User:VectorGraphics/Earth-22 Theory

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.