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{{Infobox MOS
{{Interwiki
| Name = smitonic
|en=4L 3s
| Periods = 1
|es=
| nLargeSteps = 4
|de=
| nSmallSteps = 3
|ja=4L 3s
| Equalized = 5
| Collapsed = 3
| Pattern = LLsLsLs
}}
}}
{{Infobox MOS}}


{{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==
[[TAMNAMS]] suggests the temperament-agnostic name '''smitonic''' ''smy-TON-ik'' /smaɪˈtɒnɪk/ for this scale. The name is derived from 'sharp minor third', since the central range for the dark generator (320¢ to 333.3¢) is significantly sharp of [[6/5]] (just minor 3rd, 315.6¢).
== Intervals==
:''This article assumes [[TAMNAMS]] for naming step ratios, intervals, and scale degrees.''
Names for this scale's intervals (mossteps) and scale degrees (mosdegrees) are based on the number of large and small steps from the root, starting at 0 (0-mosstep and 0-mosdegree) for the unison, per TAMNAMS. Ordinal names, such as mos-1st for the unison, are discouraged for non-diatonic MOS scales.


Except for the unison and octave, all [[Interval class|interval classes]] have two [[Interval variety|varieties]] or sizes, denoted using the terms ''major'' and ''minor'' for the large and small sizes, respectively. The exception to this rule are the generators, which use the terms ''augmented'', ''perfect'', and ''diminished'' instead.
== Name ==
{| class="wikitable"
{{TAMNAMS name}}
!Interval class
!Specific intervals
!Size (in ascending order)
|-
|'''0-smistep'''
|'''Perfect 0-smistep (unison)'''
|0
|-
| rowspan="2" |1-smistep
|Minor 1-smistep
|s
|-
|Major 1-smistep
|L
|-
| rowspan="2" |'''2-smistep'''
|Perfect 2-smistep
|L + s
|-
|Augmented 2-smistep
|2L
|-
| rowspan="2" |3-smistep
|Minor 3-smistep
|L + 2s
|-
|Major 3-smistep
|2L + s
|-
| rowspan="2" |4-smistep
|Minor 4-smistep
|2L + 2s
|-
|Major 4-smistep
|3L + s
|-
| rowspan="2" |'''5-smistep'''
|Diminished 5-smistep
|2L + 3s
|-
|Perfect 5-smistep
|3L + 2s
|-
| rowspan="2" |6-smistep
|Minor 6-smistep
|3L + 3s
|-
|Major 6-smistep
|4L + 2s
|-
|'''7-smistep (octave)'''
|'''Perfect 7-smistep (octave)'''
|4L + 3s
|}
A 7-note scale using these intervals will typically use scale degrees that represents one size from each interval class, with the true MOS upholding the step pattern of LLsLsLs, or some rotation thereof. MODMOS scales may be formed this way without upholding the step pattern, thereby creating a non-MOS pattern such as LLLssLs, or may include alterations that exceed the two varieties typical of a MOS scale.


==Notation==
== Scale properties ==
For this article, note names are based on diamond-MOS notation, where the naturals JKLMNOP are applied to the step pattern LsLsLsL and the accidentals & (pronounced "am" or "amp") and @ (pronounced "at") are used to represent sharps and flats respectively. Thus, the basic gamut for 4L 3s is the following:
{{TAMNAMS use}}


{{MOS gamut}}
=== Intervals ===
==Theory ==
{{MOS intervals}}
===Low harmonic entropy scales===
 
=== Generator chain ===
{{MOS genchain}}
 
=== Modes ===
{{MOS mode degrees}}
 
==== 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):
{{MOS modes
| Mode Names=Nerevarine $
Vivecan $
Lorkhanic $
Sothic $
Kagrenacan $
Almalexian $
Dagothic $
}}
 
== Theory ==
=== 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 10 of them make a 6/1, resulting in the intervals 4/3 and 3/2 being absent.
* [[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&nbsp;3s is required to reach 3/2 or 4/3.
===Temperament interpretations===
 
