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

Line 11:

== Notation ==

: ''This article assumes [[TAMNAMS]] for naming step ratios, intervals, and scale degrees, and [[Diamond-mos notation|diamond-MOS notation]] for note names ~~as the primary means of notation~~.''

: ''This article assumes [[TAMNAMS]] for naming step ratios, intervals, and scale degrees, and [[Diamond-mos notation|diamond-MOS notation]] for note names.''

=== Interval names ===

=== Interval and degree names ===

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.

Line 103:

== Step ratios ==

The basic tuning for 4L 3s has a large and small step size of 2 and 1 respectively, which is supported by 11edo. Raising or lowering certain nominals by a [[chroma]] produces the following scale degrees.

~~{{MOS degrees|Scale Signature=4L 3s|Step Ratio=2/1}}~~

=== 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|Scale Signature=4L 3s|Step Ratio=2/1; 3/1; 3/2}}

=== ~~Soft~~ tunings ===

=== Parasoft tunings ===

=== ~~Hard~~ 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".

* The augmented 2-mosstep is around the size of a meantone-sized major 3rd and can be used as a stand-in for such.

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.

Edos include [[18edo]], [[25edo]], and [[43edo]]. Some key considerations include:

* 18edo can be used to make the large and small steps more distinct.

** 18edo smitonic can also be considered a distorted 19edo diatonic.

** 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 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¢).

{{MOS degrees|Scale Signature=4L 3s|Step Ratio=3/2; 4/3; 7/5|Genchain Extend=9}}

=== 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]], [[18edo]], and [[29edo]]. (11edo and 18edo not shown in table below.)

{{MOS degrees|Scale Signature=4L 3s|Step Ratio=5/3|Genchain Extend=3}}

=== 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]], [[15edo]], [[26edo]], and [[37edo]].

{{MOS degrees|Scale Signature=4L 3s|Step Ratio=2/1; 3/1; 5/2; 7/3|Genchain Extend=3}}

=== 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.

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.

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]].

{{MOS degrees|Scale Signature=4L 3s|Step Ratio=3/1; 4/1; 7/2; 11/3|Genchain Extend=3}}

=== Tuning examples ===

''(add tuning examples)''

== Modes ==

{{MOS modes|Scale Signature=4L 3s|Mode Names=Nerevarine; Vivecan; Lorkhanic; Sothic; Kagrenacan; Almalexian; Dagothic}}

== Approaches ==

* [[4L 3s/Inthar's approach]]

== Scales ==

=== Scala files ===

* [[Orgone7]]

* [[Cata7]]

* [[Myna7]]

== Music ==

''(add music)''

== Tuning spectrum ==

~~{| class="wikitable"~~

{{Scale tree|4L 3s|Comments=6/5: [[Amity]]/[[hitchcock]]↑;

|+

5/4: [[Sixix]];

~~! rowspan="2" |Steps of ED~~

13/8: Golden 4L 3s (868.3282¢);

~~! colspan="2" |Cents~~

12/5: [[Hyperkleismic]];

~~! colspan="2" |Step ratio~~

5/2 [[Orgone]];

~~! rowspan="2" |Comments~~

13/5: Golden superkleismic;

|-

8/3: [[Superkleismic]];

~~!Bright gen~~

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

~~!Dark gen~~

6/1: [[Oolong]]/[[myna]]↓;

~~!L:s~~

2/1: (Generators smaller than this are proper)}}

~~!Hardness~~

|}

{{Scale tree|4L 3s|Comments=6/5: [[Amity]]/[[hitchcock]]↑; 5/4: [[Sixix]]; 13/8: Golden 4L 3s; 12/5: [[Hyperkleismic]]; 5/2 [[Orgone]]; 13/5: Golden superkleismic; 8/3: [[Superkleismic]]; 11/3: [[Hanson]]/[[keemun]]; 6/1: [[Oolong]]/[[myna]]↓; 2/1: (Generators smaller than this are proper)}}

