User:Unque/22-TET Plagal Theory
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"Plagal Theory" (Eleutheric: Χωρη Πλαγικη, Xoree Plagikee /ʃori plaʝici/) is a fictitious alternative music theory popularized across Europe in an alternate history. As such, the concepts discussed here, and the history thereof, should be understood to be fictitious, and therefore not necessarily applicable to the real world; specifically, the scales and their modes are named in accordance with the in-universe traditions, and are not legitimate proposals for conventions to use in real-world xenharmonic theory.
Overview
Plagal Theory is a system of functionality based on several scales of 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 5L2s (known as Monotonic or Unitonic), 3L4s (known as Bitonic), and 2L5s (known as Enarmonic).
Monotonic (5L 2s)
Modes of Monotonic
The modes of the Monotonic scale are grouped into three plagal pairs, with one additional mode that lacks a plagal partner. Shown below is the general UDP notation and step sizes for each mode, as well as the degrees of 22-EDO contained by that mode (with the root implied at 0\22).
| Mode Pair | Standard Mode (general) | Standard Mode (22-EDO) | Plagal Mode (general) | Plagal Mode (22-EDO) |
|---|---|---|---|---|
| Lydian | 5|1 (LLsLLLs) | 4 8 9 13 17 21 22 | 6|0 (LLLsLLs) | 4 8 12 13 17 21 22 |
| Dorian | 3|3 (LsLLLsL) | 4 5 9 13 17 18 22 | 4|2 (LLsLLsL) | 4 8 9 13 17 18 22 |
| Phrygian | 1|5 (sLLLsLL) | 1 5 9 13 14 18 22 | 2|4 (LsLLsLL) | 4 5 9 13 14 18 22 |
| Locrian | 0|6 (sLLsLLL) | 1 5 9 10 14 18 22 |
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.
| 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)
Modes of Bitonic
The modes of Bitonic number a total of four plagal pairs, and an additional "mixed" mode.
| Mode Pair | Standard Mode (general) | Standard Mode (22-EDO) | Plagal Mode (general) | Plagal Mode (22-EDO) |
|---|---|---|---|---|
| Lydian | 4|2 LssLsLs | 6 7 8 14 15 21 22 | 5|1 LsLssLs | 6 7 13 14 15 16 22 |
| Phrygian | 0|6 ssLsLsL | 1 2 8 9 15 16 22 | 1|5 sLssLsL | 1 7 8 9 15 16 22 |
| Dorian | 3|3 sLsLsLs | 1 7 8 14 15 21 22 | 4|2 LssLsLs | 6 7 8 14 15 21 22 |
| Mixodorian | 2|4 sLsLssL | 1 7 8 14 15 16 22 | 3|3 sLsLsLs | 1 7 8 14 15 21 22 |
| Locrian | 6|0 LsLsLss | 6 7 13 14 20 21 22 |
The so-called "Mixodorian" mode is a later invention by theorists, especially experimentalists, in an attempt to "fix" the issues presented by the traditional Dorian pair: traditional Plagal Dorian was the same pattern as Standard Lydian, which left two "mixed" modes instead of just one. The Mixodorian mode does not see widespread usage, but it is not entirely unheard of either.
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 6\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.
| Chord Name | Formula | 22-EDO | Modes |
|---|---|---|---|
| Major | M3 + m3 | 7 + 13 | Plagal Phrygian |
| Minor | m3 + M3 | 6 + 13 | Standard Phrygian |
| Diminished | m3 + m3 | 6 + 12 | 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)
Modes of Enarmonic
Like monotonic, the Enarmonic scale has three non-overlapping plagal pairs and only one "mixed" mode.
| Mode Pair | Standard Mode (general) | Standard Mode (22-EDO) | Plagal Mode (general) | Plagal Mode (22-EDO) |
|---|---|---|---|---|
| Lydian | 5|1 LsssLss | 6 8 10 12 18 20 22 | 6|0 LssLsss | 6 8 10 16 18 20 22 |
| Phrygian | 0|6 sssLssL | 2 4 6 12 14 16 22 | 1|5 ssLsssL | 2 4 10 12 14 16 22 |
| Dorian | 2|4 ssLssLs | 2 4 10 12 14 20 22 | 3|3 sLsssLs | 2 8 10 12 14 20 22 |
| Locrian | 4|2 sLssLss | 2 8 10 12 18 20 |
Once again, the "mixed" Locrian mode does not see widespread usage in composition.
Chords of Enarmonic
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.
| Chord Name | Formula | 22-EDO | Modes |
|---|---|---|---|
| Major | M3 + m3 | 8 + 12 | Standard Lydian, Plagal Dorian |
| Minor | m3 + M3 | 4 + 12 | Phrygian, Standard Dorian |
| Diminished | m3 + m3 | 4 + 8 | N/A |
| Augmented | M3 + M3 | 8 + 16 | Plagal Lydian |
No one chord takes priority over all the others in the Enarmonic scale, though diminished chords are particularly rare.