User:Ganaram inukshuk/5L 2s: Difference between revisions

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5L 2s has several temperament interpretations, such as:

* Flattone, with a generator size around ~~694¢~~, corresponding to a step ratio within the ~~ultrasoft to~~ parasoft range (6:5 to 3:2).

* Flattone, with a generator size around 692.3¢ to 694.7¢, corresponding to a step ratio within the parasoft range (4:3 to 3:2).

*Meantone, with a generator size around 696¢, corresponding to a step ratio within the hyposoft range (3:2 to 2:1).

*Schismic, with a generator size around 702¢ (just perfect 5th, or 3/2), corresponding to a step ratio within the hypohard range (2:1 to 3:2).

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== Step ratios==

===~~Ultrasoft to parasoft~~===

===Parasoft===

~~Ultrasoft~~ to ~~parasoft tunings~~ correspond to flattone temperaments, characterized by flattening the perfect 5th (3/2) ~~to achieve a~~ diatonic major 3rd ~~that is flat of~~ 5/4 (386¢). ~~Examples of this~~ include 26edo ~~(step ratio~~ 4:3).

:''Main article: [[Flattone]]''

Parasoft tunings (step ratios between 4:3 to 3:2) correspond to flattone temperaments, characterized by flattening the perfect 5th (3/2) so it makes the diatonic major 3rd flatter than 5/4 (386¢). Compatible edos include 26edo, 45edo, and 64edo.

===Hyposoft===

:''Main article: [[Meantone]]''

Hyposoft tunings correspond to meantone temperaments, characterized by flattening the perfect 5th (3/2) to achieve a diatonic major 3rd that approximates 5/4 (386¢). ~~Examples of this~~ include 19edo (step ~~ratio 3~~:2) and ~~31edo~~ (step ~~ratio~~ 5:3).

Hyposoft tunings (step ratio between 3:2 to 2:1) correspond to meantone temperaments, characterized by flattening the perfect 5th (3/2) to achieve a diatonic major 3rd that approximates 5/4 (386¢). Compatible edos include 19edo, 31edo, and 50edo.

===Hypohard ===

:''Main articles: [[Pythagorean tuning]] and [[Schismatic family#Schismatic aka Helmholtz|schismatic temperament]]''

The range of hypohard tunings can be divided into a minihard range (step ratios 2:1 to 5:2) and quasihard range (step ratios 5:2 to 3:1).

==== Minihard ====

Minihard tunings correspond to Pythagorean tuning and schismatic temperament, characterized by having a perfect 5th that is as close to just (701.96¢) as possible, resulting in 81/64 (407.8¢) for its major 3rd. Compatible edos include 41edo, and 53edo.

===~~Hypohard~~===

==== Quasihard ====

Quasihard tunings correspond to "neogothic" or "parapyth" systems whose perfect 5th is sharper than just, resulting in major 3rds that are sharper than 81/64. Compatible edos include 29edo and 46edo.

===Parahard to ultrahard===

17edo is considered to be on the sharper end of the neogothic spectrum, with a major 3rd that is more discordant than flatter neogothic tunings.

===Parahard and ultrahard===

Parahard and ultrahard tunings (step ratio 3:1 or sharper) correspond to "archy" systems. Compatible edos include 17edo and 22edo.

==Modes==

== Modes==

Diatonic modes have standard names from classical music theory:

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==Scales==

=== Subset and superset ~~MOS~~ scales ===

===Subset and superset scales===

5L 2s has a parent scale of 2L 3s, meaning 5L 2s contains 2L 3s as a subset. 5L 2s also has two child scales that both contain 5L 2s as a subset: either 7L 5s (if the step ratio is less than 2:1) or 5L 7s (if the step ratio is greater than 2:1). A step ratio exactly 2:1 will produce 12edo, an equalized form of 5L 7s and 7L 5s.

