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5L 2s: Difference between revisions

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{{MOS intro}}
{{MOS intro}}


The familiar pattern of 5 whole steps and 2 half steps, commonly written as WWHWWWH for the major scale, takes on a generalized form of LLsLLLs, where the large and small steps—denoted as L's and s's—represent whole number step sizes, thus producing different [[edo]]s. These [[step ratio]]s affect the sizes of the diatonic scale's intervals and correspond to different tuning systems.
The familiar pattern of 5 whole steps and 2 half steps, commonly written as WWHWWWH for the major scale, takes on a generalized form of LLsLLLs, where the large and small steps—denoted as ''L''{{'s}} and ''s''{{`s}}—represent whole number step sizes, thus producing different [[edo]]s. These [[step ratio]]s affect the sizes of the diatonic scale's intervals and correspond to different tuning systems.


Among the most well-known forms of this scale are the Pythagorean diatonic scale, and scales produced by meantone systems (including [[12edo]]).
Among the most well-known forms of this scale are the Pythagorean diatonic scale, and scales produced by meantone systems (including [[12edo]]).


== Name ==
== Name ==
{{TAMNAMS name}}
{{TAMNAMS name}} "Mosdiatonic" may also be used for the sake of specificity.


== Notation ==
== Notation ==
: ''This article assumes [[TAMNAMS]] for naming step ratios.''
: ''This article assumes [[TAMNAMS]] for naming step ratios.''
== Scale characteristics ==
{{TAMNAMS use}}


=== Intervals ===
=== Intervals ===
Intervals are identical to that of standard notation. As such, the usual [[interval qualities]] of major/minor and augmented/perfect/diminished apply here.
{{MOS intervals}}
{{MOS intervals}}
=== Generator chain ===
{{MOS genchain}}
=== Modes ===
{{MOS mode degrees}}
Diatonic modes have standard names from classical music theory.
{{MOS modes}}


=== Note names ===
=== Note names ===
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== Theory ==
== Theory ==
=== Temperament interpretations ===
=== Temperament interpretations ===
{{Main| 5L 2s/Temperaments }}
{{Main| {{PAGENAME}}/Temperaments }}
5L 2s has several rank-2 temperament interpretations, such as:
5L 2s has several rank-2 temperament interpretations, such as:
* [[Meantone]], with generators around 696.2¢. This includes:
* [[Meantone]], with generators around 696.2{{c}}. This includes:
** [[Flattone]], with generators around 693.7¢.
** [[Flattone]], with generators around 693.7{{c}}.
* [[Schismic]], with generators around 702¢.
* [[Schismic]], with generators around 702{{c}}.
* [[Parapyth]], with generators around 704.7¢.
* [[Leapfrog]], with generators around 704.7{{c}}.
* [[Archy]], with generators around 709.3¢. This includes:
* [[Archy]], with generators around 709.3{{c}}. This includes:
** Supra, with generators around 707.2¢
** Supra, with generators around 707.2{{c}}
** Superpyth, with generators around 710.3¢
** [[Superpyth]], with generators around 710.3{{c}}
** Ultrapyth, with generators around 713.7¢.
** [[Ultrapyth]], with generators around 713.7{{c}}.
 
=== Generator chain ===
{{MOS genchain}}
 
=== Warped diatonic scales ===
=== Warped diatonic scales ===
Because of most listeners’ familiarity with the 5L 2s diatonic scale, listeners may sometimes experience an effect like pareidolia, hearing 5L 2s even when it isn’t there.  
Because of most listeners' familiarity with the 5L 2s diatonic scale, listeners may sometimes experience an effect like pareidolia, hearing 5L 2s even when it isn’t there.  


A larger scale can be constructed so that it contains chains of 5L 2s, but then breaks the pattern, exploiting that pareidolic effect to surprise and disorient the listener. Scales which have this effect are called [[warped diatonic]] scales.
A larger scale can be constructed so that it contains chains of 5L 2s, but then breaks the pattern, exploiting that pareidolic effect to surprise and disorient the listener. Scales which have this effect are called [[warped diatonic]] scales.
=== Interval categories ===
''See [[5L 2s/Interval categories]]''.


== Tuning ranges ==
== Tuning ranges ==
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=== Simple tunings ===
=== Simple tunings ===
[[17edo]] and [[19edo]] are the smallest edos that offer a greater variety of pitches than 12edo. Note that any enharmonic equivalences that 12edo has no longer hold for either 17edo or 19edo, as shown in the table below.
[[17edo]] and [[19edo]] are the smallest edos that offer a greater variety of pitches than 12edo. Note that any enharmonic equivalences that 12edo has no longer hold for either 17edo or 19edo, as shown in the table below.
{{MOS tunings|JI Ratios=Int Limit: 30; Complements Only: 1|Tolerance=20}}
{{MOS tunings|JI Ratios=Int Limit: 30; Complements Only: 1|Tolerance=20}}


=== Ultrasoft tunings ===
=== Ultrasoft tunings ===
{{See also| Superflat }}
In this range, the major third is so flat that it can best be approximated by [[16/13]], tempering out [[1053/1024]].
{{MOS tunings|Step Ratios=Ultrasoft|JI Ratios=NONE}}
{{MOS tunings|Step Ratios=Ultrasoft|JI Ratios=NONE}}


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{{See also| Flattone }}
{{See also| Flattone }}


Parasoft diatonic tunings (4:3 to 3:2) correspond to flattone temperaments, characterized by flattened perfect 5ths ([[3/2]], flat of 702¢) to produce major 3rds that are flatter than [[5/4]] (386¢).
Parasoft diatonic tunings (4:3 to 3:2) correspond to flattone temperaments, characterized by flattened perfect 5ths ([[3/2]], flat of 702{{c}}) to produce major 3rds that are flatter than [[5/4]] (386{{c}}).


