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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 page is for testing MOS-related templates. For the main page, see [[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.


{{MOS intro|Scale Signature=4L 3s}}
== Scale characteristics ==
== Standing assumptions ==
''This article assumes TAMNAMS naming conventions for the following: step ratios, intervals, scale degrees, modes, step patterns. For more information, see the respective links.''
Unless otherwise stated, [[TAMNAMS]] is used in this article to name 4L 3s step ratio sizes and ranges, and intervals and scale degrees. Intervals and scale degrees are indexed starting at 0, starting at a 0-smistep and 0-smidegree, 1-smistep and 1-smidegree, and so on. 1-indexed terms, such as a smi-1st and 1st smidegree, are discouraged for MOS scales not of the form 5L 2s.


Unless otherwise stated, [[Diamond-mos notation|diamond-MOS notation]] is used in this article, applying unaltered note names JKLMNOP to the mode 3|3 (step pattern LsLsLsL, or sothic mode). Alterations by a [[chroma]] are denoted using the symbols & (pronounced "am" or "amp", which raises or "amplifies" a pitch by a chroma) and @ (pronounced "at", which rhymes with "flat").
===Name ===
{{MOS gamut|Scale Signature=4L 3s}}{{MOS gamut|Scale Signature=4L 3s|Large Step Size=3}}{{MOS gamut|Scale Signature=4L 3s|Large Step Size=3|Small Step Size=2}}
[[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"
|+Intervals of 4L 3s
! colspan="2" |Intervals
! colspan="2" |Size
! rowspan="2" |Abbrev.
|-
!Generic
!Specific
!Steps
!Range in cents
|-
|'''0-smistep (root)'''
|Perfect 0-smistep
|0
|0.0¢
|P0ms
|-
| rowspan="2" |1-smistep
|Small 1-smistep
|s
|0.0¢ to 171.4¢
|s1ms
|-
|Large 1-smistep
|L
|171.4¢ to 300.0¢
|L1ms
|-
| rowspan="2" |'''2-smistep'''
|'''Small 2-smistep'''
|L + s
|300.0¢ to 342.9¢
|s2ms
|-
|Large 2-smistep
|2L
|342.9¢ to 600.0¢
|L2ms
|-
| rowspan="2" |3-smistep
|Small 3-smistep
|L + 2s
|300.0¢ to 514.3¢
|s3ms
|-
|Large 3-smistep
|2L + s
|514.3¢ to 600.0¢
|L3ms
|-
| rowspan="2" |4-smistep
|Small 4-smistep
|2L + 2s
|600.0¢ to 685.7¢
|s4ms
|-
|Large 4-smistep
|3L + s
|685.7¢ to 900.0¢
|L4ms
|-
| rowspan="2" |'''5-smistep'''
|Small 5-smistep
|2L + 3s
|600.0¢ to 857.1¢
|s5ms
|-
|'''Large 5-smistep'''
|3L + 2s
|857.1¢ to 900.0¢
|L5ms
|-
| rowspan="2" |6-smistep
|Small 6-smistep
|3L + 3s
|900.0¢ to 1028.6¢
|s6ms
|-
|Large 6-smistep
|4L + 2s
|1028.6¢ to 1200.0¢
|L6ms
|-
|'''7-smistep (octave)'''
|Perfect 7-smistep
|4L + 3s
|1200.0¢
|P7ms
|}
=== 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:


==Modes==
*The major 1-mosstep, or large step, is around [[10/9]] to [[9/8]], thus making it a "meantone".
{{MOS modes|Scale Signature=4L 3s|Mode Names=Nerevarine; Vivecan; Lorkhanic; Sothic; Kagrenacan; Almalexian; Dagothic}}
* The augmented 2-mosstep is around the size of a meantone-sized major 3rd and can be used as a stand-in for such.


==Scale tree==
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.
{{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)}}
 
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 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.
 
===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".
 
Edos include [[11edo]] (not shown), [[18edo]], and [[29edo]].
 
===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.
 
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]].
 
== Scales ==
''Move to quickstart guide.''
 
== 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;↓
}}
 
== 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]])
* [[File:Sixix Fugue.mp3|256x256px]] A fugue in [[18edo]] smitonic functional harmony (WIP)
 
== References ==
<references />
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