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. | * [[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 | * [[Schismic]], with generators around 702{{c}}. | ||
* [[Parapyth]], with generators around 704. | * [[Parapyth]], with generators around 704.7{{c}}. | ||
* [[Archy]], with generators around 709. | * [[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 | 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 | 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. | 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]] ( | 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 | 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. | 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. | 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. | 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 | ||