1; 11/3; 7/2}}		{{MOS tunings\|Step Ratios=4/1; 11/3; 7/2}}

	==Scales==		== Scales ==
	*[[Orgone7]]		* [[Orgone7]]
	*[[Cata7]]		* [[Cata7]]
	*[[Myna7]]		* [[Myna7]]

	== Scale tree==		== Scale tree==
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	11/3: [[Hanson]]/[[keemun]];		11/3: [[Hanson]]/[[keemun]];
	6/1: [[Oolong]]/[[myna]]↓}}		6/1: [[Oolong]]/[[myna]]↓}}
	~~==Music==~~
	*[[City of the Asleep]], [https://cityoftheasleep.bandcamp.com/album/an-amputated-elliptic-knob-of-the-cryptocurve-regenerates "An Amputated Elliptic Knob of the Cryptocurve Regenerates"] (Various orgone edos)
	*[[User:Ks26\|ks26]], [https://www.youtube.com/watch?v=AEnEYk3X1as Ghost Bridge] (11edo)
	*[[User:Ayceman\|Alexandru Ianu]], [https://youtu.be/81uZbsmbet8 Sylvian Moon Dance] (11edo) ([[:File:Sylvian_Moon_Dance.pdf\|sheet music]])

	==References==		== Music ==
			* [[City of the Asleep]], [https://cityoftheasleep.bandcamp.com/album/an-amputated-elliptic-knob-of-the-cryptocurve-regenerates "An Amputated Elliptic Knob of the Cryptocurve Regenerates"] (Various orgone edos)
			* [[User:Ks26\|ks26]], [https://www.youtube.com/watch?v=AEnEYk3X1as Ghost Bridge] (11edo)
			* [[User:Ayceman\|Alexandru Ianu]], [https://youtu.be/81uZbsmbet8 Sylvian Moon Dance] (11edo) ([[:File:Sylvian_Moon_Dance.pdf\|sheet music]])

			== References ==
	<references />		<references />

	[[Category:Smitonic\|*]]<!--Main article-->		[[Category:Smitonic\|*]] <!--Main article-->
	[[Category:7-tone scales]]		[[Category:7-tone scales]]

Lériendil: chromatic pairs link

2024-12-20T04:56:47Z

chromatic pairs link

← Older revision		Revision as of 04:56, 20 December 2024
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	This range contains very accurate edos such as [[53edo]] and [[72edo]], and has very accurate approximations to many [[low-overtone JI]] intervals, namely basic [[5-limit]] ratios and some ratios involving 13. However, 4L 3s only has one interval of 3/2, so it's suggested to use a larger MOS, such as [[4L 7s]], to achieve 5-limit harmony.		This range contains very accurate edos such as [[53edo]] and [[72edo]], and has very accurate approximations to many [[low-overtone JI]] intervals, namely basic [[5-limit]] ratios and some ratios involving 13. However, 4L 3s only has one interval of 3/2, so it's suggested to use a larger MOS, such as [[4L 7s]], to achieve 5-limit harmony.

	These JI approximations are associated with [[kleismic]] temperament, ~~though~~ the 2.3.5.13 extension ~~described here is called~~ [[~~Chromatic pairs~~#Cata\|cata]].		These JI approximations are associated with [[kleismic]] temperament, through the 2.3.5.13 extension known as [[Kleismic family#Cata\|cata]].

	Parahard edos smaller than 53edo include [[15edo]] (not shown), [[19edo]], and [[34edo]].		Parahard edos smaller than 53edo include [[15edo]] (not shown), [[19edo]], and [[34edo]].

Lériendil at 18:39, 6 October 2024

2024-10-06T18:39:15Z

← Older revision		Revision as of 18:39, 6 October 2024
Line 26:		Line 26:
	There are two notable harmonic entropy minima:		There are two notable harmonic entropy minima:
	*[[Kleismic family\|Kleismic temperament]], in which the generator is 6/5 and 6 of them make a 3/1.		*[[Kleismic family\|Kleismic temperament]], in which the generator is 6/5 and 6 of them make a 3/1.
	*[[myna\|Myna temperament]], in which the generator is also 6/5 ~~and~~ 10 of them make a 6/1.		*[[myna\|Myna temperament]], in which the generator is also 6/5 but it takes 10 of them to make a 6/1, meaning that a larger MOS than 4L 3s is required to reach 3/2 or 4/3.
	===Temperament interpretations===		===Temperament interpretations===
	:''Main article: [[4L 3s/Temperaments]]''		:''Main article: [[4L 3s/Temperaments]]''