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→Chords of Bitonic: Fixed information regarding step sizes in triadic chords of Bitonic.
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Huge overhaul on notation and chords; tertian triads are no longer the king of the world.
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Plagal Theory is a system of functionality based on several scales of [[22edo|22-EDO]]. The main defining feature of compositions in this tradition are the modulation from one mode of a scale to another by sharpening a single note; for instance, a piece written in the 5|1 mode of 5L2s would traditionally modulate to the 6|0 mode (with the same root pitch) to add a sense of grandeur and finality to the last movement of a piece. These modes are often grouped into "plagal pairs" that indicate how scales are related and how modulation tends to occur between pairs of scales.
Plagal Theory is a system of functionality based on several scales of [[22edo|22-EDO]]. The main defining feature of compositions in this tradition are the modulation from one mode of a scale to another by sharpening a single note; for instance, a piece written in the 5|1 mode of 5L2s would traditionally modulate to the 6|0 mode (with the same root pitch) to add a sense of grandeur and finality to the last movement of a piece. These modes are often grouped into "plagal pairs" that indicate how scales are related and how modulation tends to occur between pairs of scales.


The main scales considered in Plagal Theory are the MOSses [[5L 2s|5L2s]] (known as ''Monotonic'' or ''Unitonic''), [[3L 4s|3L4s]] (known as ''Bitonic''), and [[2L 5s|2L5s]] (known as ''Enarmonic'').
The main scales considered in Plagal Theory are the [[MOS scale|MOS]] scales [[5L 2s|5L2s]] (known as ''Monotonic'' or ''Unitonic''), [[3L 4s|3L4s]] (known as ''Bitonic''), and [[2L 5s|2L5s]] (known as ''Enarmonic'').


== Monotonic (5L 2s) ==
== Monotonic (5L 2s) ==
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|}
|}
The Locrian mode is considered to be a "mixed" mode with no plagal form, and is seldom considered in traditional composition.
The Locrian mode is considered to be a "mixed" mode with no plagal form, and is seldom considered in traditional composition.
=== Chords of Monotonic ===
Chords in Monotonic are created by stacking Major and Minor thirds (8\22 and 5\22, respectively), typically alternating.  Below are shown the primary types of chords, the shapes that they take in the Monotonic scale, the degrees of 22-EDO that they include, and the modes that are characterized by these chords.
{| class="wikitable"
|+Triads of Monotonic
!Chord Name
!Formula
!22-EDO
!Modes
|-
|Major
|M3 + m3
|8 + 13
|Lydian
|-
|Minor
|m3 + M3
|5 + 13
|Phrygian
|-
|Diminished
|m3 + m3
|5 + 10
|Locrian
|-
|Augmented
|M3 + M3
|8 + 16
|N/A
|}
The Monotonic Minor Chord is the most important of these triads in the Monotonic scale, followed closely by the Major chord.  The other two are seldom used.


== Bitonic (3L 4s) ==
== Bitonic (3L 4s) ==
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Just like with Monotonic, the "mixed" modes do not see widespread usage.
Just like with Monotonic, the "mixed" modes do not see widespread usage.
=== Chords of Bitonic ===
While the Monotonic chords were made by stacking Major and Minor thirds, Bitonic chords are made by stacking perfect and diminished Bitonic generators (7\22 and 2\22, respectively); in the context of this scale, these intervals are still called Major and Minor thirds, despite being much closer together than the Monotonic thirds.
{| class="wikitable"
|+Chords of Bitonic
!Chord Name
!Formula
!22-EDO
!Modes
|-
|Major
|M3 + m3
|7 + 9
|Plagal Phrygian
|-
|Minor
|m3 + M3
|2 + 9
|Standard Phrygian
|-
|Diminished
|m3 + m3
|2 + 4
|N/A
|-
|Augmented
|M3 + M3
|7 + 14
|Lydian, Dorian, Locrian
|}
The Bitonic Augmented Chord is the most important of these triads in the Bitonic scale; the other three are seldom used.


== Enarmonic (2L5s) ==
== Enarmonic (2L5s) ==
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Once again, the "mixed" Locrian mode does not see widespread usage in composition.
Once again, the "mixed" Locrian mode does not see widespread usage in composition.


