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{{Infobox MOS|Tuning=4L 3s|debug=true}}
{{User:Ganaram inukshuk/Template:Rewrite draft
|4L 3s|compare=https://en.xen.wiki/w/Special:ComparePages?page1=4L+3s&rev1=&page2=User%3AGanaram+inukshuk%2F4L+3s&rev2=&action=&diffonly=&unhide=
|changes=see what the page looks like with proposed changes (scale characteristics section, new intro wording); see what it looks like with a quickstart guide}}
{{Has quickstart|Quickstart guide for 4L 3s}}
{{Infobox MOS|debug=1|Tuning=4L 3s}}
'''4L 3s''', named '''smitonic''', is a moment-of-symmetry scale characterized by having 4 large steps and 3 small steps distributed as evenly as possible within the octave. Generators that produce this scale range from (bright-gen-range), or from (dark-gen-range).


:''This is a test page. For the main page, see [[4L 3s]].''
{{MOS intro|Scale Signature=4L 3s}}
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 ==
== Scale characteristics ==
[[TAMNAMS]] suggests the 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¢).
''This article assumes TAMNAMS naming conventions for the following: step ratios, intervals, scale degrees, modes, step patterns. For more information, see the respective links.''
 
== Notation ==
 
: ''This article assumes [[TAMNAMS]] and [[Diamond-mos notation|diamond-MOS notation]] for naming intervals, scale degrees, and note names.''
 
=== Interval names ===
Names for intervals and scale degrees are based on [[TAMNAMS]], where names for mossteps (intervals) and mosdegrees (scale degrees) are numbered starting at 0 for the unison. Ordinal names, such as mos-1st for the unison, are discouraged for non-diatonic MOS scales.


Being a moment-of-symmetry scale, every [[interval class]] of 4L 3s, except for the unison and octave, has two [[Interval variety|varieties]] (or sizes), whose [[Interval quality|relative qualities]] are denoted as major or minor, or augmented, perfect, and diminished for the generators.
===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 sizes===
{| class="wikitable"
{| class="wikitable"
|+TODO: make this into a template
|+Intervals of 4L 3s
! rowspan="2" |Interval class
! colspan="2" |Intervals
! colspan="2" |Large variety
! colspan="2" |Size
! colspan="2" |Small variety
! rowspan="2" |Abbrev.
|-
|-
!Size
!Generic
!Quality
!Specific
!Size
!Steps
!Quality
!Range in cents
|-
|-
|'''0-mosstep (unison)'''
|'''0-smistep (root)'''
|Perfect 0-smistep
|0
|0
|Perfect
|0.0¢
|0
|P0ms
|Perfect
|-
| rowspan="2" |1-smistep
|Small 1-smistep
|s
|0.0¢ to 171.4¢
|s1ms
|-
|-
|1-mosstep
|Large 1-smistep
|L
|L
|Major
|171.4¢ to 300.0¢
|s
|L1ms
|Minor
|-
| rowspan="2" |'''2-smistep'''
|'''Small 2-smistep'''
|L + s
|300.0¢ to 342.9¢
|s2ms
|-
|-
|2-mosstep
|Large 2-smistep
|L+s
|Augmented
|2L
|2L
|Perfect
|342.9¢ to 600.0¢
|L2ms
|-
|-
|3-mosstep
| rowspan="2" |3-smistep
|Small 3-smistep
|L + 2s
|L + 2s
|Major
|300.0¢ to 514.3¢
|s3ms
|-
|Large 3-smistep
|2L + s
|2L + s
|Minor
|514.3¢ to 600.0¢
|L3ms
|-
|-
|4-mosstep
| rowspan="2" |4-smistep
|Small 4-smistep
|2L + 2s
|2L + 2s
|Perfect
|600.0¢ to 685.7¢
|3L + 1s
|s4ms
|Minor
|-
|-
|5-mosstep
|Large 4-smistep
|3L + s
|685.7¢ to 900.0¢
|L4ms
|-
| rowspan="2" |'''5-smistep'''
|Small 5-smistep
|2L + 3s
|2L + 3s
|Perfect
|600.0¢ to 857.1¢
|s5ms
|-
|'''Large 5-smistep'''
|3L + 2s
|3L + 2s
|Diminished
|857.1¢ to 900.0¢
|L5ms
|-
|-
|6-mosstep
| rowspan="2" |6-smistep
|2L + 3s
|Small 6-smistep
|Major
|3L + 3s
|3L + 3s
|Minor
|900.0¢ to 1028.6¢
|s6ms
|-
|-
|'''7-mosstep (octave)'''
|Large 6-smistep
|4L + 2s
|1028.6¢ to 1200.0¢
|L6ms
|-
|'''7-smistep (octave)'''
|Perfect 7-smistep
|4L + 3s
|4L + 3s
|Perfect
|1200.0¢
|4L + 3s
|P7ms
|Perfect
|}
|}
=== Modes and scale degrees ===
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 mode degrees|Mode Names=Nerevarine; Vivecan; Lorkhanic; Sothic; Kagrenacan; Almalexian; Dagothic|Scale Signature=4L 3s}}
==Theory==
===Low harmonic entropy scales===
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.
*[[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.
===Temperament interpretations===
:''Main article: [[4L 3s/Temperaments]]''
4L 3s has the following temperament interpretations:
*[[Sixix]], with generators around 338.6¢.
*[[Orgone]], with generators around 323.4¢.
*[[Kleismic]], with generators around 317¢.
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]].
===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".
* The augmented 2-mosstep is around the size of a meantone-sized major 3rd and can be used as a stand-in for such.


