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

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Moved approaches to "see also", adjusted degree tables to not display redundant edos (mainly 11edo)
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Edos include [[18edo]], [[25edo]], and [[43edo]]. Some key considerations include:
Edos include [[18edo]], [[25edo]], and [[43edo]]. Some key considerations include:


*18edo can be used to make the large and small steps more distinct.
*18edo can be used to make the large and small steps more distinct, or can be considered a distorted 19edo diatonic.
**18edo smitonic can also be considered a distorted 19edo diatonic.
**18edo has a major 1-mosstep that is close to 9/8 (203¢).
**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 3/2 (702¢).
**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.
**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 augmented 2-mosstep of 25edo is very close to 5/4 (386¢).
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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]], [[18edo]], and [[29edo]]. (11edo and 18edo not shown in table below.)
Edos include [[11edo]] (not shown), [[18edo]], and [[29edo]].
{{MOS degrees|Scale Signature=4L 3s|Step Ratio=5/3|Genchain Extend=3}}
{{MOS degrees|Scale Signature=4L 3s|Step Ratio=3/2; 5/3|Genchain Extend=3}}
===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]], [[15edo]], [[26edo]], and [[37edo]].
Other hypohard edos include [[11edo]] (not shown), [[15edo]] and [[37edo]].
{{MOS degrees|Scale Signature=4L 3s|Step Ratio=2/1; 3/1; 5/2; 7/3|Genchain Extend=3}}
{{MOS degrees|Scale Signature=4L 3s|Step Ratio=3/1; 5/2; 7/3|Genchain Extend=3}}
===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¢), six of which and octave-reducing approximates 3/2 (702¢), a diatonic perfect 5th.
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.
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.
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These JI approximations are associated with [[kleismic]] temperament, though the 2.3.5.13 extension described here is called [[Chromatic pairs#Cata|cata]].
These JI approximations are associated with [[kleismic]] temperament, though the 2.3.5.13 extension described here is called [[Chromatic pairs#Cata|cata]].


Other edos smaller than 53edo include [[15edo]], [[19edo]], and [[34edo]].
Parahard edos smaller than 53edo include [[15edo]] (not shown), [[19edo]], and [[34edo]].
{{MOS degrees|Scale Signature=4L 3s|Step Ratio=3/1; 4/1; 7/2; 11/3|Genchain Extend=3}}
{{MOS degrees|Scale Signature=4L 3s|Step Ratio=4/1; 7/2; 11/3; 15/4|Genchain Extend=3|Prefix=smi}}
===Tuning examples===
===Tuning examples===
''(add tuning examples)''
''(add tuning examples)''
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==Modes==
==Modes==
{{MOS modes|Scale Signature=4L 3s|Mode Names=Nerevarine; Vivecan; Lorkhanic; Sothic; Kagrenacan; Almalexian; Dagothic}}
{{MOS modes|Scale Signature=4L 3s|Mode Names=Nerevarine; Vivecan; Lorkhanic; Sothic; Kagrenacan; Almalexian; Dagothic}}
==Approaches==
*[[4L 3s/Inthar's approach]]
==Scales==
==Scales==


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==Music==
==Music==
''(add music)''
''(add music)''
== See also ==
Approaches:
*[[4L 3s/Inthar's approach]]
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