=== Chords of Enarmonic ===
== Notation ==
Just like in the Monotonic and Bitonic scales, the Enarmonic scale builds chords by stacking major and minor thirds, this time being 8\22 and 4\22 respectively.
The notation system used in Plagal Theory utilizes three types of clefs to describe the three primary MOS scales: the G-clef (𝄞) is used for the Monotonic Scale, the F-clef (𝄢) is used for the Bitonic scale, and the C-clef (𝄡) is used for the Enarmonic scale.  Each scale has seven nominals and uses accidentals to alter those nominals, just like in common-practice Western theory in the real world.
 
The accidentals ♭ and ♯ respectively lower and raise the note by the chroma of the current scale; in other words, they are the difference between a large and small step.  A circular accidental placed above or below a note also occurs in later iterations of musical notation, and is used to respectively raise or lower the note by a single step of 22edo, regardless of the scale being used.
 
Note that this notation system arbitrarily treats G as the "default" starting point, akin to how real-world descriptions of musical structure often treat C as the "default" tonic.
{| class="wikitable"
{| class="wikitable"
|+Chords of Enarmonic
|+Notation
!Chord Name
!EDO steps
!Formula
!Monotonic (G Dorian)
!22-EDO
!Bitonic (G Dorian)
!Modes
!Enarmonic (G Dorian)
!Harmonic Category (See below)
|-
|0
|G
|G
|G
|
|-
|1
|A♭
|A
|
|Hard Dissonance
|-
|-
|Major
|2
|M3 + m3
|B♭
|8 + 12
|B♭
|Standard Lydian, Plagal Dorian
|A ~ F♯
|Hard Dissonance
|-
|-
|Minor
|3
|m3 + M3
|G♯
|4 + 12
|C♭
|Phrygian, Standard Dorian
|
|Soft Dissonance
|-
|-
|Diminished
|4
|m3 + m3
|A
|4 + 8
|F♯
|N/A
|B ~ G♯
|Soft Consonance
|-
|-
|Augmented
|5
|M3 + M3
|B
|8 + 16
|G♯
|Plagal Lydian
|
|Soft Consonance
|-
|6
|C♭
|A♯
|A♯ ~ C♭
|Soft Consonance
|-
|7
|A♯
|B
|
|Hard Consonance
|-
|8
|B♯
|C
|B♯ ~ D♭
|Soft Dissonance
|-
|9
|C
|D♭
|
|Hard Consonance
|-
|10
|D♭
|E♭
|C ~ E♭
|Soft Consonance
|-
|11
|E♭
|
|
|Hard Dissonance
|-
|12
|C♯
|B♯
|D
|Soft Consonance
|-
|13
|D
|C♯
|
|Hard Consonance
|-
|14
|E
|D
|E ~ C♯
|Soft Dissonance
|-
|15
|F♭
|E
|
|Hard Consonance
|-
|16
|D♯
|F♭
|D♯ ~ F♭
|Soft Consonance
|-
|17
|E♯
|G♭
|
|Soft Consonance
|-
|18
|F
|A♭
|G♭
|Soft Consonance
|-
|19
|G♭
|D♯
|
|Soft Dissonance
|-
|20
|
|E♯
|F
|Hard Dissonance
|-
|21
|F♯
|F
|
|Hard Dissonance
|-
|22
|G
|G
|G
|Hard Consonance
|}
|}
No one chord takes priority over all the others in the Enarmonic scale, though diminished chords are particularly rare.
Note that, unlike in real-world musical notation, the semitones of 5L2s occur between A-B and D-E, rather than B-C and E-F.  Additionally, the Monotonic notation is only productive for notating 11edo, because the intervals of the 2L5s scale can only be used to reach every other note of 22edo.
 
Finally, the Monotonic and Ditonic scales each have a singular "blind spot" note that cannot be reached by a single alteration of the nominals.  This note must instead be reached by use of double-accidentals or the over/under dot accidentals.
 
== Harmony ==
Over time, elements of chord-based harmony begin to take shape in the Plagal system, beginning with Parallel Generator dyads and later extending to triads and tetrads.  Unlike in real-world Western classical theory, chords in Plagal Theory do not have a conventional method of construction by stacking flavors of thirds, and instead are built off of the mode that they begin on.
 
All intervals are categorized as "soft" and "hard" consonances and dissonances, with "hard" categories being the strongest resolutions and tensions, and "soft" categories being passing intervals that are used more often, without extreme weight placed on their harmonic content.  These categories arose from rules of counterpoint composition, with the most concordant intervals being favored as ending points and the least concordant intervals being used as controlled dissonances to provide tension and set up for resolutions.
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