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4L 3s: Difference between revisions

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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¢).
== Notation==
:''This article assumes [[TAMNAMS]] for naming step ratios, intervals, and scale degrees, and [[Diamond-mos notation|diamond-MOS notation]] for note names.''
=== Intervals and 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.


Being a moment-of-symmetry scale, every [[interval class]] of 4L 3s, except for the unison and octave, has two [[Interval variety|varieties]] – large and small – whose [[Interval quality|relative qualities]] are denoted as major or minor, or augmented, perfect, and diminished for the generators.
== Name ==
{| class="wikitable"
{{TAMNAMS name}}
|+
! rowspan="2" |Interval class
! colspan="2" |Large variety
! colspan="2" |Small variety
|-
!Size
!Quality
!Size
! Quality
|-
|'''0-mosstep (unison)'''
|0
|Perfect
| 0
|Perfect
|-
|1-mosstep
| L
|Major
|s
|Minor
|-
|2-mosstep
|2L
| Augmented
|L + s
| Perfect
|-
|3-mosstep
|2L + s
|Major
| L + 2s
|Minor
|-
|4-mosstep
| 3L + 1s
| Perfect
|2L + 2s
|Minor
|-
|5-mosstep
|3L + 2s
|Perfect
| 2L + 3s
|Diminished
|-
|6-mosstep
|3L + 3s
| Major
|2L + 3s
|Minor
|-
|'''7-mosstep (octave)'''
|4L + 3s
|Perfect
|4L + 3s
|Perfect
|}
===Note names===
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:


{{MOS gamut|Scale Signature=4L 3s}}
== Scale properties ==
==Theory ==
{{TAMNAMS use}}
===Low harmonic entropy scales===
 
=== Intervals ===
{{MOS intervals}}
 
=== 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|Scale Signature=4L 3s|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|Scale Signature=4L 3s|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|Scale Signature=4L 3s|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|Scale Signature=4L 3s|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|Scale Signature=4L 3s|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|Scale Signature=4L 3s|Mode Names=Nerevarine; Vivecan; Lorkhanic; Sothic; Kagrenacan; Almalexian; Dagothic}}
{{MOS tunings|Step Ratios=4/1; 11/3; 7/2}}
==Scales==


===Scala files===
== Scales ==
*[[Orgone7]]
* [[Orgone7]]
*[[Cata7]]
* [[Cata7]]
*[[Myna7]]
* [[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]]
2/1: (Generators smaller than this are proper)}}
| 11/3 = [[Hanson]]/[[keemun]]
==Music==
| 6/1 = [[Oolong]]/[[myna]]&nbsp;↓
*[[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]])
== Music ==
*[[File:Sixix Fugue.mp3|256x256px]] A fugue in [[18edo]] smitonic functional harmony (WIP)
* [[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)
==See also==
* [[User:Ks26|ks26]], [https://www.youtube.com/watch?v=AEnEYk3X1as Ghost Bridge] (11edo)
Approaches:
* [[User:Ayceman|Alexandru Ianu]], [https://youtu.be/81uZbsmbet8 Sylvian Moon Dance] (11edo) ([[:File:Sylvian_Moon_Dance.pdf|sheet music]])
*[[4L 3s/Inthar's approach]]
 
==References==
== References ==
<references />
<references />


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