=== MODMOS scales and muddles ===

===MODMOS scales and muddles===

{{main| 5L 2s MODMOSes }} ''and [[5L 2s Muddles]]''

=== Scala files ===

===Scala files===

* [[Meantone7]] – 19edo and 31edo tunings

*[[Meantone7]] – 19edo and 31edo tunings

* [[Nestoria7]] – 171edo tuning

*[[Nestoria7]] – 171edo tuning

* [[Pythagorean7]] – Pythagorean tuning

*[[Pythagorean7]] – Pythagorean tuning

* [[Garibaldi7]] – 94edo tuning

*[[Garibaldi7]] – 94edo tuning

* [[Cotoneum7]] – 217edo tuning

*[[Cotoneum7]] – 217edo tuning

* [[Pepperoni7]] – 271edo tuning

*[[Pepperoni7]] – 271edo tuning

* [[Supra7]] – 56edo tuning

*[[Supra7]] – 56edo tuning

* [[Archy7]] – 472edo tuning

*[[Archy7]] – 472edo tuning

==Tuning spectrum==

{{Scale tree|5L 2s|depth=6|Comments=7/5:[[Flattone]] is in this region;21/13:[[Golden meantone]] (696.2145¢);5/3:[[Meantone]] is in this region;2/1:(Generators smaller than this are proper);9/4:The generator closest to a just [[3/2]] for EDOs less than 200;16/7:[[Garibaldi]] / [[Cassandra]];21/8:Golden neogothic (704.0956¢);8/3:[[Neogothic]] is in this region;4/1:[[Archy]] is in this region|tuning=5L 2s}}

== See also ==

==See also==

* [[Diatonic functional harmony]]

*[[Diatonic functional harmony]]

