Xenverse/Earth 22

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This page is part of a worldbuilding project. It describes musical tuning concepts from a fictional or alternate world, rather than the real world. 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. (Please see our worldbuilding policy for more.)

This page discusses the 22EDO music theory used in Earth#22. Earth#22 treats 22edo as a 2.3.7.5 system, with the basic chord being 4:6:7 and 5 being included optionally.

Greek music theory

Trichords

A trichord is a set of three notes spanning a perfect fourth. For example, C-D-F is a trichord. They are analogous to real-world tetrachords, but with only one movable tone, rather than two. A trichord may be joined with another by the interval of 9/8 to span an octave. The loss of a degree of freedom in the trichord's construction means that its size is now entirely determined by its characteristic interval, and the fact that the characteristic interval is necessarily greater than a semifourth implies that the diatonic genus does not exist; regardless, the chromatic genus is, in this universe, called "diatonic". Several tunings of the trichord follow:

Characteristic interval	Complement	Name	Genus	Notes
7/6	8/7	Equable	Diatonic	7-limit pentatonic. Later inherited into Zarlino's theory of 2.3.7 harmony.
32/27	9/8	Pythagorean[b]	Diatonic	Pythagorean pentatonic MOS
6/5	10/9	Didymian[b]	Diatonic
5/4	16/15	Didymian[b]	Enharmonic
81/64	256/243	Pythagorean[b]	Enharmonic
9/7	28/27	Archytas[b]	Enharmonic

Instruments

The usage of instruments is similar to real-world Greek music, but with trichords instead of tetrachords. The lyre would accompany vocals for the melody, and wind instruments would provide doubling of the melody or a drone. Note that at this point there are no proper chords or polyphony, hence the theory dealing mainly in the tuning of the scale.

Modern theory

The modern bidiatonic scale is perceived as two pentatonic^[a] scales interleaved together. The theory is based on Archy^[c] temperament as a simplification of Zarlino^[b]'s septal pentatonic, much as real-world theory is based on Meantone temperament as a simplification of Zarlino's 5-limit diatonic. In order to aid melodic structure, a second diatonic is added with its notes spaced in between the primary ones, which by extension provides access to the full 7-limit via Pajara^[c] temperament; however this addition was relatively late, and so alphabetic notation was already established for the primary diatonic and failed to cover the additional notes. Hence, notation utilizes an extended, modified fixed solfege. Que ("kay") is equivalent to A, then Jo ("yo"), Mi, Ra, Fa, Mu or Nu, Sol, Ve, La, and Bi. These are abbreviated in Northern Europe to their initial letters, QJMRFNSVLB.

As a result of the advent of fixed-pitch keyboard instruments, the tuning of Pajara collapsed to 22edo or well-temperaments thereof.

The fundamental triad is 4:6:7, which is just as commonly voiced as 6:7:8. Note that qualities of fourth and fifth are not called perfect.

Note that the mode of the naturals on Q is this universe's basic minor scale. The major scale may be found on J, and is identical to the minor scale except for the third/semifourth and semitwelfth/fifth being sharpened. There are three other modes, and from brightest to darkest major and minor are the third and fourth respectively.

Eaeth#22 interval table

Note on Que	Note function	Degree	Real-World Name	Belongs to scale	Quality	22edo	Notes
que	Tonic	Unison	Unison	Primary pentatonic	Perfect	0.0
que sharp					Augmented	54.5
jo	Antidominant	Semitone (1S)	Second	Secondary pentatonic	Minor	109.1
jo sharp					Major	163.6
mi	Subcapitant	Second	Semifourth	Primary pentatonic	Minor	218.2
mi sharp					Major	272.7
ra	Mediant	Semifourth (2S)	Third	Secondary pentatonic	Minor	327.3	5-limit minor third, used in tetrads
ra sharp					Major	381.8	5-limit major third, used in tetrads
fa flat	Subdominant	Third	Fourth	Primary pentatonic	Minor	436.4
fa					Major	490.9	Perfect fourth
nu flat	Antitonic	Median (3S)	Tritone	Secondary pentatonic	Diminished	545.5
nu (mu)					Perfect	600.0	Dissonant but important structurally
nu sharp					Augmented	654.5
sol	Dominant	Fourth	Fifth	Primary pentatonic	Minor	709.1	Perfect fifth
sol sharp					Major	763.6
ve	Submediant	Semieighth (4S)	Sixth	Secondary pentatonic	Minor	818.2
ve sharp					Major	872.7
la	Capitant	Fifth	Semitwelfth	Primary pentatonic	Minor	927.3	Defining note in minor triad
la sharp					Major	981.8	Defining note in major triad
bi flat	Antisubdominant	Semitenth (5S)	Seventh	Secondary pentatonic	Minor	1036.4
bi					Major	1090.9
que flat	Tonic	Sixth	Eighth	Primary pentatonic	Diminished	1145.5
que					Perfect	1200.0	Exact 2/1 octave

Functional harmony

The functions of the primary pentatonic are tonic (1/6), subcapitant (2), subdominant (3), dominant (4), and capitant (5). The capitant is named as such because it is the top note in a proper chord on the tonic. The functions of the secondary pentatonic are supertonic (1S), mediant (2S), antitonic (3S), submediant (4S), and subtonic (5S).

For the following section, all interval names will be based on the "Real-World Name" column above, for the sake of clarity, but all degree and interval abbreviations will be from the "Degree" column.

As for chord functions, the essential form of a chord consists of the root and the semitwelfth 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 a semitwelfth 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 semifourths rather than thirds. Thus, we have the tonic (1, 2, and 5) and dominant (3 and 4) functions opposing the antitonic (2S, 3S, and 4S) and antidominant (1S and 5S) 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. In the major scale, the degrees 2 and 4S do not have perfect fifths over them; in the minor scale, this is instead 2S and 5.

	Stable	Unstable
Static	Tonic	Antitonic
Progressive	Dominant	Antidominant

Melodic scale

The melodic scale is the non-MOS form of the Pajara decatonic scale (LLLsLLLLLs), which has ten modes and serves a role similar to the flattening of B in choral music, or to our harmonic or melodic minor, to alter chord qualities on degrees where functionally appropriate. It becomes especially prevalent in Earth-22 music as there are two augmented fifths and two diminished fourths in the scale, unlike the one imperfect fifth and fourth each found in real-world diatonic.

Instruments

The standard

Notes

[a] In Earth#22, "diatonic" refers to pentatonic scales, as per the Greek theory established earlier.

[b] Or the equivalent figure, who is for the sake of clarity simply called by the name of their real-world counterpart.

[c] In Earth#22, Archy temperament is called ptolemaic and Pajara temperament is called semitonal.

[d] For clarity, in-universe interval names are always capitalized. So, "Fifth" refers to a semitwelfth, the actual diatonic fifth is the Fourth.