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{{User:IlL/Template:RTT_restriction}}
{{Interwiki
{{Infobox MOS
|en=4L 3s
| Name = smitonic
|es=
| Periods = 1
|de=
| nLargeSteps = 4
|ja=4L 3s
| nSmallSteps = 3
| Equalized = 2
| Paucitonic = 1
| Pattern = LLsLsLs
}}
}}
{{Infobox MOS}}


'''4L 3s''' or '''smitonic''' ''smy-TON-ik'' /smaɪˈtɒnɪk/ refers to the structure of [[MOS]] scales with generators ranging from 1\4edo (one degree of [[4edo]], 300¢) to 2\7edo (two degrees of [[7edo]], or approx. 342.857¢). ''Smitonic'' is derived from 'sharp minor third', since the central range of the spectrum, 4\15 = 320¢ to 7\18 = 333.33¢ have minor third generators that are significantly sharp of 6/5.
{{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 is a distorted diatonic, because it has one large step of diatonic (5L 2s, LLsLLLs) replaced with a small step (yielding LLsLsLs).
== Name ==
<!--
{{TAMNAMS name}}
4L 3s has several temperament interpretations:


# With generator size between 5\18 (333.3c) and 11\39 (338.5c): [[Sixix]], corresponding to a L/s ratio between 3/2 and 6/5.
== Scale properties ==
# With generator size between 4\15 (320.0c) and 3\11 (327.3c): [[Orgone]], corresponding to a L/s ratio between 3 and 2.
{{TAMNAMS use}}
# With generator size between 5\19 (315.8c) and 4\15 (320.0c): [[Kleismic]], corresponding to a L/s ratio between 4 and 3.


There are also other temperaments in the 4L 3s range, particularly [[amity]] and [[myna]], but 7 notes in the generator chain are not enough to contain the most concordant chords in these temperaments; you would need to use a [[MODMOS]] or use a larger MOS gamut.-->
=== Intervals ===
== Notation==
{{MOS intervals}}
The notation used in this article is LsLsLsL = JKLMNOPJ unless specified otherwise. We denote raising and lowering by a chroma (L &minus; s) by & "amp" and @ "at". (Mnemonics: & "and" means additional pitch. @ "at" rhymes with "flat".)


Thus the [[11edo]] gamut is as follows:
=== Generator chain ===
{{MOS genchain}}


'''J/Q&''' J&/K@ '''K/L@''' '''L/K&''' L&/M@ '''M/N@''' '''N/M&''' N&/O@ '''O/P@''' '''P/O@''' P&/J@ '''J'''
=== Modes ===
== Intervals ==
{{MOS mode degrees}}
{| class="wikitable center-all"
 
|-
==== Proposed names ====
! Generators
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 (1/1 = J)
{{MOS modes
! Interval category name
| Mode Names=Nerevarine $
! Generators
Vivecan $
! Notation of 2/1 inverse
Lorkhanic $
! Interval category name
Sothic $
|-
Kagrenacan $
| colspan="6" style="text-align:left" | The 7-note MOS has the following intervals (from some root):
Almalexian $
|-
Dagothic $
| 0
}}
| J
 
| perfect unison
== Theory ==
| 0
=== Low harmonic entropy scales ===
| J
There are two notable harmonic entropy minima:
| octave
* [[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 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.
| 1
 
| L
=== Temperament interpretations ===
| perfect smithird
{{main|4L&nbsp;3s/Temperaments}}
| -1
4L&nbsp;3s has the following temperament interpretations:
| O
* [[Sixix]], with generators around 338.6{{c}}.
| perfect smisixth
* [[Orgone]], with generators around 323.4{{c}}.
|-
* [[Kleismic]], with generators around 317{{c}}.
| 2
 
| N
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.
| minor smififth (aka minor fifth)
| -2
| M
| major smifourth (aka major fourth)
|-
| 3
| P
| minor smiseventh
| -3
| K
| major smisecond
|-
| 4
| K@
| minor smisecond
| -4
| Q&
| major smiseventh
|-
| 5
| M@
| minor smifourth (aka minor fourth)
| -5
| N&
| major smififth (aka major fifth)
|-
| 6
| O@
| diminished smisixth
| -6
| L&
| augmented smithird
|-
| colspan="6" style="text-align:left" | The chromatic 11-note MOS (either [[7L 4s]], [[4L 7s]], or [[11edo]]) also has the following intervals (from some root):
|-
| 7
| J@
| diminished smioctave
| -7
| J&
| augmented smiunison; smichroma; smicomma
|-
| 8
| L@
| diminished smithird
| -8
| O&
| augmented smisixth
|-
| 9
| N@
| diminished smififth
| -9
| M&
| augmented smifourth
|-
| 10
| P@
| diminished smiseventh
| -10
| K&
| augmented smisecond
|}