@@ Line 129: / Line 129: @@
 L 2s has several temperament interpretations, such as:
-* Flattone, with a generator size around 694¢, corresponding to a step ratio within the ultrasoft to parasoft range (6:5 to 3:2).
+* Flattone, with a generator size around 692.3¢ to 694.7¢, corresponding to a step ratio within the parasoft range (4:3 to 3:2).
 *Meantone, with a generator size around 696¢, corresponding to a step ratio within the hyposoft range (3:2 to 2:1).
 *Schismic, with a generator size around 702¢ (just perfect 5th, or 3/2), corresponding to a step ratio within the hypohard range (2:1 to 3:2).
@@ Line 137: / Line 137: @@
 == Step ratios==
-===Ultrasoft to parasoft===
+===Parasoft===
-Ultrasoft to parasoft tunings correspond to flattone temperaments, characterized by flattening the perfect 5th (3/2) to achieve a diatonic major 3rd that is flat of 5/4 (386¢). Examples of this include 26edo (step ratio 4:3).
+:''Main article: [[Flattone]]''
+Parasoft tunings (step ratios between 4:3 to 3:2) correspond to flattone temperaments, characterized by flattening the perfect 5th (3/2) so it makes the diatonic major 3rd flatter than 5/4 (386¢). Compatible edos include 26edo, 45edo, and 64edo.
+{{MOS degrees|Scale Signature=5L 2s|Step Ratio=4/3; 7/5; 10/7}}
 ===Hyposoft===
 :''Main article: [[Meantone]]''
-Hyposoft tunings correspond to meantone temperaments, characterized by flattening the perfect 5th (3/2) to achieve a diatonic major 3rd that approximates 5/4 (386¢). Examples of this include 19edo (step ratio 3:2) and 31edo (step ratio 5:3).
+Hyposoft tunings (step ratio between 3:2 to 2:1) correspond to meantone temperaments, characterized by flattening the perfect 5th (3/2) to achieve a diatonic major 3rd that approximates 5/4 (386¢). Compatible edos include 19edo, 31edo, and 50edo.
+{{MOS degrees|Scale Signature=5L 2s|Step Ratio=3/2; 5/3; 8/5}}
+===Hypohard ===
+:''Main articles: [[Pythagorean tuning]] and [[Schismatic family#Schismatic aka Helmholtz|schismatic temperament]]''
+The range of hypohard tunings can be divided into a minihard range (step ratios 2:1 to 5:2) and quasihard range (step ratios 5:2 to 3:1).
-{{MOS degrees|Scale Signature=5L 2s|Step Ratio=3/2; 5/3}}
+==== Minihard ====
+Minihard tunings correspond to Pythagorean tuning and schismatic temperament, characterized by having a perfect 5th that is as close to just (701.96¢) as possible, resulting in 81/64 (407.8¢) for its major 3rd. Compatible edos include 41edo, and 53edo.
+{{MOS degrees|Scale Signature=5L 2s|Step Ratio=7/3; 9/4}}
-===Hypohard===
+==== Quasihard ====
+Quasihard tunings correspond to "neogothic" or "parapyth" systems whose perfect 5th is sharper than just, resulting in major 3rds that are sharper than 81/64. Compatible edos include 29edo and 46edo.
-===Parahard to ultrahard===
+edo is considered to be on the sharper end of the neogothic spectrum, with a major 3rd that is more discordant than flatter neogothic tunings.
+{{MOS degrees|Scale Signature=5L 2s|Step Ratio=5/2; 8/3; 3/1}}
+===Parahard and ultrahard===
+Parahard and ultrahard tunings (step ratio 3:1 or sharper) correspond to "archy" systems. Compatible edos include 17edo and 22edo.
+{{MOS degrees|Scale Signature=5L 2s|Step Ratio=3/1; 4/1}}
-==Modes==
+== Modes==
 Diatonic modes have standard names from classical music theory:
@@ Line 156: / Line 172: @@
 ==Scales==
-=== Subset and superset MOS scales ===
+===Subset and superset scales===
 L 2s has a parent scale of 2L 3s, meaning 5L 2s contains 2L 3s as a subset. 5L 2s also has two child scales that both contain 5L 2s as a subset: either 7L 5s (if the step ratio is less than 2:1) or 5L 7s (if the step ratio is greater than 2:1). A step ratio exactly 2:1 will produce 12edo, an equalized form of 5L 7s and 7L 5s.
-=== MODMOS scales and muddles ===
+===MODMOS scales and muddles===
 {{main| 5L 2s MODMOSes }} ''and [[5L 2s Muddles]]''
-=== Scala files ===
+===Scala files===
-* [[Meantone7]] – 19edo and 31edo tunings
+*[[Meantone7]] – 19edo and 31edo tunings
-* [[Nestoria7]] – 171edo tuning
+*[[Nestoria7]] – 171edo tuning
-* [[Pythagorean7]] – Pythagorean tuning
+*[[Pythagorean7]] – Pythagorean tuning
-* [[Garibaldi7]] – 94edo tuning
+*[[Garibaldi7]] – 94edo tuning
-* [[Cotoneum7]] – 217edo tuning
+*[[Cotoneum7]] – 217edo tuning
-* [[Pepperoni7]] – 271edo tuning
+*[[Pepperoni7]] – 271edo tuning
-* [[Supra7]] – 56edo tuning
+*[[Supra7]] – 56edo tuning
-* [[Archy7]] – 472edo tuning
+*[[Archy7]] – 472edo tuning
 ==Tuning spectrum==
 {{Scale tree|5L 2s|depth=6|Comments=7/5:[[Flattone]] is in this region;21/13:[[Golden meantone]] (696.2145¢);5/3:[[Meantone]] is in this region;2/1:(Generators smaller than this are proper);9/4:The generator closest to a just [[3/2]] for EDOs less than 200;16/7:[[Garibaldi]] / [[Cassandra]];21/8:Golden neogothic (704.0956¢);8/3:[[Neogothic]] is in this region;4/1:[[Archy]] is in this region|tuning=5L 2s}}
-== See also ==
+==See also==
-* [[Diatonic functional harmony]]
+*[[Diatonic functional harmony]]