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{{Infobox MOS|Tuning=4L 3s | {{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). | |||
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. | |||
== Scale characteristics == | |||
''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 === | ||
[[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" | {| 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: | |||
*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¢), 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: | |||
*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]] ↑ | |||
| 5/4 = [[Sixix]] | |||
| 13/8 = Golden 4L 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]] ↓ | |||
}} | |||
== | == 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 /> | |||