4L 3s: Difference between revisions
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{{Interwiki | |||
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{{Infobox MOS}} | |||
4L 3s | {{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. | |||
== Name == | |||
{{TAMNAMS name}} | |||
== Scale properties == | |||
{{TAMNAMS use}} | |||
=== 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: | ||
* | * [[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 3s is required to reach 3/2 or 4/3. | |||
== | === Temperament interpretations === | ||
{{main|4L 3s/Temperaments}} | |||
4L 3s has the following temperament interpretations: | |||
* [[Sixix]], with generators around 338.6{{c}}. | |||
* [[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. | |||
== | == Tuning ranges == | ||
=== | {{Todo|Populate|comment=Populate with JI ratios from prior edits of this page.|inline=1}} | ||
=== | |||
=== | === Simple tunings === | ||
=== Sixix ( | The simplest tunings are those with step ratios 2:1, 3:1, and 3:2, producing 11edo, 15edo, and 18edo, respectively. | ||
[[Category: | {{MOS tunings}} | ||
[[Category:scales]] | |||
=== 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: | |||
* 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{{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}} | |||
=== 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". | |||
Edos include [[11edo]] (not shown), [[18edo]], and [[29edo]]. | |||
{{MOS tunings|Step Ratios=3/2; 5/3; 7/4}} | |||
=== Hypohard 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. | |||
Other hypohard edos include [[11edo]] (not shown), [[15edo]] and [[37edo]]. | |||
{{MOS tunings|Step Ratios=3/1; 5/2; 7/3}} | |||
=== 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. | |||
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]]. | |||
{{MOS tunings|Step Ratios=4/1; 11/3; 7/2}} | |||
== Scales == | |||
* [[Orgone7]] | |||
* [[Cata7]] | |||
* [[Myna7]] | |||
== Scale tree== | |||
{{MOS tuning spectrum | |||
| 6/5 = [[Amity]]/[[hitchcock]] ↑ | |||
| 5/4 = [[Sixix]] | |||
| 4/3 = [[Supramin]] | |||
| 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]]) | |||
== References == | |||
<references /> | |||
[[Category:Smitonic|*]] <!--Main article--> | |||
[[Category:7-tone scales]] | |||