5L 2s: Difference between revisions

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

[[TAMNAMS]] suggests the temperament-agnostic name '''diatonic''' for this scale, which commonly refers to a scale with 5 whole steps and 2 half steps. Under TAMNAMS and for all scale pattern pages on the wiki, '''the term ''diatonic'' exclusively refers to 5L 2s'''.

The term ''diatonic'' may also refer to scales that have more than one size of whole step, such as those produced using [[Tetrachord|tetrachords]] or [[just intonation]]. Such diatonic-like scales, such as [[Zarlino]], [[blackdye]] and [[diasem]], are called ''[[Detempering|detempered]] diatonic scales'' (for an RTT-based philosophy) or ''deregularized diatonic scales'' (for an RTT-agnostic philosophy). The terms ''diatonic-like'' or ''diatonic-based'' may also be used to refer such scales, depending on what's contextually the most appropriate.

:''This article assumes [[TAMNAMS]] for naming step ratios.''

===Intervals===

Intervals are identical to that of standard notation. As such, the usual [[Interval quality|interval qualities]] of major/minor and augmented/perfect/diminished apply here.

== Tuning ranges==

===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.{{MOS degrees|Step Ratio=2/1; 3/1; 3/2|Genchain Extend=7}}

=== Parasoft tunings===

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¢).

Edos include [[19edo]], [[26edo]], [[45edo]], and [[64edo]].{{MOS degrees|Step Ratio=3/2; 4/3; 7/5; 10/7|Genchain Extend=0, 5|MOS Prefix=dia}}

===Hyposoft tunings===

:''Main article: [[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¢).

====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¢).

====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¢).

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.{{MOS degrees|Step Ratio=3/1; 5/2; 8/3|Genchain Extend=0, 5}}

Edos include [[17edo]], [[22edo]], [[27edo]], and [[32edo]], among others.{{MOS degrees|Step Ratio=3/1; 4/1; 5/1; 6/1|Genchain Extend=0, 5}}

Diatonic modes have standard names from classical music theory.

Each mode has the following scale degrees, reached by raising or lowering certain naturals by a chroma.

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==Scales==

5L 2s has a parent scale of [[2L 3s]], a pentatonic scale, meaning 2L 3s is a subset. 5L 2s also has two child scales, which are supersets of 5L 2s:

*[[7L 5s]], a chromatic scale produced using soft-of-basic step ratios.

*[[5L 7s]], a chromatic scale produced using hard-of-basic step ratios.

12edo, the equalized form of both 7L 5s and 5L 7s, is also a superset of 5L 2s.

===MODMOS scales and muddles===

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

* [[Archy7]] – 472edo tuning

===Step ratio diagram===

==See also==

 

*[[Diatonic functional harmony]]

[[Category:Diatonic| ]] <!-- main article -->