== Tuning ranges ==
== Tuning ranges ==
=== Parasoft ===
{{Todo|Populate|comment=Populate with JI ratios from prior edits of this page.|inline=1}}
[[Parasoft]] smitonic tunings have step ratios between 4/3 and 3/2, which implies a generator sharper than 5\18 = 333.3¢ and flatter than 7\25 = 336.0¢.
 
=== 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 smitonic can be considered "meantone smitonic". This is because these tunings share the following features with [[meantone]] diatonic tunings:  
=== Parasoft tunings ===
* The large step is a "meantone", somewhere between near-10/9 (as in [[32edo]]) and near-9/8 (as in [[18edo]]).
Parasoft smitonic tunings can be considered "meantone smitonic" since it has the following features of [[meantone]] diatonic tunings:
* The major mosthird (made of two large steps) is a roughly [[meantone]]-sized major third, thus is a stand-in for the classical diatonic major third.
Parasoft smitonic tunings have both minor fifths and major fifths about equally off a just perfect fifth, and they have otherwise fairly convincing versions of both diatonic structure and tertian harmony. For this reason, parasoft might be the most accessible smitonic tuning range.


Parasoft smitonic EDOs include [[18edo]], [[25edo]], and [[43edo]].
* The major 1-mosstep, or large step, is around [[10/9]] to [[9/8]], thus making it a "meantone".
* 18edo can be used to make large and small steps more distinct (the step ratio is 3/2, thus 18edo smitonic is distorted [[19edo]] diatonic), or for its nearly pure 9/8. It also makes rising fifths (733.3c, a perfect mossixth) and falling fifths (666.7c, a major mosfifth) almost equally off from a just perfect fifth. 18edo is also more suited for conventionally jazz styles due to its 6-fold symmetry.
* The augmented 2-mosstep is around the size of a meantone-sized major 3rd and can be used as a stand-in for such.
* [[25edo]] can be used to make the major mosthird a good [[5/4]] (384¢).


The sizes of the generator, large step and small step of smitonic are as follows in various parasoft smitonic tunings.
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.
{| class="wikitable right-2 right-3 right-4 right-5"
|-
!
! [[18edo]] (soft)
! [[25edo]] (supersoft)
! [[43edo]]
! Optimized (2.9.5 [[POTE]]) tuning
|-
| generator (g)
| 5\18, 333.3
| 7\25, 336.0
| 12\43, 334.9
| 335.84
|-
| L (octave - 3g)
| 3\18, 200.0
| 4\25, 192.0
| 7\43, 195.3
| 193.16
|-
| s (4g - octave)
| 2\18, 133.3
| 3\25, 144.0
| 5\43, 139.5
| 143.36
|}


