5L 2s: Difference between revisions

{{MOS intro}}

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

{{MOS intervals}}

{{MOS gamut}}

5L 2s has several rank-2 temperament interpretations, such as:

[[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 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¢).

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¢).

The range of hypohard tunings can be divided into a minihard range (2:1 to 5:2) and quasihard range (5:2 to 3:1).

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 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¢).

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¢.

Diatonic modes have standard names from classical music theory.

{{MOS modes}}

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

|-

! 1st

|-

|-

|-

| Major (A)

| Minor (Bb)

| Perfect (C)

|-

| LsLLLsL

|-

| Perfect (C)

|-

| Perfect (C)

|-

| Minor (Ab)

| Perfect (C)

|}

=== 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 two child scales, which are supersets of 5L 2s:

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

=== Scala files ===

* [[Archy7]] – 472edo tuning

{{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;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}}

[[File:5L2s.jpg|alt=5L2s.jpg|5L2s.jpg]]

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

[[Category:7-tone scales]]