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

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Line 1:

:''This is a test page. For the main page, see [[5L 2s]].''

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==

TAMNAMS suggests the name '''diatonic''' for this scale, which commonly refers to a scale with 5 whole steps and 2 small steps. Under TAMNAMS and for all scale pattern pages on the wiki, '''the term ''diatonic'' exclusively refers to 5L 2s'''.

[[TAMNAMS]] suggests the temperament-agnostic name '''diatonic''' for this scale, which commonly refers to a scale with 5 whole steps and 2 small 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 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==

:''This article assumes [[TAMNAMS]] for naming step ratios, mossteps, and mosdegrees.''

Names for this scale's intervals (mossteps) and scale degrees (mosdegrees) are based on the number of large and small steps from the root, starting at 0 (the 0-mosstep and 0-mosdegree) for the unison.

~~===Intervals===~~

Except for the unison and octave, all [[Interval class|interval classes]] have two [[Interval variety|varieties]] or sizes, denoted using the terms ''major'' and ''minor'' for the large and small sizes, respectively. The exception to this rule are the generators, which use the terms ''augmented'', ''perfect'', and ''diminished'' instead.

~~Intervals are identical to that of standard notation. As such~~, the ~~usual interval qualities of~~ major/minor and augmented/perfect/diminished ~~apply here~~.

{| class="wikitable"

! ~~rowspan="2" |~~Interval class

|+5L 2s interval varieties

! ~~colspan="2" |Large variety~~

!Interval class

! ~~colspan="2" |Small variety~~

!Specific intervals

!Size (in ascending order)

|-

~~!Size~~

|'''0-diastep'''

~~! Quality~~

|'''Perfect 0-diastep (unison)'''

~~!Size~~

|0

~~!Quality~~

|-

|~~'''1st (unison)'''~~

| rowspan="2" |1-diastep

|0

|Minor 1-diastep

|~~Perfect~~

|s

|0

| ~~Perfect~~

|-

|~~2nd~~

|Major 1-diastep

|L

~~| Major~~

|s

~~|Minor~~

|-

|~~3rd~~

| rowspan="2" |2-diastep

|Minor 2-diastep

|L + s

|-

|Major 2-diastep

|2L

~~| Major~~

~~|L + s~~

~~| Minor~~

|-

|~~4th~~

| rowspan="2" |'''3-diastep'''

|'''Perfect 3-diastep'''

|2L + s

|-

|Augmented 3-diastep

|3L

~~|Augmented~~

~~|2L + 1s~~

~~|Perfect~~

|-

|~~5th~~

| rowspan="2" |'''4-diastep'''

|~~3L + 1s~~

|Diminished 4-diastep

|~~Perfect~~

|2L + 2s

~~|Diminished~~

|-

|~~6th~~

|'''Perfect 4-diastep'''

|4L + 1s

|3L + s

|~~Major~~

|-

| rowspan="2" |5-diastep

|Minor 5-diastep

|3L + 2s

~~|Minor~~

|-

|~~7th~~

|Major 5-diastep

| 5L + 1s

|4L + s

|~~Major~~

|-

| rowspan="2" |6-diastep

|Minor 6-diastep

|4L + 2s

~~| Minor~~

|-

|'''~~8th~~ (octave)'''

|Major 6-diastep

|~~5L + 2s~~

|5L + s

|Perfect

|-

|'''7-diastep (octave)'''

|'''Perfect 7-diastep (octave)'''

|5L + 2s

~~|Perfect~~

|}

A 7-note scale using these intervals will typically use scale degrees that represents one size from each interval class, with the true MOS upholding the step pattern of LLLsLLs, or some rotation thereof. MODMOS scales may be formed this way without upholding the step pattern, thereby creating a non-MOS pattern such as LLLLsLs, or may include alterations that exceed the two varieties typical of a MOS scale.

==~~=Note names=~~==

==Notation==

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

:''See [[5L 2s/Notation]]''

==Theory==

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

==Theory ==

===Introduction to step sizes===

Line 87:

Line 85:

!Step pattern

!EDO

!Selected multiples

! Selected multiples

|-

|1:1

Line 95:

Line 93:

|-

|4:3

|4 4 3 4 4 4 3

| 4 4 3 4 4 4 3

|[[26edo]]

|

Line 104:

Line 102:

|[[38edo]]

|-

|5:3

| 5:3

| 5 5 3 5 5 5 3

|[[31edo]]

|

|-

|2:1

| 2:1

| 2 2 1 2 2 2 1

|2 2 1 2 2 2 1

|[[12edo]] (standard tuning)

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

|-

|5:2

|5 5 2 5 5 5 2

| 5 5 2 5 5 5 2

|[[29edo]]

|

|-

| 3:1

|3:1

|3 3 1 3 3 3 1

|[[17edo]]

Line 125:

Line 123:

|-

|4:1

| 4 4 1 4 4 4 1

|4 4 1 4 4 4 1

|[[22edo]]

|

Line 152:

Line 150:

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

**Supra, with generators around 707.2¢

** Superpyth, with generators around 710.3¢

**Superpyth, with generators around 710.3¢

**Ultrapyth, with generators around 713.7¢.

==Tuning ranges==

===Simple tunings===

17edo and 19edo~~, produced using step ratios of 3:1 and 3:2 respectively,~~ 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}}~~

[[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.