==== Intervals ====
Edos include [[18edo]], [[25edo]], and [[43edo]]. Some key considerations include:
Sortable table of the extended generator chain (-13 to 13 generators) in parasoft smitonic tunings. The several different interval flavors separated by the smichroma shows that parasoft smitonic is a useful [[cluster MOS]].
{| class="wikitable right-2 right-3 right-4 sortable "
|-
! class="unsortable"|Degree
! [[18edo]] (soft)
! [[25edo]] (supersoft)
! [[43edo]]
! class="unsortable"| Note name on J
! class="unsortable"| Approximate ratios
! #Gens up
|-
| unison
| 0\18, 0.0
| 0\25, 0.0
| 0\43, 0.0
| J
| 1/1
| 0
|-
| smichroma
| 1\18, 66.7
| 1\25, 48.0
| 2\43, 55.8
| J&
|
| -7
|-
| dim. smi2nd
| 1\18, 66.7
| 2\25, 96.0
| 3\43, 83.7
| K@@
|
| +11
|-
| min. smi2nd
| 2\18, 133.3
| 3\25, 144.0
| 5\43, 139.5
| K@
|
| +4
|-
| maj. smi2nd
| 3\18, 200.0
| 4\25, 192.0
| 7\43, 195.3
| K
| 9/8, 10/9
| -3
|-
| aug. smi2nd
| 4\18, 266.7
| 5\25, 240.0
| 9\43, 251.2
| K&
|
| -10
|-
| dim. smi3rd
| 4\18, 266.7
| 6\25, 288.0
| 10\43, 279.1
| L@
|
| +8
|-
| perf. smi3rd
| 5\18, 333.3
| 7\25, 336.0
| 12\43, 334.9
| L
| 17/14, 40/33
| +1
|-
| aug. smi3rd
| 6\18, 400.0
| 8\25, 384.4
| 14\43, 390.7
| L&
| 5/4
| -6
|-
| doubly aug. smi3rd
| 7\18, 466.7
| 9\25, 432.0
| 16\43, 446.5
| L&&
|
| -13
|-
| dim. smi4th
| 6\18, 400.0
| 9\25, 432.0
| 15\43, 418.6
| M@@
|
| +12
|-
| min. smi4th
| 7\18, 466.7
| 10\25, 480.0
| 17\43, 474.4
| M@
| 21/16
| +5
|-
| maj. smi4th
| 8\18, 533.3
| 11\25, 528.0
| 19\43, 530.2
| M
| 19/14, 34/25
| -2
|-
| aug. smi4th
| 9\18, 600.0
| 12\25, 576.0
| 21\43, 586.0
| M&
| 7/5
| -9
|-
| dim. smi5th
| 9\18, 600.0
| 13\25, 624.0
| 22\43, 614.0
| N@
| 10/7
| +9
|-
| min. smi5th
| 10\18, 666.7
| 14\25, 672.0
| 24\43, 669.8
| N
| 28/19, 25/17
| +2
|-
| maj. smi5th
| 11\18, 733.3
| 15\25, 720.0
| 26\43, 725.6
| N&
| 32/21
| -5
|-
| aug. smi5th
| 12\18, 800.0
| 16\25, 768.0
| 28\43, 781.4
| N&&
|
| -12
|-
| doubly dim. smi6th
| 11\18, 733.3
| 16\25, 768.0
| 27\43, 753.5
| O@@
|
| +13
|-
| dim. smi6th
| 12\18, 800.0
| 17\25, 816.0
| 29\43, 809.3
| O@
| 8/5
| +6
|-
| perf. smi6th
| 13\18, 866.7
| 18\25, 864.0
| 31\43, 865.1
| O
| 28/17, 33/20
| -1
|-
| aug. smi6th
| 14\18, 933.3
| 19\25, 912.0
| 33\43, 920.9
| O&
|
| -8
|-
| dim. smi7th
| 14\18, 933.3
| 20\25, 960.0
| 34\34, 948.8
| P@
|
| +10
|-
| min. smi7th
| 15\18, 1000.0
| 21\25, 1008.0
| 36\43, 1004.7
| P
| 16/9, 9/5
| +3
|-
| maj. smi7th
| 16\18, 1066.7
| 22\25, 1056.0
| 38\43, 1060.5
| P&
|
| -4
|-
| aug. smi7th
| 17\18, 1133.3
| 23\25, 1104.0
| 40\43, 1116.3
| P&
|
| -11
|-
| dim. smioctave
| 17\18, 1133.3
| 24\25, 1152.0
| 41\43, 1144.2
| J@
|
| +7
|}


=== Hyposoft ===
* 18edo can be used to make the large and small steps more distinct, or can be considered a distorted 19edo diatonic.
[[Hyposoft]] tunings of smitonic  have [[step ratio]]s between 3/2 and 2/1 which implies that the generator is a supraminor third sharper than 3\11 = 327.27¢ and flatter than 5\18 = 333.33¢.
** 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{{c}}) by 33.3{{c}}.
** 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{{c}}).
{{MOS tunings|Step Ratios=3/2; 7/5; 4/3}}


The large step is a sharper major second in these tunings than in parasoft tunings. These tunings could be considered "[[Gentle region|neogothic]] smitonic" or "[[archy]] smitonic", in analogy to parasoft smitonic being meantone smitonic.
=== Hyposoft tunings ===
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".


