Xenharmonic Wiki

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

← Older editNewer edit →
VisualWikitext
Ganaram inukshuk (talk | contribs)
autopatrolled, emailconfirmed
4,810 edits
Ganaram inukshuk (talk | contribs)
autopatrolled, emailconfirmed
4,810 edits
Partial cleanup of sandboxed page
Line 120: Line 120:
== 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|Step Ratio=2/1; 3/1; 3/2|JI Ratios=M1md: [[8/7]];
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]].
P2md: [[6/5]], [[77/64]];
m3md: [[14/11]];
M3md: [[11/8]];
m4md: [[16/11]];
M4md: [[11/7]];
P5md: [[5/3]];
m6md: [[7/4]]
|Scale Signature=4L 3s}}
===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:
Line 145: Line 137:
* 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|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]]
|Scale Signature=4L 3s}}
===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]];
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]]
|Scale Signature=4L 3s}}
===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]];
m3md: [[14/11]];
M3md: [[11/8]];
m4md: [[16/11]];
M4md: [[11/7]];
P5md: [[5/3]];
m6md: [[7/4]];
|Scale Signature=4L 3s}}
===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.
Line 198: Line 153:


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]];
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]]
|Scale Signature=4L 3s}}
== Scales ==
== Scales ==
''Move to quickstart guide.''
''Move to quickstart guide.''
Retrieved from "https://en.xen.wiki/w/User:Ganaram_inukshuk/4L_3s"