@@ Line 11: / Line 11: @@
 == Notation ==
-: ''This article assumes [[TAMNAMS]] for naming step ratios, intervals, and scale degrees, and [[Diamond-mos notation|diamond-MOS notation]] for note names as the primary means of notation.''
+: ''This article assumes [[TAMNAMS]] for naming step ratios, intervals, and scale degrees, and [[Diamond-mos notation|diamond-MOS notation]] for note names.''
-=== Interval names ===
+=== Interval and degree names ===
 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.
@@ Line 103: / Line 103: @@
 == Step ratios ==
-The basic tuning for 4L 3s has a large and small step size of 2 and 1 respectively, which is supported by 11edo. Raising or lowering certain nominals by a [[chroma]] produces the following scale degrees.
-{{MOS degrees|Scale Signature=4L 3s|Step Ratio=2/1}}
 === Simple tunings ===
-{{MOS degrees|Scale Signature=4L 3s|Step Ratio=2/1; 3/1; 3/2}}
+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|Scale Signature=4L 3s|Step Ratio=2/1; 3/1; 3/2}}
-=== Soft tunings ===
-{{MOS degrees|Scale Signature=4L 3s|Step Ratio=3/2; 4/3; 5/3}}
+=== Parasoft tunings ===
-=== Hard tunings ===
+Parasoft smitonic tunings (4:3 to 3:2) can be considered "meantone smitonic" since it has the following features of [[meantone]] diatonic tunings:
-{{MOS degrees|Scale Signature=4L 3s|Step Ratio=3/1; 4/1; 5/2}}
+* The major 1-mosstep, or large step, is around [[10/9]] to [[9/8]], thus making it a "meantone".
+* The augmented 2-mosstep is around the size of a meantone-sized major 3rd and can be used as a stand-in for such.
+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.
+Edos include [[18edo]], [[25edo]], and [[43edo]]. Some key considerations include:
+* 18edo can be used to make the large and small steps more distinct.
+** 18edo smitonic can also be considered a distorted 19edo diatonic.
+** 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 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¢).
+{{MOS degrees|Scale Signature=4L 3s|Step Ratio=3/2; 4/3; 7/5|Genchain Extend=9}}
+=== 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]], [[18edo]], and [[29edo]]. (11edo and 18edo not shown in table below.)
+{{MOS degrees|Scale Signature=4L 3s|Step Ratio=5/3|Genchain Extend=3}}
+=== 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]], [[15edo]], [[26edo]], and [[37edo]].
+{{MOS degrees|Scale Signature=4L 3s|Step Ratio=2/1; 3/1; 5/2; 7/3|Genchain Extend=3}}
+=== 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.
+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.
+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]].
+{{MOS degrees|Scale Signature=4L 3s|Step Ratio=3/1; 4/1; 7/2; 11/3|Genchain Extend=3}}
+=== Tuning examples ===
+''(add tuning examples)''
 == Modes ==
 {{MOS modes|Scale Signature=4L 3s|Mode Names=Nerevarine; Vivecan; Lorkhanic; Sothic; Kagrenacan; Almalexian; Dagothic}}
+== Approaches ==
+* [[4L 3s/Inthar's approach]]
+== Scales ==
+=== Scala files ===
+* [[Orgone7]]
+* [[Cata7]]
+* [[Myna7]]
+== Music ==
+''(add music)''
 == Tuning spectrum ==
-{| class="wikitable"
+{{Scale tree|4L 3s|Comments=6/5: [[Amity]]/[[hitchcock]]↑;
-|+
+/4: [[Sixix]];
-! rowspan="2" |Steps of ED
+/8: Golden 4L 3s (868.3282¢);
-! colspan="2" |Cents
+/5: [[Hyperkleismic]];
-! colspan="2" |Step ratio
+/2 [[Orgone]];
-! rowspan="2" |Comments
+/5: Golden superkleismic;
-|-
+/3: [[Superkleismic]];
-!Bright gen
+/3: [[Hanson]]/[[keemun]];
-!Dark gen
+/1: [[Oolong]]/[[myna]]↓;
-!L:s
+/1: (Generators smaller than this are proper)}}
-!Hardness
-|}
-{{Scale tree|4L 3s|Comments=6/5: [[Amity]]/[[hitchcock]]↑; 5/4: [[Sixix]]; 13/8: Golden 4L 3s; 12/5: [[Hyperkleismic]]; 5/2 [[Orgone]]; 13/5: Golden superkleismic; 8/3: [[Superkleismic]]; 11/3: [[Hanson]]/[[keemun]]; 6/1: [[Oolong]]/[[myna]]↓; 2/1: (Generators smaller than this are proper)}}