{| class="wikitable right-2 right-3 right-4 right-5"
Edos include [[11edo]] (not shown), [[18edo]], and [[29edo]].
|-
!
! [[11edo]] (basic)
! [[18edo]] (soft)
! [[29edo]] (semisoft)
|-
| generator (g)
| 3\11, 327.27
| 5\18, 333.33
| 8\29, 331.03
|-
| L (octave - 3g)
| 2\11, 218.18
| 3\18, 200.00
| 5\29, 206.90
|-
| s (4g - octave)
| 1\11, 109.09
| 2\18, 133.33
| 3\29, 124.14
|}
==== Intervals ====
Sortable table of major and minor intervals in hyposoft smitonic tunings (11edo and 18edo not shown):
{| class="wikitable right-2 sortable "
|-
! class="unsortable"|Degree
! [[29edo]] (semisoft)
! class="unsortable"| Note name on J
! class="unsortable"| Approximate ratios (for 29edo)
! #Gens up
|-
| unison
| 0\29, 0.0
| J
| 1/1
| 0
|-
| min. smi2nd
| 3\29, 124.1
| K@
| 14/13
| +4
|-
| maj. smi2nd
| 5\29, 206.9
| K
| 9/8
| -3
|-
| perf. smi3rd
| 8\29, 331.0
| L
| 23/19, 40/33
| +1
|-
| aug. smi3rd
| 10\29, 413.8
| L&
| 14/11
| -6
|-
| min. smi4th
| 11\29, 455.2
| M@
| 13/10
| +5
|-
| maj. smi4th
| 13\29, 537.9
| M
| 15/11
| -2
|-
| min. smi5th
| 16\29, 662.1
| N
| 19/13, 22/15
| +2
|-
| maj. smi5th
| 18\26, 744.8
| N&
| 20/13
| -5
|-
| dim. smi6th
| 19\29, 786.2
| O@
| 11/7
| +6
|-
| perf. smi6th
| 21\29, 869.0
| O
| 33/20, 38/23
| -1
|-
| min. smi7th
| 24\29, 993.1
| P
| 16/9
| +3
|-
| maj. smi7th
| 26\28, 1075.9
| P&
| 13/7
| -4
|}


=== Hypohard ===
{{MOS tunings|Step Ratios=3/2; 5/3; 7/4}}
[[Hypohard]] tunings have [[step ratio]]s between 2 and 3, implying a generator sharper than 4\15 = 320¢ and flatter than 3\11 = 327.27¢. The large step tends to approximate [[8/7]], and the major smifourth (2 large steps + 1 small step) tends to approximate [[11/8]]; [[26edo]] is stellar in both of these approximations.


