5L 2s: Difference between revisions

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{{Main| 5L 2s/Temperaments }}
{{Main| 5L 2s/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.. This includes:
* [[Meantone]], with generators around 696.2{{c}}. This includes:
** [[Flattone]], with generators around 693..
** [[Flattone]], with generators around 693.7{{c}}.
* [[Schismic]], with generators around 702¢.
* [[Schismic]], with generators around 702{{c}}.
* [[Parapyth]], with generators around 704..
* [[Parapyth]], with generators around 704.7{{c}}.
* [[Archy]], with generators around 709.. This includes:
* [[Archy]], with generators around 709.3{{c}}. This includes:
** Supra, with generators around 707.
** Supra, with generators around 707.2{{c}}
** Superpyth, with generators around 710.
** Superpyth, with generators around 710.3{{c}}
** Ultrapyth, with generators around 713..
** Ultrapyth, with generators around 713.7{{c}}.
=== 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.  
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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.
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{{Scale tree|depth=6|Comments=
{{Scale tree|depth=6|Comments=
7/5:[[Flattone]] is in this region;
7/5:[[Flattone]] is in this region;
21/13:[[Golden meantone]] (696.214¢);
21/13:[[Golden meantone]] (696.214{{c}});
5/3:[[Meantone]] is in this region;
5/3:[[Meantone]] is in this region;
9/4:[[Pythagorean tuning]] (701.955¢);
9/4:[[Pythagorean tuning]] (701.955{{c}});
16/7:[[Garibaldi]] / [[cassandra]];
16/7:[[Garibaldi]] / [[cassandra]];
5/2:[[Dominant (temperament)|Dominant]] is in this region;  
5/2:[[Dominant (temperament)|Dominant]] is in this region;  
21/8:Golden neogothic (704.096¢);
21/8:Golden neogothic (704.096{{c}});
8/3:[[Neogothic]] is in this region;
8/3:[[Neogothic]] is in this region;
4/1:[[Archy]] is in this region
4/1:[[Archy]] is in this region