===Parasoft tunings===

===Parasoft 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¢).

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}}~~

Edos include [[19edo]], [[26edo]], [[45edo]], and [[64edo]].

=== Hyposoft tunings===

===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¢).

Edos include [[19edo]], [[31edo]], [[43edo]], and [[50edo]].~~{{MOS degrees|Scale Signature=5L 2s|Step Ratio=3/2; 5/3; 7/4; 8/5|Genchain Extend=0, 5}}~~

Edos include [[19edo]], [[31edo]], [[43edo]], and [[50edo]].

===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 ====

====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¢).

Edos include [[41edo]] and [[53edo]].~~{{MOS degrees|Scale Signature=5L 2s|Step Ratio=7/3; 9/4|Genchain Extend=0, 5}}~~

Edos include [[41edo]] and [[53edo]].

====Quasihard tunings====

==== Quasihard tunings====

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]], [[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.

===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¢.

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}}~~

Edos include [[17edo]], [[22edo]], [[27edo]], and [[32edo]], among others.

== Modes ==

==Modes==

Diatonic modes have standard names from classical music theory:

Line 200:

Line 198:

!4th

!5th

!6th

! 6th

!7th

!8th

Line 207:

Line 205:

|LLLsLLs

|Perfect (C)

|Major (D)

| Major (D)

|Major (E)

|Augmented (F#)

Line 224:

Line 222:

|Major (A)

|Major (B)

|Perfect (C)

| Perfect (C)

|-

|<nowiki>4|2</nowiki>

Line 239:

Line 237:

|<nowiki>3|3</nowiki>

|LsLLLsL

|Perfect (C)

| Perfect (C)

|Major (D)

|Minor (Eb)

Line 253:

Line 251:

|Major (D)

|Minor (Eb)

|Perfect (F)

| Perfect (F)

|Perfect (G)

|Minor (Ab)

Line 263:

Line 261:

|Perfect (C)

|Minor (Db)

|Minor (Eb)

| Minor (Eb)

|Perfect (F)

|Perfect (G)

Line 278:

Line 276:

|Diminished (Gb)

|Minor (Ab)

| Minor (Bb)

|Minor (Bb)

| Perfect (C)

|Perfect (C)

|}

== Generator chain ==

''Explain how the scale can also be generated by stacking 6 generating intervals in any combination of up or down from the root. Also explain how this can be extended further to 11 generators to produce chromatic scales.''

==Scales==

=== Subset and superset scales===

===Subset and superset scales===

5L 2s has a parent scale of 2L 3s, meaning ~~5L 2s contains~~ 2L 3s as a subset. 5L 2s also has two child scales ~~that both contain~~ 5L 2s ~~as a subset~~: ~~either~~ 7L 5s ~~(if the~~ step ~~ratio is less than 2:1) or~~ 5L 7s ~~(if the~~ step ~~ratio is greater than 2:1)~~. ~~A step ratio exactly 2:1 will produce~~ 12edo~~, an~~ equalized form of 5L 7s and 7L 5s.

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

===MODMOS scales and muddles===

Line 300:

Line 306:

*[[Archy7]] – 472edo tuning

==Scale tree==

==Scale tree ==

{{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~~}}

{{MOS tuning spectrum

| Scale Signature = 5L 2s

| Depth = 6

| 7/5 = [[Flattone]] is in this region

| 21/13 = [[Golden meantone]] (696.2145{{c}})

| 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{{c}})

| 8/3 = [[Neogothic]] is in this region

| 4/1 = [[Archy]] is in this region

}}

==See also==

* [[Diatonic functional harmony]]

*[[Diatonic functional harmony]]

