5L 2s: Difference between revisions

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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:

{| class="wikitable"

|+

!Step ratio (L:s)

|1:1

|[[7edo]]

|[[14edo]], [[21edo]], etc.

|[[26edo]]

|3:2

|3 3 2 3 3 3 2

|[[19edo]]

|[[38edo]]

|[[31edo]]

|[[12edo]] (standard tuning)

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

|-

|5 5 2 5 5 5 2

|[[29edo]]

|

|-

|3:1

|3 3 1 3 3 3 1

|[[17edo]]

|[[34edo]]

|[[22edo]]

|[[5edo]]

|[[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]].

TAMNAMS has names for regions of this spectrum based on whether they are "soft" (between 1:1 and 2:1) or "hard" (between 2:1 and 1:0).

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

**Ultrapyth, with generators around 713.7¢.

[[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 tunings===

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

====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¢).

Edos include [[41edo]] and [[53edo]].{{MOS degrees|Step Ratio=7/3; 9/4|Genchain Extend=0, 5}}

====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}}

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.

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

=== Scala files===

*[[Meantone7]] – 19edo and 31edo tunings

*[[Nestoria7]] – 171edo tuning

*[[Pythagorean7]] – Pythagorean tuning

*[[Garibaldi7]] – 94edo tuning

*[[Cotoneum7]] – 217edo tuning

*[[Pepperoni7]] – 271edo tuning

*[[Supra7]] – 56edo tuning

*[[Archy7]] – 472edo tuning

=== Step ratio diagram===

==See also==

*[[Diatonic functional harmony]]