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{{Infobox MOS|Tuning=4L 3s|debug=1}}
{{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]].''
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 ==
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.
''This article assumes TAMNAMS naming conventions for the following: step ratios, intervals, scale degrees, modes, step patterns. For more information, see the respective links.''


== Name ==
===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¢).
[[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===
== 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.
{| class="wikitable"
{| class="wikitable"
|+Intervals of 4L 3s
|+Intervals of 4L 3s
!Interval class
! colspan="2" |Intervals
!Specific intervals
! colspan="2" |Size
!Size (in ascending order)
! rowspan="2" |Abbrev.
|-
!Generic
!Specific
!Steps
!Range in cents
|-
|-
|'''0-smistep'''
|'''0-smistep (root)'''
|'''Perfect 0-smistep (unison)'''
|Perfect 0-smistep
|0
|0
|0.0¢
|P0ms
|-
|-
| rowspan="2" |1-smistep
| rowspan="2" |1-smistep
|Minor 1-smistep
|Small 1-smistep
|s
|s
|0.0¢ to 171.4¢
|s1ms
|-
|-
|Major 1-smistep
|Large 1-smistep
|L
|L
|171.4¢ to 300.0¢
|L1ms
|-
|-
| rowspan="2" |'''2-smistep'''
| rowspan="2" |'''2-smistep'''
|'''Perfect 2-smistep'''
|'''Small 2-smistep'''
|L + s
|L + s
|300.0¢ to 342.9¢
|s2ms
|-
|-
|Augmented 2-smistep
|Large 2-smistep
|2L
|2L
|342.9¢ to 600.0¢
|L2ms
|-
|-
| rowspan="2" |3-smistep
| rowspan="2" |3-smistep
|Minor 3-smistep
|Small 3-smistep
|L + 2s
|L + 2s
|300.0¢ to 514.3¢
|s3ms
|-
|-
|Major 3-smistep
|Large 3-smistep
|2L + s
|2L + s
|514.3¢ to 600.0¢
|L3ms
|-
|-
| rowspan="2" |4-smistep
| rowspan="2" |4-smistep
|Minor 4-smistep
|Small 4-smistep
|2L + 2s
|2L + 2s
|600.0¢ to 685.7¢
|s4ms
|-
|-
| Major 4-smistep
|Large 4-smistep
|3L + s
|3L + s
|685.7¢ to 900.0¢
|L4ms
|-
|-
| rowspan="2" |'''5-smistep'''
| rowspan="2" |'''5-smistep'''
|Diminished 5-smistep
|Small 5-smistep
| 2L + 3s
|2L + 3s
|600.0¢ to 857.1¢
|s5ms
|-
|-
|'''Perfect 5-smistep'''
|'''Large 5-smistep'''
|3L + 2s
|3L + 2s
|857.1¢ to 900.0¢
|L5ms
|-
|-
| rowspan="2" |6-smistep
| rowspan="2" |6-smistep
|Minor 6-smistep
|Small 6-smistep
|3L + 3s
|3L + 3s
|900.0¢ to 1028.6¢
|s6ms
|-
|-
|Major 6-smistep
|Large 6-smistep
|4L + 2s
|4L + 2s
|1028.6¢ to 1200.0¢
|L6ms
|-
|-
|'''7-smistep (octave)'''
|'''7-smistep (octave)'''
|'''Perfect 7-smistep (octave)'''
|Perfect 7-smistep
|4L + 3s
|4L + 3s
|1200.0¢
|P7ms
|}
|}
Different forms of this MOS are generally built using one specific interval for each interval class, while the step pattern LLsLsLs, or some rotation thereof, is formed between consecutive scale degrees. Alternatively, MODMOS scales can be formed by deviating from the step pattern, such as with LLLssLs, or by including alterations outside the specific sizes described.
=== 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):
== Notation ==
{{MOS mode degrees|Mode Names=Nerevarine; Vivecan; Lorkhanic; Sothic; Kagrenacan; Almalexian; Dagothic|Scale Signature=4L 3s}}
Names for notes in this scale can be denoted using the following notation schemes.
 