Hypohard smitonic edos include [[11edo]], [[15edo]], [[26edo]], and [[37edo]].
=== Hypohard tunings===
The sizes of the generator, large step and small step of smitonic are as follows in various hypohard smitonic tunings.
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.
{| class="wikitable right-2 right-3 right-4"
|-
!
! [[11edo]] (basic)
! [[15edo]] (hard)
! [[26edo]] (semihard)
! Some JI approximations
|-
| generator (g)
| 3\11, 327.27
| 4\15, 320.00
| 7\26, 323.08
| 77/64, 6/5
|-
| L (octave - 3g)
| 2\11, 218.18
| 3\15, 240.00
| 5\26, 230.77
| 8/7
|-
| s (4g - octave)
| 1\11, 109.09
| 1\15, 80.00
| 2\26, 92.31
| 128/121, (16/15)
|}
==== Intervals ====
Sortable table of major and minor intervals in hypohard smitonic tunings:
{| class="wikitable right-2 right-3 right-4 sortable "
|-
! class="unsortable"|Degree
! [[11edo]] (basic)
! [[15edo]] (hard)
! [[26edo]] (semihard)
! class="unsortable"| Note name on J
! class="unsortable"| Approximate ratios
! #Gens up
|-
| unison
| 0\11, 0.0
| 0\15, 0.0
| 0\26, 0.0
| J
| 1/1
| 0
|-
| min. smi2nd
| 1\11, 109.1
| 1\15, 80.0
| 2\26, 92.3
| K@
|
| +4
|-
| maj. smi2nd
| 2\11, 218.2
| 3\15, 240.0
| 5\26, 230.8
| K
| 8/7
| -3
|-
| perf. smi3rd
| 3\11, 327.3
| 4\15, 320.0
| 7\26, 323.1
| L
| 77/64, 6/5
| +1
|-
| aug. smi3rd
| 4\11, 436.4
| 6\15, 480.0
| 10\26, 461.5
| L&
|
| -6
|-
| min. smi4th
| 4\11, 436.4
| 5\15, 400.0
| 9\26, 415.4
| M@
| 14/11
| +5
|-
| maj. smi4th
| 5\11, 545.5
| 7\15, 560.0
| 12\26, 553.9
| M
| 11/8
| -2
|-
| min. smi5th
| 6\11, 656.6
| 8\15, 640.0
| 14\26, 646.2
| N
| 16/11
| +2
|-
| maj. smi5th
| 7\11, 763.6
| 10\15, 800.0
| 17\26, 784.62
| N&
| 11/7
| -5
|-
| dim. smi6th
| 7\11, 763.6
| 9\15, 720.0
| 16\26, 738.5
| O@
|
| +6
|-
| perf. smi6th
| 8\11, 872.7
| 11\15, 880.0
| 19\26, 876.9
| O
| 5/3
| -1
|-
| min. smi7th
| 9\11, 981.8
| 12\15, 960.0
| 21\26, 969.2
| P
| 7/4
| +3
|-
| maj. smi7th
| 10\11, 1090.9
| 14\15, 1120.0
| 24\26, 1107.7
| P&
|
| -4
|}


=== Parahard ===
Other hypohard edos include [[11edo]] (not shown), [[15edo]] and [[37edo]].
In [[parahard]] smitonic (step ratio between 3 and 4, thus with generator between 5\19, 315.79¢ and 4\15, 320¢), the generator is close to a pure [[6/5]] minor third, and 6 minor thirds are used to reach a perfect fifth. The parahard 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, the 7-note MOS only has one perfect fifth, so extending the chain to bigger MOSes, such as the [[4L 7s]] 11-note MOS, is suggested for getting 5-limit harmony.


EDOs that have parahard smitonic include [[15edo]], [[19edo]], [[34edo]], and [[53edo]].
{{MOS tunings|Step Ratios=3/1; 5/2; 7/3}}


The sizes of the generator, large step and small step of smitonic are as follows in various parahard smitonic tunings (not including 15edo).
=== Parahard tunings ===
{| class="wikitable right-2 right-3 right-4"
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.
|-
!
! [[19edo]] (superhard)
! [[34edo]]
! [[53edo]]
! JI intervals represented
|-
| generator (g)
| 5\19, 315.79
| 9\34, 317.65
| 14\53, 316.98
| 6/5
|-
| L (octave - 3g)
| 4\19, 252.63
| 7\34, 247.06
| 11\53, 249.06
| 15/13
|-
| s (4g - octave)
| 1\19, 63.16
| 2\34, 70.59
| 3\53, 67.92
| 25/24, 26/25
|}


