User:Ganaram inukshuk/5L 2s: Difference between revisions

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.

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.

===Introduction to step sizes===

!Step pattern

!EDO

|-

|1:1

|-

|4:3

|[[26edo]]

|

|[[38edo]]

|-

| 5 5 3 5 5 5 3

|[[31edo]]

|

|-

|[[12edo]] (standard tuning)

|[[24edo]], [[36edo]], etc.

|-

|5:2

|[[29edo]]

|

|-

|3 3 1 3 3 3 1

|[[17edo]]

|-

|4:1

|[[22edo]]

|

*[[Archy]], with generators around 709.3¢. This includes:

**Supra, with generators around 707.2¢

**Ultrapyth, with generators around 713.7¢.

==Tuning ranges==

===Simple tunings===

:''Main article: [[Flattone]]''

Parasoft 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¢).

:''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¢).

===Hypohard tunings===

:''Main article: [[Pythagorean tuning]] and [[Schismatic family#Schismatic aka Helmholtz|schismatic temperament]]''

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 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¢).

===Parahard and ultrahard tunings===

:''Main article: [[Archy]]''

Parahard (3:1 to 4:1) and ultrahard tunings (4:1 to 1:0) 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|Scale Signature=5L 2s}}

!4th

!5th

!7th

!8th

|LLLsLLs

|Perfect (C)

|Major (E)

|Augmented (F#)

|Major (A)

|Major (B)

|-

|<nowiki>4|2</nowiki>

|<nowiki>3|3</nowiki>

|LsLLLsL

|Major (D)

|Minor (Eb)

|Major (D)

|Minor (Eb)

|Perfect (G)

|Minor (Ab)

|Perfect (C)

|Minor (Db)

|Perfect (F)

|Perfect (G)

|Diminished (Gb)

|Minor (Ab)

|}

==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:

12edo contains 5L 2s as the equalized form of both 5L 7s and 7L 5s.

*[[Archy7]] – 472edo tuning

{{Scale tree|5L 2s|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|tuning=5L 2s}}

==See also==

*[[Diatonic functional harmony]]