@@ Line 1: / Line 1: @@
-{{Infobox MOS|Tuning=5L 2s}}
+{{Infobox MOS|Tuning=5L 2s|debug=1}}
 :''This is a test page. For the main page, see [[5L 2s]].''
 {{MOS intro|Scale Signature=5L 2s}}
 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==
-TAMNAMS suggests the name '''diatonic''' for this scale, which commonly refers to a scale with 5 whole steps and 2 small steps. Under TAMNAMS and for all scale pattern pages on the wiki, '''the term ''diatonic'' exclusively refers to 5L 2s'''.
+[[TAMNAMS]] suggests the temperament-agnostic name '''diatonic''' for this scale, which commonly refers to a scale with 5 whole steps and 2 small 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 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==
+:''This article assumes [[TAMNAMS]] for naming step ratios, mossteps, and mosdegrees.''
+Names for this scale's intervals (mossteps) and scale degrees (mosdegrees) are based on the number of large and small steps from the root, starting at 0 (the 0-mosstep and 0-mosdegree) for the unison.
-===Intervals===
+Except for the unison and octave, all [[Interval class|interval classes]] have two [[Interval variety|varieties]] or sizes, denoted using the terms ''major'' and ''minor'' for the large and small sizes, respectively. The exception to this rule are the generators, which use the terms ''augmented'', ''perfect'', and ''diminished'' instead.
-Intervals are identical to that of standard notation. As such, the usual interval qualities of major/minor and augmented/perfect/diminished apply here.
 {| class="wikitable"
-! rowspan="2" |Interval class
+|+5L 2s interval varieties
-! colspan="2" |Large variety
+!Interval class
-! colspan="2" |Small variety
+!Specific intervals
+!Size (in ascending order)
 |-
-!Size
+|'''0-diastep'''
-! Quality
+|'''Perfect 0-diastep (unison)'''
-!Size
+|0
-!Quality
 |-
-|'''1st (unison)'''
+| rowspan="2" |1-diastep
-|0
+|Minor 1-diastep
-|Perfect
+|s
-|0
-| Perfect
 |-
-|2nd
+|Major 1-diastep
 |L
-| Major
-|s
-|Minor
 |-
-|3rd
+| rowspan="2" |2-diastep
+|Minor 2-diastep
+|L + s
+|-
+|Major 2-diastep
 |2L
-| Major
-|L + s
-| Minor
 |-
-|4th
+| rowspan="2" |'''3-diastep'''
+|'''Perfect 3-diastep'''
+|2L + s
+|-
+|Augmented 3-diastep
 |3L
-|Augmented
-|2L + 1s
-|Perfect
 |-
-|5th
+| rowspan="2" |'''4-diastep'''
-|3L + 1s
+|Diminished 4-diastep
-|Perfect
 |2L + 2s
-|Diminished
 |-
-|6th
+|'''Perfect 4-diastep'''
-|4L + 1s
+|3L + s
-|Major
+|-
+| rowspan="2" |5-diastep
+|Minor 5-diastep
 |3L + 2s
-|Minor
 |-
-|7th
+|Major 5-diastep
-| 5L + 1s
+|4L + s
-|Major
+|-
+| rowspan="2" |6-diastep
+|Minor 6-diastep
 |4L + 2s
-| Minor
 |-
-|'''8th (octave)'''
+|Major 6-diastep
-|5L + 2s
+|5L + s
-|Perfect
+|-
+|'''7-diastep (octave)'''
+|'''Perfect 7-diastep (octave)'''
 |5L + 2s
-|Perfect
 |}
+A 7-note scale using these intervals will typically use scale degrees that represents one size from each interval class, with the true MOS upholding the step pattern of LLLsLLs, or some rotation thereof. MODMOS scales may be formed this way without upholding the step pattern, thereby creating a non-MOS pattern such as LLLLsLs, or may include alterations that exceed the two varieties typical of a MOS scale.
-===Note names===
+==Notation==
-Note names are identical to that of standard notation. Thus, the basic (12edo) gamut for 5L 2s is the following:
+:''See [[5L 2s/Notation]]''
+==Theory==
-{{MOS gamut|Scale Signature=5L 2s}}
-==Theory ==
 ===Introduction to step sizes===
@@ Line 87: / Line 85: @@
 !Step pattern
 !EDO
-!Selected multiples
+! Selected multiples
 |-
 |1:1
@@ Line 95: / Line 93: @@
 |-
 |4:3
-|4 4 3 4 4 4 3
+| 4 4 3 4 4 4 3
 |[[26edo]]
 |
@@ Line 104: / Line 102: @@
 |[[38edo]]
 |-
-|5:3
+| 5:3
 | 5 5 3 5 5 5 3
 |[[31edo]]
 |
 |-
-|2:1
+| 2:1
-| 2 2 1 2 2 2 1
+|2 2 1 2 2 2 1
 |[[12edo]] (standard tuning)
 |[[24edo]], [[36edo]], etc.
 |-
 |5:2
-|5 5 2 5 5 5 2
+| 5 5 2 5 5 5 2
 |[[29edo]]
 |
 |-
-| 3:1
+|3:1
 |3 3 1 3 3 3 1
