4L 3s: Difference between revisions
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For this article, note names are based on diamond-MOS notation, where the naturals JKLMNOP are applied to the step pattern LsLsLsL and the accidentals & (pronounced "am" or "amp") and @ (pronounced "at") are used to represent sharps and flats respectively. Thus, the basic gamut for 4L 3s is the following: | For this article, note names are based on diamond-MOS notation, where the naturals JKLMNOP are applied to the step pattern LsLsLsL and the accidentals & (pronounced "am" or "amp") and @ (pronounced "at") are used to represent sharps and flats respectively. Thus, the basic gamut for 4L 3s is the following: | ||
{{MOS gamut | {{MOS gamut}} | ||
==Theory == | ==Theory == | ||
===Low harmonic entropy scales=== | ===Low harmonic entropy scales=== | ||
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==Tuning ranges== | ==Tuning ranges== | ||
===Simple tunings=== | ===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]].{{MOS degrees | 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]].{{MOS degrees|Step Ratio=2/1; 3/1; 3/2}} | ||
===Parasoft 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: | Parasoft smitonic tunings (4:3 to 3:2) can be considered "meantone smitonic" since it has the following features of [[meantone]] diatonic tunings: | ||
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*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¢). | ||
*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. | *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. | ||
{{MOS degrees | {{MOS degrees|Step Ratio=3/2; 4/3; 7/5|Genchain Extend=9}} | ||
===Hyposoft tunings=== | ===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". | 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]]. | Edos include [[11edo]] (not shown), [[18edo]], and [[29edo]]. | ||
{{MOS degrees | {{MOS degrees|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]] (not shown), [[15edo]] and [[37edo]]. | Other hypohard edos include [[11edo]] (not shown), [[15edo]] and [[37edo]]. | ||
{{MOS degrees | {{MOS degrees|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¢). Stacking six generators and octave-reducing approximates 3/2 (702¢), a diatonic perfect 5th, represented by the diminished 5-mosstep. | 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. | ||
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Parahard edos smaller than 53edo include [[15edo]] (not shown), [[19edo]], and [[34edo]]. | Parahard edos smaller than 53edo include [[15edo]] (not shown), [[19edo]], and [[34edo]]. | ||
{{MOS degrees | {{MOS degrees|Step Ratio=4/1; 7/2; 11/3; 15/4|Genchain Extend=3|Prefix=smi}} | ||
==Modes== | ==Modes== | ||
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): | 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 | {{MOS modes|Mode Names=Nerevarine; Vivecan; Lorkhanic; Sothic; Kagrenacan; Almalexian; Dagothic}} | ||
==Scales== | ==Scales== | ||
===Subset and superset scales=== | ===Subset and superset scales=== | ||