=== Ups and downs notation ===
:''Main article: [[Ups and downs notation]]''
(Insert [[Ups and downs notation|ups-and-downs]] example here)
 
=== Diamond-mos notation ===
:''Main article: [[Diamond-mos notation]]''
[[Diamond-mos notation|Diamond-mos]] can be used by assigning the note names JKLMNOP to one of the modes and using the symbols "&" and "@" to denote generalized sharps and flats, respectively. Using the symmetric mode (LsLsLsL), the basic 10edo gamut is as follows:
 
{{MOS gamut|Scale Signature=4L 3s}}
==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 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 10 of them make a 6/1, resulting in the intervals 4/3 and 3/2 being absent.
===Temperament interpretations===
===Temperament interpretations===
:''Main article: [[4L 3s/Temperaments]]''
:''Main article: [[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¢.
*[[Orgone]], with generators around 323.4¢.
*[[Orgone]], with generators around 323.4¢.
*[[Kleismic]], with generators around 317¢.
*[[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.
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==
===Simple tunings===
===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|Scale Signature=4L 3s|Step Ratio=2/1; 3/1; 3/2|Notation=NONE}}
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 tunings===
Parasoft smitonic tunings (4:3 to 3:2) can be considered "meantone smitonic" since it has the following features of [[meantone]] diatonic 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 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¢), 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.
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**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¢).
**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¢) by 33.3¢.
**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¢).
{{MOS degrees|Scale Signature=4L 3s|Step Ratio=3/2; 4/3; 7/5|Genchain Extend=9|Notation=NONE}}
*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 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¢ 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]].
Edos include [[11edo]] (not shown), [[18edo]], and [[29edo]].
{{MOS degrees|Scale Signature=4L 3s|Step Ratio=3/2; 5/3|Genchain Extend=3|Notation=NONE}}
 
===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¢ 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]].
Other hypohard edos include [[11edo]] (not shown), [[15edo]] and [[37edo]].
{{MOS degrees|Scale Signature=4L 3s|Step Ratio=3/1; 5/2; 7/3|Genchain Extend=3|Notation=NONE}}
===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¢ 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.
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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|Scale Signature=4L 3s|Step Ratio=4/1; 7/2; 11/3; 15/4|Genchain Extend=3|Prefix=smi|Notation=NONE}}
==Modes==
{{MOS modes|Scale Signature=4L 3s|Mode Names=Nerevarine; Vivecan; Lorkhanic; Sothic; Kagrenacan; Almalexian; Dagothic}}
==Scales==
=== Subset and superset 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:
* [[7L 4s]], a smitonic chromatic scale produced using soft-of-basic step ratios.
* [[4L 7s]], a smitonic chromatic scale produced using hard-of-basic step ratios.
11edo, the equalized form of both 7L 4s and 4L 7s, is also a superset of 4L 3s.


===Scala files===
== Scales ==
''Move to quickstart guide.''


*[[Orgone7]]
== Scale tree ==
*[[Cata7]]
{{MOS tuning spectrum
*[[Myna7]]
| 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;↓
}}


==Scale tree==
== Music ==
{{Scale tree|4L 3s|Comments=6/5: [[Amity]]/[[hitchcock]]↑;
* [[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)
5/4: [[Sixix]];
* [[User:Ks26|ks26]], [https://www.youtube.com/watch?v=AEnEYk3X1as Ghost Bridge] (11edo)
13/8: Golden 4L 3s (868.3282¢);
* [[User:Ayceman|Alexandru Ianu]], [https://youtu.be/81uZbsmbet8 Sylvian Moon Dance] (11edo) ([[:File:Sylvian_Moon_Dance.pdf|sheet music]])
12/5: [[Hyperkleismic]];
* [[File:Sixix Fugue.mp3|256x256px]] A fugue in [[18edo]] smitonic functional harmony (WIP)
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)}}
==Music==
''(add music)''


== See also ==
== References ==
Approaches:
<references />
*[[4L 3s/Inthar's approach]]
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