Edos include [[19edo]], [[26edo]], [[45edo]], and [[64edo]].
Edos include [[19edo]], [[26edo]], [[45edo]], and [[64edo]].
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{{See also| Meantone }}
{{See also| Meantone }}


Hyposoft diatonic tunings (3:2 to 2:1) correspond to meantone temperaments, characterized by flattened perfect 5ths (flat of 702¢) to produce diatonic major 3rds that approximate 5/4 (386¢).
Hyposoft diatonic tunings (3:2 to 2:1) correspond to meantone temperaments, characterized by flattened perfect 5ths (flat of 702{{c}}) to produce diatonic major 3rds that approximate 5/4 (386{{c}}).


Edos include [[19edo]], [[31edo]], [[43edo]], and [[50edo]].
Edos include [[19edo]], [[31edo]], [[43edo]], and [[50edo]].
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==== Minihard tunings ====
==== Minihard tunings ====
Minihard diatonic 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 a major 3rd of [[81/64]] (407¢).
Minihard diatonic tunings correspond to Pythagorean tuning and schismatic temperament, characterized by having a perfect 5th that is as close to just (701.96{{c}}) as possible, resulting in a major 3rd of [[81/64]] (407{{c}}).


Edos include [[41edo]] and [[53edo]].
Edos include [[41edo]] and [[53edo]].
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==== Quasihard tunings ====
==== Quasihard tunings ====
Quasihard diatonic tunings correspond to "neogothic" or "parapyth" systems whose perfect 5th is slightly sharper than just, resulting in major 3rds that are sharper than 81/64 and minor 3rds that are slightly flat of [[32/27]] (294¢).
Quasihard diatonic tunings correspond to "neogothic" or "parapyth" systems whose perfect 5th is slightly sharper than just, resulting in major 3rds that are sharper than 81/64 and minor 3rds that are slightly flat of [[32/27]] (294{{c}}).


Edos include [[17edo]], [[29edo]], and [[46edo]]. 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.
Edos include [[17edo]], [[29edo]], and [[46edo]]. 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.
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{{See also| Archy }}
{{See also| Archy }}


Parahard (3:1 to 4:1) and ultrahard (4:1 to 1:0) diatonic tunings correspond to archy systems, with perfect 5ths that are significantly sharper than than 702¢.
Parahard (3:1 to 4:1) and ultrahard (4:1 to 1:0) diatonic tunings correspond to archy systems, with perfect 5ths that are significantly sharper than than 702{{c}}.


Edos include [[17edo]], [[22edo]], [[27edo]], and [[32edo]], among others.
Edos include [[17edo]], [[22edo]], [[27edo]], and [[32edo]], among others.
{{MOS tunings|Step Ratios=3/1; 4/1; 5/1; 6/1|JI Ratios=Subgroup: 2.3.7 ; Int Limit: 80; Complements Only: 1|Tolerance=15}}
{{MOS tunings|Step Ratios=3/1; 4/1; 5/1; 6/1|JI Ratios=Subgroup: 2.3.7 ; Int Limit: 80; Complements Only: 1|Tolerance=15}}
== Modes ==
{{MOS mode degrees}}
Diatonic modes have standard names from classical music theory.
{{MOS modes}}


== Scales ==
== Scales ==
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=== MODMOS scales and muddles ===
=== MODMOS scales and muddles ===
{{Main|5L 2s MODMOSes|5L 2s Muddles}}
{{Main|5L 2s/MODMOSes|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
* [[Edson7]] – 29edo tuning
* [[Edson7]] – 29edo tuning
* [[Pepperoni7]] – 271edo tuning
* [[Pepperoni7]] – 271edo tuning
* [[Supra7]] – 56edo tuning
* [[Supra7]] – 56edo tuning
* [[Archy7]] – 472edo tuning
* [[Archy7]] – 49edo tuning


== Scale tree ==
== Scale tree ==
{{Scale tree|depth=6|Comments=
{{MOS tuning spectrum
7/5:[[Flattone]] is in this region;
| Depth = 6
21/13:[[Golden meantone]] (696.214¢);
| 7/5 = [[Flattone]] region
5/3:[[Meantone]] is in this region;
| 21/13 = [[Golden meantone]] (696.214{{c}})
9/4:[[Pythagorean tuning]] (701.955¢);
| 5/3 = [[Meantone]] region
16/7:[[Garibaldi]] / [[cassandra]];
| 9/4 = [[Pythagorean tuning]] (701.955{{c}})
5/2:[[Dominant (temperament)|Dominant]] is in this region;
| 16/7 = [[Garibaldi]] / [[cassandra]]
21/8:Golden neogothic (704.096¢);
| 5/2 = [[Dominant (temperament)|Dominant]] region
8/3:[[Neogothic]] is in this region;
| 21/8 = Golden neogothic (704.096{{c}})
4/1:[[Archy]] is in this region
| 8/3 = [[Neogothic]] region
| 7/2 = [[Quasisuper]] region
| 9/2 = [[Superpyth]] region
| 11/2 = [[Quasiultra]] region
| 7/1 = [[Ultrapyth]] region
}}
}}


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