5L 2s: Difference between revisions

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| Neutral = 3L 4s

The term ''diatonic'' may also refer to scales produced using [[Tetrachord|tetrachords]], [[just intonation]], or in general have more than one size of whole tone. Such scales, such as [[Zarlino]], [[blackdye]] and [[diasem]], are specifically 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.

==Notation==

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.

{| class="wikitable"

! rowspan="2" |Interval class

! colspan="2" |Large variety

! colspan="2" | Small variety

===Note names ===

Note names are identical to that of standard notation. Thus, the basic (12edo) gamut for 5L 2s is the following:

{{MOS gamut|Scale Signature=5L 2s}}

==Theory ==

===Introduction to step sizes===<!-- The 5L 2s page already had an introduction to step sizes, but this may be worth moving to its own page. -->

:''Main article: [[Scale tree]] and [[TAMNAMS#Step ratio spectrum]]''

The familiar pattern of 5 whole steps and 2 half steps, commonly written as WWHWWWH for the major scale, has step sizes of 2 (whole step) and 1 (half step), producing [[12edo]]. This can be generalized into the form LLsLLLs, with whole-number sizes for the large steps and small steps, denoted as "L" and "s" respectively.

Different edos are produced by using different ratios of step sizes. A few examples are shown below.

!Step pattern

|[[10edo]], [[15edo]], etc.

|}Edos that are multiples of the examples above can be reached by entering non-simplified step ratios. For example, edos that are multiples of 12 are reached by using larger values whose ratio simplifies to 2:1, such as 4:2 for [[24edo]].

All step ratios lie on a spectrum from 1:1 to 1:0, referred to on the wiki as a scale tree. The step ratios 1:1 and 1:0 represent the limits for valid step ratios. A step ratio that approaches 1:1, where the large and small step are equal to one another, approaches [[7edo]], and a step ratio that approaches 1:0, where the small step "collapses" to zero, approaches [[5edo]].

===Temperament interpretations===

:''Main article: [[5L 2s/Temperaments]]''

===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|Scale Signature=5L 2s|Step Ratio=2/1; 3/1; 3/2|Genchain Extend=7}}

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

===Hyposoft tunings ===

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

Hyposoft 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 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 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|Scale Signature=5L 2s|Step Ratio=3/1; 5/2; 8/3|Genchain Extend=0, 5}}

Edos include [[17edo]], [[22edo]], [[27edo]], and [[32edo]], among others.{{MOS degrees|Scale Signature=5L 2s|Step Ratio=3/1; 4/1; 5/1; 6/1|Genchain Extend=0, 5}}

==Modes==

{{MOS modes}}

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

{| class="wikitable"

|<nowiki>6|0</nowiki>

|<nowiki>5|1</nowiki>

|<nowiki>2|4</nowiki>

|<nowiki>1|5</nowiki>

|<nowiki>0|6</nowiki>

|sLLsLLL

|Perfect (C)

==Scales==

===Subset and superset scales===

5L 2s has a parent scale of [[2L 3s]], a pentatonic scale, meaning 2L 3s is a subset. 5L 2s also has the 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 also contains 5L 2s as the equalized form of both 5L 7s and 7L 5s.

===MODMOS scales and muddles===

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

===Scala files===

==Scale tree==

{{Scale tree|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}}

==See also==

* [[Diatonic functional harmony]]