User:VectorGraphics/Earth-22 Theory
|
This page is part of a worldbuilding project. It describes musical tuning concepts from a fictional alternate world, rather than the real world.
It may contain references to people, cultures, or places that do not actually exist, or events that did not actually happen. This does not mean that it can’t be used to make real music—it still could be; it just means this article shouldn’t be used as a factual source about real history or traditions, or as a source of terminology and principle compatible with real established common practices and conventions. |
Earth-22 uses the system of 22 equal divisions of the octave, and the Pajara[10] scale.
Early history
Middle-Eastern music relies more heavily on pentatonic subsets of diatonic, most "purely" directly tuned "trichords".
In the West, this is borrowed into European music theory, where for a while, music is tuned to the four church modes of Pythagorean pentatonic: Lydian (in our world, major pentatonic), Mixolydian (in our world, Mixolydian pentatonic), Dorian (in our world, Dorian pentatonic), and Phrygian (minor pentatonic). Their plagal counterparts were also present.
Septimal harmony
Gioseffo Zarlino supported tuning the pentatonic to Ptolemy's soft pentatonic, with the intervals [1/1 7/6 4/3 3/2 7/4], and introduced triadic harmony by adding the 7/4 on top of a normal 3/2 dyad.
Ultimately, this led to Archytas temperament, though it will be called Ptolemaic temperament instead in-universe, and quarter-comma ptolemaic becomes this universe's equivalent of quarter-comma meantone. However, unlike meantone, it roughly stays around, because the 22-form becomes the defining structure of chromatic music
Pajara and the 5-limit
The 22-form naturally encapsulates intervals of 5 as well as 7, so it was natural to begin adding thirds to chords. This locked in 22edo, as the natural form of a minor chord was derived by flattening 5/4 and 7/4 by the same amount to reach 6/5 and 12/7.
Modern theory
The basic scale of Earth-22 is the pajara decatonic scale, which can be seen as two pentatonic scales separated by a tritone, or "median" as it is called in-universe. Only fixed-do solfege is used, as the shift to pajara in the 18th century heavily disrupted existing letter notation forcing solfege to be adopted worldwide. The solfege syllabes are que ("kay"), jo ("yo"), mi, ra, fa, mu, sol, ve, la, and bi, repeating at que an octave up. These derive from the Ut Queant Laxis hymn, or its equivalent in Earth-22. These are abbreviated in Northern Europe to their initial letters, with a duplicate M changed to N. Accidentals originate while letter notation was still in use, so that b (flat) and # (sharp) still use the same symbols and names in their respective languages.
The terms for note functions include "capitant" (The top note of a chord) and "subcapitant" (the complement of the capitant).
Due to the way pentatonic was extended into pajara, it meas that the Lydian mode is actually the darkest, and the Locrian mode the brightest. Thus, the "major scale" is the Phrygian mode, but notation is based on Mixolydian or "minor".
| Note name | Abbreviation | Function | Name |
|---|---|---|---|
| que | Q | tonic | unison |
| jo flat | Jb | diminished grade | |
| jo | J | supertonic | perfect grade |
| jo sharp | J# | augmented grade | |
| mi | M | subcapitant | minor second |
| mi sharp | M# | major second | |
| ra | R | mediant | minor trigrade |
| ra sharp | R# | major trigrade | |
| fa flat | Fb | diminished third | |
| fa | F | subdominant | perfect third |
| fa sharp | F# | augmented third | |
| nu (mu) | N | antitonic | pentagrade |
| sol flat | Sb | diminished fourth | |
| sol | S | dominant | perfect fourth |
| sol sharp | S# | augmented fourth | |
| ve | V | submediant | minor heptagrade |
| ve sharp | V# | major heptagrade | |
| la | L | capitant | minor fifth |
| la sharp | L# | major fifth | |
| bi flat | Bb | diminished degrade | |
| bi | B | subtonic | perfect degrade |
| bi sharp | B# | augmented degrade | |
| que | Q | tonic | sexte |
As for chord functions, the essential form of a chord consists of the root and the 8-step ("fifth") above it, which can alternatively and somewhat more discordantly be voiced as a 2-step dyad, similar to the minor or major third dyad in our music. Triads similarly span an 8-step in the default voicing or a fourth in an inversion. Thus, there are two "rings" of chords connected by mediants. This means that functional harmony derives from the opposition between the two rings of fifths, and so chords sharing a function tend to differ by 2-steps rather than 3-steps. Thus, we have the tonic (1, 3, and 9) and dominant (5 and 7) functions opposing the antitonic (4, 6, and 8) and antidominant (2 and 10) functions, although the dominant function acts more like our world's subdominant, and the role of our dominant function is split into the antitonic and antidominant; the 4 functions are generally thought of in terms of stability vs. instability, and stasis vs. progression.