User:Ganaram inukshuk/4L 3s: Difference between revisions

{{MOS intro|Scale Signature=4L 3s}}

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.

[[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¢).

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.

{{MOS gamut|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.

===Simple 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:

*The major 1-mosstep, or large step, is around [[10/9]] to [[9/8]], thus making it a "meantone".

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.

**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¢.

===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.

Parahard edos smaller than 53edo include [[15edo]] (not shown), [[19edo]], and [[34edo]].

==Modes==

11edo, the equalized form of both 7L 4s and 4L 7s, is also a superset of 4L 3s.

===Scala files===

*[[Orgone7]]

*[[Cata7]]

8/3: [[Superkleismic]];

11/3: [[Hanson]]/[[keemun]];

==Music==