=== Note names ===
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.
For this article, note names are based on [[Diamond-mos notation|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:


{{MOS gamut|Scale Signature=4L 3s}}
Edos include [[18edo]], [[25edo]], and [[43edo]]. Some key considerations include:


== Theory ==
*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's major and minor 4-mossteps are both equally off from 12edo's diatonic perfect 5th (700¢) by 33.3¢.
** 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 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.


=== Low harmonic entropy scales ===
===Hyposoft tunings===
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 ((6/5)^6, tempered, equals 3/1), and [[myna]], in which the generator is also 6/5 but 10 of them make a 6/1 ((6/5)^10, tempered, equals 6/1), resulting in the intervals 4/3 and 3/2 being absent.
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".


=== Temperament interpretations ===
Edos include [[11edo]] (not shown), [[18edo]], and [[29edo]].


: ''Main article: [[4L 3s/Temperaments]]''
===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.


4L 3s has the following temperament interpretations:
Other hypohard edos include [[11edo]] (not shown), [[15edo]] and [[37edo]].
===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.
 
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]].
 
Parahard edos smaller than 53edo include [[15edo]] (not shown), [[19edo]], and [[34edo]].


# With generator size between 5\18 (333.3c) and 11\39 (338.5c): [[Sixix]], corresponding to a step ratio between 3/2 and 6/5.
== Scales ==
# With generator size between 4\15 (320.0c) and 3\11 (327.3c): [[Orgone]], corresponding to a step ratio between 3/1 and 2/1.
''Move to quickstart guide.''
# With generator size between 5\19 (315.8c) and 4\15 (320.0c): [[Kleismic]], corresponding to a step ratio between 4/1 and 3/1.


There are also other temperaments in the 4L 3s range, particularly [[amity]] and [[myna]], but 7 pitches are not enough to contain the concordant chords optimized by these temperaments; a [[MODMOS]] or a larger MOS gamut is necessary to access these pitches, if restricted to a rank-2 approach.
== Scale tree ==
{{MOS tuning spectrum
| Scale Signature = 4L 3s
| 6/5 = [[Amity]]/[[hitchcock]]&nbsp;↑
| 5/4 = [[Sixix]]
| 13/8 = Golden 4L&nbsp;3s (868.3282{{c}})
| 12/5 = [[Hyperkleismic]]
| 5/2 = [[Orgone]]
| 13/5 = Golden superkleismic
| 8/3 = [[Superkleismic]]
| 11/3 = [[Hanson]]/[[keemun]]
| 6/1 = [[Oolong]]/[[myna]]&nbsp;↓
}}


== Step ratios ==
== Music ==
The basic tuning for 4L 3s has a large and small step size of 2 and 1 respectively, which is supported by 11edo. Raising or lowering certain nominals by a [[chroma]] produces the following scale degrees.
* [[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)
{{MOS degrees|Scale Signature=4L 3s|Step Ratio=2/1}}
* [[User:Ks26|ks26]], [https://www.youtube.com/watch?v=AEnEYk3X1as Ghost Bridge] (11edo)
=== Simple tunings ===
* [[User:Ayceman|Alexandru Ianu]], [https://youtu.be/81uZbsmbet8 Sylvian Moon Dance] (11edo) ([[:File:Sylvian_Moon_Dance.pdf|sheet music]])
{{MOS degrees|Scale Signature=4L 3s|Step Ratio=2/1; 3/1; 3/2}}
* [[File:Sixix Fugue.mp3|256x256px]] A fugue in [[18edo]] smitonic functional harmony (WIP)
=== Soft tunings ===
{{MOS degrees|Scale Signature=4L 3s|Step Ratio=3/2; 4/3; 5/3}}
=== Hard tunings ===
{{MOS degrees|Scale Signature=4L 3s|Step Ratio=3/1; 4/1; 5/2}}
== Modes ==
{{MOS modes|Scale Signature=4L 3s|Mode Names=Nerevarine; Vivecan; Lorkhanic; Sothic; Kagrenacan; Almalexian; Dagothic}}


== Tuning spectrum ==
== References ==
{{Scale tree|4L 3s|Comments=6/5: [[Amity]]/[[hitchcock]]↑; 5/4: [[Sixix]]; 13/8: Golden 4L 3s; 12/5: [[Hyperkleismic]]; 5/2 [[Orgone]]; 13/5: Golden superkleismic; 8/3: [[Superkleismic]]; 11/3: [[Hanson]]/[[keemun]]; 6/1: [[Oolong]]/[[myna]]↓; 2/1: (Generators smaller than this are proper)}}
<references />
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