 |[[17edo]]
@@ Line 125: / Line 123: @@
 |-
 |4:1
-| 4 4 1 4 4 4 1
+|4 4 1 4 4 4 1
 |[[22edo]]
 |
@@ Line 152: / Line 150: @@
 *[[Archy]], with generators around 709.3¢. This includes:
 **Supra, with generators around 707.2¢
-** Superpyth, with generators around 710.3¢
+**Superpyth, with generators around 710.3¢
 **Ultrapyth, with generators around 713.7¢.
 ==Tuning ranges==
 ===Simple tunings===
-edo and 19edo, produced using step ratios of 3:1 and 3:2 respectively, 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}}
+[[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.
-===Parasoft tunings===
+===Parasoft 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¢).
-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}}
+Edos include [[19edo]], [[26edo]], [[45edo]], and [[64edo]].
-=== Hyposoft tunings===
+===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¢).
-Edos include [[19edo]], [[31edo]], [[43edo]], and [[50edo]].{{MOS degrees|Scale Signature=5L 2s|Step Ratio=3/2; 5/3; 7/4; 8/5|Genchain Extend=0, 5}}
+Edos include [[19edo]], [[31edo]], [[43edo]], and [[50edo]].
 ===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 ====
+====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¢).
-Edos include [[41edo]] and [[53edo]].{{MOS degrees|Scale Signature=5L 2s|Step Ratio=7/3; 9/4|Genchain Extend=0, 5}}
+Edos include [[41edo]] and [[53edo]].
-====Quasihard tunings====
+==== Quasihard tunings====
 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]], [[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.
 ===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¢.
-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}}
+Edos include [[17edo]], [[22edo]], [[27edo]], and [[32edo]], among others.
-== Modes ==
+==Modes==
 Diatonic modes have standard names from classical music theory:
 {{MOS modes|Scale Signature=5L 2s}}
@@ Line 200: / Line 198: @@
 !4th
 !5th
-!6th
+! 6th
 !7th
 !8th
@@ Line 207: / Line 205: @@
 |LLLsLLs
 |Perfect (C)
-|Major (D)
+| Major (D)
 |Major (E)
 |Augmented (F#)
@@ Line 224: / Line 222: @@
 |Major (A)
 |Major (B)
-|Perfect (C)
+| Perfect (C)
 |-
 |<nowiki>4|2</nowiki>
@@ Line 239: / Line 237: @@
 |<nowiki>3|3</nowiki>
 |LsLLLsL
-|Perfect (C)
+| Perfect (C)
 |Major (D)
 |Minor (Eb)
@@ Line 253: / Line 251: @@
 |Major (D)
 |Minor (Eb)
-|Perfect (F)
+| Perfect (F)
 |Perfect (G)
 |Minor (Ab)
@@ Line 263: / Line 261: @@
 |Perfect (C)
 |Minor (Db)
-|Minor (Eb)
+| Minor (Eb)
 |Perfect (F)
 |Perfect (G)
@@ Line 278: / Line 276: @@
 |Diminished (Gb)
 |Minor (Ab)
-| Minor (Bb)
+|Minor (Bb)
-| Perfect (C)
+|Perfect (C)
 |}
+== Generator chain ==
+''Explain how the scale can also be generated by stacking 6 generating intervals in any combination of up or down from the root. Also explain how this can be extended further to 11 generators to produce chromatic scales.''
 ==Scales==
-=== Subset and superset scales===
+===Subset and superset scales===
-L 2s has a parent scale of 2L 3s, meaning 5L 2s contains 2L 3s as a subset. 5L 2s also has two child scales that both contain 5L 2s as a subset: either 7L 5s (if the step ratio is less than 2:1) or 5L 7s (if the step ratio is greater than 2:1). A step ratio exactly 2:1 will produce 12edo, an equalized form of 5L 7s and 7L 5s.
+L 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.
+edo contains 5L 2s as the equalized form of both 5L 7s and 7L 5s.
 ===MODMOS scales and muddles===
@@ Line 300: / Line 306: @@
 *[[Archy7]] – 472edo tuning
-==Scale tree==
+==Scale tree ==
-{{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}}
+{{MOS tuning spectrum
+| Scale Signature = 5L 2s
+| Depth = 6
+| 7/5 = [[Flattone]] is in this region
+| 21/13 = [[Golden meantone]] (696.2145{{c}})
+| 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{{c}})
+| 8/3 = [[Neogothic]] is in this region
+| 4/1 = [[Archy]] is in this region
+}}
 ==See also==
+* [[Diatonic functional harmony]]
-*[[Diatonic functional harmony]]