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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.
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==
==Tuning ranges==
{{Todo|Populate|comment=Populate with JI ratios from prior edits of this page.|inline=1}}
===Simple tunings===
===Simple tunings===
The simplest tunings are those with step ratios 2:1, 3:1, and 3:2, producing 11edo, 15edo, and 18edo, respectively.
The simplest tunings are those with step ratios 2:1, 3:1, and 3:2, producing 11edo, 15edo, and 18edo, respectively.
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===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 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 major 1-mosstep, or large step, is around [[10/9]] to [[9/8]], thus making it a "meantone".
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**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¢).
*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 tunings|Step Ratios=3/2; 4/3; 7/5}}
{{MOS degrees|Step Ratio=3/2; 4/3; 7/5|Number of Alterations=1|JI Ratios=m1md: [[13/12]];
 
M1md: [[9/8]], [[10/9]];
P2md: [[17/14]], [[40/33]];
A2md: [[5/4]];
m3md: [[21/16]];
M3md: [[19/14]], [[34/25]];
A3md: [[7/5]];
d4md: [[10/7]];
m4md: [[28/19]], [[25/17]];
M4md: [[32/21]];
d5md: [[8/5]];
P5md: [[28/17]], [[33/20]];
m6md: [[16/9]], [[9/5]];
M6md: [[24/13]]}}
===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|Step Ratio=3/2; 5/3|JI Ratios=m1md: [[14/13]];
 
M1md: [[9/8]];
{{MOS tunings|Step Ratios=3/2; 5/3}}
P2md: [[23/19]], [[40/33]];
 
A2md: [[14/11]];
m3md: [[13/10]];
M3md: [[15/11]];
m4md: [[19/13]], [[22/15]];
M4md: [[20/13]];
d5md: [[11/7]];
P5md: [[33/20]], [[38/23]];
m6md: [[16/9]];
M6md: [[13/7]]}}
=== 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|Step Ratio=3/1; 5/2; 7/3|JI Ratios=M1md: [[8/7]];
 
P2md: [[6/5]], [[77/64]];
{{MOS tunings|Step Ratios=3/1; 5/2; 7/3}}
m3md: [[14/11]];
 
M3md: [[11/8]];
m4md: [[16/11]];
M4md: [[11/7]];
P5md: [[5/3]];
m6md: [[7/4]];}}
===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|Step Ratio=4/1; 7/2; 11/3; 15/4|JI Ratios=m1md: [[25/24]], [[26/25]];
 
M1md: [[15/13]];
{{MOS tunings|Step Ratios=4/1; 7/2; 11/3}}
P2md: [[6/5]];
 
A2md: [[4/3]];
m3md: [[5/4]];
M3md: [[18/13]];
m4md: [[13/9]];
M4md: [[8/5]];
d5md: [[3/2]];
P5md: [[5/3]];
m6md: [[26/15]];
M6md: [[25/13]]}}
==Scales==
==Scales==
*[[Orgone7]]
*[[Orgone7]]
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