4L 3s: Difference between revisions

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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}}

{{MOS intervals}}

=== Generator chain ===

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):

== Theory ==

=== Low harmonic entropy scales ===

* [[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.

 

{{main|4L&nbsp;3s/Temperaments}}

4L&nbsp;3s has the following temperament interpretations:

* [[Sixix]], with generators around 338.6{{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.

 

=== Simple tunings ===

The simplest tunings are those with step ratios 2:1, 3:1, and 3:2, producing 11edo, 15edo, and 18edo, respectively.

 

=== Parasoft 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 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}}

== References ==

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

[[Category:7-tone scales]]