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== Scale characteristics ==
== Scale characteristics ==
''This article assumes TAMNAMS conventions for interval, degree, and scale naming.''
''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 sizes===
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.
{| class="wikitable"
 
|+Intervals of 4L 3s
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.
! colspan="2" |Intervals
{{MOS intervals|Scale Signature=4L 3s}}
! 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 ===
=== 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):
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):
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== 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|Step Ratio=2/1; 3/1; 3/2|JI Ratios=M1md: [[8/7]];
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]].
P2md: [[6/5]], [[77/64]];
m3md: [[14/11]];
M3md: [[11/8]];
m4md: [[16/11]];
M4md: [[11/7]];
P5md: [[5/3]];
m6md: [[7/4]]
|Scale Signature=4L 3s}}
===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:
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* 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¢).
*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.
*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 degrees|Step Ratio=3/2; 4/3; 7/5|Number of Alterations=1|JI Ratios=m1md: [[13/12]];
 
M1md: [[9/8]], [[10/9]];
P2md: [[17/14]], [[40/33]];
A2md: [[5/4]];
m3md: [[21/16]];
M3md: [[19/14]], [[34/25]];
A3md: [[7/5]];
d4md: [[10/7]];
m4md: [[28/19]], [[25/17]];
M4md: [[32/21]];
d5md: [[8/5]];
P5md: [[28/17]], [[33/20]];
m6md: [[16/9]], [[9/5]];
M6md: [[24/13]]
|Scale Signature=4L 3s}}
===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|Step Ratio=3/2; 5/3|JI Ratios=m1md: [[14/13]];
 
M1md: [[9/8]];
P2md: [[23/19]], [[40/33]];
A2md: [[14/11]];
m3md: [[13/10]];
M3md: [[15/11]];
m4md: [[19/13]], [[22/15]];
M4md: [[20/13]];
d5md: [[11/7]];
P5md: [[33/20]], [[38/23]];
m6md: [[16/9]];
M6md: [[13/7]]
|Scale Signature=4L 3s}}
===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|Step Ratio=3/1; 5/2; 7/3|JI Ratios=M1md: [[8/7]];
P2md: [[6/5]], [[77/64]];
m3md: [[14/11]];
M3md: [[11/8]];
m4md: [[16/11]];
M4md: [[11/7]];
P5md: [[5/3]];
m6md: [[7/4]];
|Scale Signature=4L 3s}}
===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|Step Ratio=4/1; 7/2; 11/3; 15/4|JI Ratios=m1md: [[25/24]], [[26/25]];
M1md: [[15/13]];
P2md: [[6/5]];
A2md: [[4/3]];
m3md: [[5/4]];
M3md: [[18/13]];
m4md: [[13/9]];
M4md: [[8/5]];
d5md: [[3/2]];
P5md: [[5/3]];
m6md: [[26/15]];
M6md: [[25/13]]
|Scale Signature=4L 3s}}


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


==Scale tree==
== Scale tree ==
{{Scale tree|4L 3s|Comments=6/5: [[Amity]]/[[hitchcock]]↑;
{{MOS tuning spectrum
5/4: [[Sixix]];
| Scale Signature = 4L 3s
13/8: Golden 4L 3s (868.3282¢);
| 6/5 = [[Amity]]/[[hitchcock]]&nbsp;↑
12/5: [[Hyperkleismic]];
| 5/4 = [[Sixix]]
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]]
==Music==
| 11/3 = [[Hanson]]/[[keemun]]
*[[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)
| 6/1 = [[Oolong]]/[[myna]]&nbsp;↓
*[[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)
== 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 ==
<references />
<references />
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