:''Main article: [[4L 3s/Temperaments]]''
=== Temperament interpretations ===
4L 3s has the following temperament interpretations:
{{main|4L&nbsp;3s/Temperaments}}
*[[Sixix]], with generators around 338.6¢.
4L&nbsp;3s has the following temperament interpretations:
*[[Orgone]], with generators around 323.4¢.
* [[Sixix]], with generators around 338.6{{c}}.
*[[Kleismic]], with generators around 317¢.
* [[Orgone]], with generators around 323.4{{c}}.
* [[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==
===Simple tunings===
The basic tuning for 4L 3s has a large and small step size of 2 and 1 respectively, which is supported by 11edo. Other small edos include [[15edo]] and [[18edo]].{{MOS degrees|Step Ratio=2/1; 3/1; 3/2}}
===Parasoft tunings===
Parasoft smitonic tunings (4:3 to 3:2) 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".
== Tuning ranges ==
*The augmented 2-mosstep is around the size of a meantone-sized major 3rd and can be used as a stand-in for such.
{{Todo|Populate|comment=Populate with JI ratios from prior edits of this page.|inline=1}}


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.
=== Simple tunings ===
The simplest tunings are those with step ratios 2:1, 3:1, and 3:2, producing 11edo, 15edo, and 18edo, respectively.
{{MOS tunings}}
 
=== Parasoft 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 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{{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}}).
*The various interval flavors separated by a chroma shows that parasoft smitonic is a useful [[cluster MOS]]. However, many of these intervals lack simple JI interpretations.
{{MOS tunings|Step Ratios=3/2; 7/5; 4/3}}
{{MOS degrees|Step Ratio=3/2; 4/3; 7/5|Genchain Extend=9}}
 
===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]].
{{MOS degrees|Step Ratio=3/2; 5/3|Genchain Extend=3}}
 
{{MOS tunings|Step Ratios=3/2; 5/3; 7/4}}
 
=== 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]].
{{MOS degrees|Step Ratio=3/1; 5/2; 7/3|Genchain Extend=3}}
 
===Parahard tunings===
{{MOS tunings|Step Ratios=3/1; 5/2; 7/3}}
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 tunings ===
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.


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]].
{{MOS degrees|Step Ratio=4/1; 7/2; 11/3; 15/4|Genchain Extend=3|Prefix=smi}}
==Modes==
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 tunings|Step Ratios=4/1; 11/3; 7/2}}
==Scales==
 
===Subset and superset scales===
== Scales ==
4L 3s has a parent scale of [[1L 3s]], a tetratonic scale, meaning 1L 3s is a subset. 4L 3s also has two child scales, which are supersets of 4L 3s:
* [[Orgone7]]
*[[7L 4s]], a smitonic chromatic scale produced using soft-of-basic step ratios.
* [[Cata7]]
*[[4L 7s]], a smitonic chromatic scale produced using hard-of-basic step ratios.
* [[Myna7]]
11edo, the equalized form of both 7L 4s and 4L 7s, is also a superset of 4L 3s.
===Scala files===
*[[Orgone7]]
*[[Cata7]]
*[[Myna7]]


== Scale tree==
== Scale tree==
{{Scale tree|4L 3s|Comments=6/5: [[Amity]]/[[hitchcock]]↑;
{{MOS tuning spectrum
5/4: [[Sixix]];
| 6/5 = [[Amity]]/[[hitchcock]]&nbsp;↑
13/8: Golden 4L 3s (868.3282¢);
| 5/4 = [[Sixix]]
12/5: [[Hyperkleismic]];
| 4/3 = [[Supramin]]
5/2 [[Orgone]];
| 13/8 = Golden 4L&nbsp;3s (868.3282{{c}})
13/5: Golden superkleismic;
| 12/5 = [[Hyperkleismic]]
8/3: [[Superkleismic]];
| 5/2 = [[Orgone]]
11/3: [[Hanson]]/[[keemun]];
| 13/5 = Golden superkleismic
6/1: [[Oolong]]/[[myna]]↓}}
| 8/3 = [[Superkleismic]]
==Music==
| 11/3 = [[Hanson]]/[[keemun]]
*[[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)
| 6/1 = [[Oolong]]/[[myna]]&nbsp;↓
*[[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]])
 
*[[File:Sixix Fugue.mp3|256x256px]] A fugue in [[18edo]] smitonic functional harmony (WIP)
== Music ==
==See also==
* [[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)
Approaches:
* [[User:Ks26|ks26]], [https://www.youtube.com/watch?v=AEnEYk3X1as Ghost Bridge] (11edo)
*[[4L 3s/Inthar's approach]]
* [[User:Ayceman|Alexandru Ianu]], [https://youtu.be/81uZbsmbet8 Sylvian Moon Dance] (11edo) ([[:File:Sylvian_Moon_Dance.pdf|sheet music]])
==References==
 
== References ==
<references />
<references />


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