==== Intervals ====
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.
Sortable table of major and minor intervals in parahard smitonic tunings:
{| class="wikitable right-2 right-3 right-4 sortable "
|-
! class="unsortable"|Degree
! [[19edo]] (superhard)
! [[34edo]]
! [[53edo]]
! class="unsortable"| Note name on J
! class="unsortable"| Approximate ratios
! #Gens up
|-
| unison
| 0\19, 0.0
| 0\34, 0.0
| 0\53, 0.0
| J
| 1/1
| 0
|-
| min. smi2nd
| 1\19, 63.2
| 2\34, 70.6
| 3\53, 67.9
| K@
| 25/24, 26/25
| +4
|-
| maj. smi2nd
| 4\19, 252.6
| 7\34, 247.1
| 11\53, 249.1
| K
| 15/13
| -3
|-
| perf. smi3rd
| 5\19, 315.8
| 9\34, 317.6
| 14\53, 317.0
| L
| 6/5
| +1
|-
| aug. smi3rd
| 8\19, 505.3
| 14\34, 494.1
| 22\53, 498.1
| L&
| 4/3
| -6
|-
| min. smi4th
| 6\19, 378.9
| 11\34, 388.2
| 17\53, 384.9
| M@
| 5/4
| +5
|-
| maj. smi4th
| 9\19, 568.4
| 16\34, 564.7
| 25\53, 566.0
| M
| 18/13
| -2
|-
| min. smi5th
| 10\19, 631.6
| 18\34, 635.3
| 28\53, 634.0
| N
| 13/9
| +2
|-
| maj. smi5th
| 16\19, 821.1
| 23\34, 811.8
| 39\53, 815.0
| N&
| 8/5
| -5
|-
| dim. smi6th
| 11\19, 694.7
| 20\34, 705.9
| 31\53, 701.9
| O@
| 3/2
| +6
|-
| perf. smi6th
| 14\19, 884.2
| 25\34, 882.4
| 39\53, 883.0
| O
| 5/3
| -1
|-
| min. smi7th
| 15\19, 947.4
| 27\34, 952.9
| 42\53, 950.9
| P
| 26/15
| +3
|-
| maj. smi7th
| 18\19, 1136.8
| 32\34, 1129.4
| 50\53, 1132.1
| P&
| 25/13
| -4
|}


== Modes ==
These JI approximations are associated with [[kleismic]] temperament, through the 2.3.5.13 extension known as [[Kleismic family#Cata|cata]].
A naming scheme proposed by Alexandru Ianu ([[User:Ayceman]]), here<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>, relating to the Almsivi in Morrowind (TES):
* LLsLsLs: Nerevarine (the most major-like)
* LsLLsLs: Vivecan (harmonic minor-like)
* LsLsLLs: Lorkhanic (melodic-minor-like)
* LsLsLsL: Sothic (symmetric)
* sLLsLsL: Kagrenacan (locrian-like?)
* sLsLLsL: Almalexian (dorian but with a minor second)
* sLsLsLL: Dagothic (freygish-like)


== Pseudo-diatonic theory ==
Parahard edos smaller than 53edo include [[15edo]] (not shown), [[19edo]], and [[34edo]].
=== Hypohard ===
=== Parasoft ===
== Primodal theory ==
=== Primodal chords ===
=== Nejis ===
== Temperaments ==
:''Main article: [[4L 3s/Temperaments]]''


== Samples ==
{{MOS tunings|Step Ratios=4/1; 11/3; 7/2}}
[[File:Sixix Fugue.mp3]] A fugue in [[18edo]] smitonic (WIP)


== Scale tree ==
== Scales ==
The spectrum looks like this:
* [[Orgone7]]
* [[Cata7]]
* [[Myna7]]
 
== Scale tree==
{{MOS tuning spectrum
| 6/5 = [[Amity]]/[[hitchcock]]&nbsp;↑
| 5/4 = [[Sixix]]
| 4/3 = [[Supramin]]
| 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]])


