5L 2s: Difference between revisions
Table of mos intervals is now a template |
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The familiar pattern of 5 whole steps and 2 half steps, commonly written as WWHWWWH for the major scale, takes on a generalized form of LLsLLLs, where the large and small steps – denoted as L's and s's – represent whole number step sizes, thus producing different [[EDO|edos]]. These [[Step ratio|step ratios]] affect the sizes of the diatonic scale's intervals and correspond to different tuning systems. | |||
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. | 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. | ||
==Name== | ==Name== | ||
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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. | 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. | ||
==Notation== | ==Notation == | ||
:''This article assumes [[TAMNAMS]] for naming step ratios.'' | |||
===Intervals=== | ===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. | 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 intervals}} | ||
=== Note names=== | ===Note names=== | ||
Note names are identical to that of standard notation. Thus, the basic gamut for 5L 2s is the following: | Note names are identical to that of standard notation. Thus, the basic gamut for 5L 2s is the following: | ||
{{MOS gamut}} | {{MOS gamut}} | ||
==Theory== | ==Theory== | ||
===Temperament interpretations=== | ===Temperament interpretations=== | ||
:''Main article: [[5L 2s/Temperaments]]'' | :''Main article: [[5L 2s/Temperaments]]'' | ||
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*[[Archy]], with generators around 709.3¢. This includes: | *[[Archy]], with generators around 709.3¢. This includes: | ||
**Supra, with generators around 707.2¢ | **Supra, with generators around 707.2¢ | ||
** Superpyth, with generators around 710.3¢ | **Superpyth, with generators around 710.3¢ | ||
**Ultrapyth, with generators around 713.7¢. | **Ultrapyth, with generators around 713.7¢. | ||
==Tuning ranges== | == Tuning ranges== | ||
===Simple tunings=== | ===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}} | [[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 tunings=== | ||
:''Main article: [[Flattone]]'' | :''Main article: [[Flattone]]'' | ||
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¢). | 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¢). | ||
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! colspan="8" |Scale degree (on C) | ! colspan="8" |Scale degree (on C) | ||
|- | |- | ||
! UDP | !UDP | ||
!Step pattern | !Step pattern | ||
!1st | ! 1st | ||
! 2nd | !2nd | ||
!3rd | !3rd | ||
!4th | !4th | ||
!5th | !5th | ||
! 6th | !6th | ||
!7th | !7th | ||
!8th | !8th | ||
|- | |- | ||
|<nowiki>6|0</nowiki> | |<nowiki>6|0</nowiki> | ||
| LLLsLLs | |LLLsLLs | ||
|Perfect (C) | |Perfect (C) | ||
|Major (D) | |Major (D) | ||
| Major (E) | |Major (E) | ||
|Augmented (F#) | |Augmented (F#) | ||
|Perfect (G) | |Perfect (G) | ||
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|Perfect (F) | |Perfect (F) | ||
|Perfect (G) | |Perfect (G) | ||
|Major (A) | | Major (A) | ||
|Minor (Bb) | | Minor (Bb) | ||
|Perfect (C) | | Perfect (C) | ||
|- | |- | ||
|<nowiki>3|3</nowiki> | |<nowiki>3|3</nowiki> | ||
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|Perfect (F) | |Perfect (F) | ||
|Perfect (G) | |Perfect (G) | ||
| Major (A) | |Major (A) | ||
| Minor (Bb) | |Minor (Bb) | ||
|Perfect (C) | |Perfect (C) | ||
|- | |- | ||
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|<nowiki>1|5</nowiki> | |<nowiki>1|5</nowiki> | ||
|sLLLsLL | |sLLLsLL | ||
|Perfect (C) | | Perfect (C) | ||
|Minor (Db) | |Minor (Db) | ||
|Minor (Eb) | |Minor (Eb) | ||
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|Perfect (F) | |Perfect (F) | ||
|Diminished (Gb) | |Diminished (Gb) | ||
|Minor (Ab) | | Minor (Ab) | ||
|Minor (Bb) | |Minor (Bb) | ||
|Perfect (C) | | Perfect (C) | ||
|} | |} | ||
==Scales== | ==Scales== | ||
===Subset and superset 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 two child scales, which are supersets of 5L 2s: | 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. | *[[7L 5s]], a chromatic scale produced using soft-of-basic step ratios. | ||
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{{main| 5L 2s MODMOSes }} ''and [[5L 2s Muddles]]'' | {{main| 5L 2s MODMOSes }} ''and [[5L 2s Muddles]]'' | ||
=== Scala files=== | ===Scala files === | ||
*[[Meantone7]] – 19edo and 31edo tunings | *[[Meantone7]] – 19edo and 31edo tunings | ||
*[[Nestoria7]] – 171edo tuning | *[[Nestoria7]] – 171edo tuning | ||
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*[[Archy7]] – 472edo tuning | *[[Archy7]] – 472edo tuning | ||
==Scale tree== | ==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}} | {{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}} | ||
=== Step ratio diagram=== | ===Step ratio diagram=== | ||
[[File:5L2s.jpg|alt=5L2s.jpg|5L2s.jpg]] | [[File:5L2s.jpg|alt=5L2s.jpg|5L2s.jpg]] | ||