{| class="wikitable"
|-
! colspan="8" | Generator
! | Tetrachord
! | g in cents
! | 2g
! | 3g
! | 4g
! | Comments
|-
| | 1\4
| |
| |
| |
| |
| |
| |
| |
| | 1 0 1
| | 300
| | 600
| | 900
| | 0
| style="text-align:center;" |
|-
|
|
|
|
|
|
|
|9\35
|8 1 8
|308.571
|617.143
|925.714
|34.286
|
|-
| |
| |
| |
| |
| |
| |
| | 8\31
| |
| | 7 1 7
| | 309.677
| | 619.355
| | 929.023
| | 38.71
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| | 7\27
| |
| |
| | 6 1 6
| | 311.111
| | 622.222
| | 933.333
| | 44.444
| style="text-align:center;" |
|-
| |
| |
| |
| |
| | 6\23
| |
| |
| |
| | 5 1 5
| | 313.043
| | 626.087
| | 939.13
| | 52.174
| style="text-align:center;" |
|-
| |
| |
| |
| | 5\19
| |
| |
| |
| |
| | 4 1 4
| | 315.789
| | 631.579
| | 947.368
| | 63.158
| style="text-align:center;" |
|-
| |
| |
| |
| |
| | 9\34
| |
| |
| |
| | 7 2 7
| | 317.647
| | 634.294
| | 951.941
| | 70.588
| style="text-align:center;" |
|-
| |
| |
| | 4\15
| |
| |
| |
| |
| |
| | 3 1 3
| | 320
| | 640
| | 960
| | 80
| style="text-align:center;" | L/s = 3.
|-
| |
| |
| |
| |
| | 11\41
| |
| |
| |
| | 8 3 8
| | 321.951
| | 643.902
| | 965.854
| | 87.805
| |
|-
| |
| |
| |
| |
| |
| |
| | 29\108
| |
| | 21 8 21
| | 322.222
| | 644.444
| | 966.667
| | 88.889
| |
|-
| |
| |
| |
| |
| |
| | 18\67
| |
| |
| | 13 5 13
| | 322.388
| | 644.776
| | 967.364
| | 89.522
| |
|-
| |
| |
| |
| | 7\26
| |
| |
| |
| |
| | 5 2 5
| | 323.077
| | 646.154
| | 969.231
| | 92.308
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| | 31/115
| | 22 9 22
| | 323.478
| | 646.956
| | 970.434
| | 93.913
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| | 2.44 1 2.44
| | 323.501
| | 647.002
| | 970.003
| | 94.004
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 24/89
| |
| | 17 7 17
| | 323.595
| | 647.191
| | 970.786
| | 94.382
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| | 17/63
| |
| |
| | 12 5 12
| | 323.809
| | 647.619
| | 971.428
| | 95.238
| style="text-align:center;" |
|-
| |
| |
| |
| |
| | 10/37
| |
| |
| |
| | 7 3 7
| | 324.324
| | 648.648
| | 972.972
| | 97.297
| style="text-align:center;" |
|-
| |
| | 3\11
| |
| |
| |
| |
| |
| |
| | 2 1 2
| | 327.273
| | 654.545
| | 981.818
| | 109.091
| style="text-align:center;" | Boundary of propriety (generators <br>larger than this are proper)
|-
| |
| |
| |
| | 8\29
| |
| |
| |
| |
| | 5 3 5
| | 331.034
| | 662.069
| | 993.013
| | 124.138
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| | 21\76
| |
| |
| | 13 8 13
| | 331.579
| | 663.158
| | 994.739
| | 126.316
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| | 34\123
| | 21 13 21
| | 331.707
| | 663.415
| | 995.122
| | 126.829
| style="text-align:center;" | Golden smitonic
|-
| |
| |
| |
| |
| | 13\47
| |
| |
| |
| | 8 5 8
| | 331.915
| | 663.83
| | 995.745
| | 127.66
| style="text-align:center;" |
|-
| |
| |
| | 5\18
| |
| |
| |
| |
| |
| | 3 2 3
| | 333.333
| | 666.667
| | 1000
| | 133.333
| style="text-align:center;" | Optimum rank range (L/s=3/2)
|-
| |
| |
| |
| | 7\25
| |
| |
| |
| |
| | 4 3 4
| | 336
| | 672
| | 1008
| | 144
| style="text-align:center;" |
|-
| |
| |
| |
| |
| | 9\32
| |
| |
| |
| | 5 4 5
| | 337.5
| | 675
| | 1012.5
| | 150
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| | 11\39
| |
| |
| | 6 5 6
| | 338.462
| | 676.923
| | 1015.385
| | 153.846
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 13\46
| |
| | 7 6 7
| | 339.13
| | 678.261
| | 1017.391
| | 156.522
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| | 15\53
| | 8 7 8
| | 339.623
| | 679.245
| | 1018.868
| | 158.491
| style="text-align:center;" |
|-
| | 2\7
| |
| |
| |
| |
| |
| |
| |
| | 1 1 1
| | 342.857
| | 685.714
| | 1028.571
| | 171.429
| style="text-align:center;" |
|}
== References ==
== References ==
[[Category:Smitonic|*]]<!--Main article-->
<references />
[[Category:Scales]]
 
[[Category:MOS scales]]
[[Category:Smitonic|*]] <!--Main article-->
[[Category:Abstract MOS patterns]]
[[Category:7-tone scales]]
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