22edo/Unque's compositional approach: Difference between revisions

| [[Orwell]]

| E♭, B𝄪

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| 6\22

| 327.3

| [[6/5]], [[11/9]]

| F♭, C𝄪

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| 7\22

| Magic

| B𝄫, F𝄪

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| 16\22

| 872.7

| [[18/11]], [[5/3]]

| G♯, C𝄫

|  

The [[5L 2s]] scale is one of two types of Diatonic scales represented in 22edo, and represents the shade of Diatonic popularized by the Greek mathematician Archytas, which uses the 2.3.7 subgroup of Just Intonation.  It is generated by the Circle of Fifths just as in common practice tunings, though the perfect fifth of 22edo is significantly sharper than any tuning attested in common practice, which makes the scale and its chords behave somewhat differently from standard Diatonic functionality.  Notably, suspended chords feel less tense and more restful, while typical tertian triads tend to sound tenser and more energetic; this is the opposite of how these chords behave in Meantone tunings, and as such Western music translated into 22edo's Diatonic may sound strange if it is not adjusted to account for its unique properties.

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| C - D♭ - E♭ - F - G - A♭ - B♭ - C

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| C - D♭ - E♭ - F - G♭ - A♭ - B♭ - C

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The [[5L 7s]] scale is an extension of 5L 2s created by continuing the generator sequence.  Because the Circle of Fifths is bidirectional, the seven modes can be extended either by continuing the sequence upwards or downwards; those created by going up the chain are called grave modes, and those extended by going down the chain are called acute modes.

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! Notation

! Name

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| Also accounts for Acute Lydian

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| Also accounts for Grave Locrian

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=== 3L 2M 2s ===

The 5-limit harmony of this scale is much more reminiscent of the familiar harmony used in common-practice music, so popular music translated into this scale will be much more faithful to the harmony of the original piece than it would be using 5L 2s.

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! Notes

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| 6

| C - D - vE - vF♯ - G - A - vB - C

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| 4

| LMsLMLs

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|  

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| C - vD - vE - F - G - vA - B♭ - C

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| Dorian

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! Gens Up

! Name

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| 4

|  

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| C - vD - vE - F - G - vA - vB - C

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| 2

| sLMLsML

| C - ^D♭ - ^E♭ - F - G - ^A♭ - B♭ - C

|  

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| MLsMLsL

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When disambiguation is needed between the modes of 5L 2s and 3L 2M 2s, the former can be described as "Superpyth" or "Archy," while the latter can be called "Nicetone" or "Zarlino"

The [[Blackdye|5L 2m 3s]] scale functions as an extension to 3L 2M 2s, created by adding a commatic step into each large step of that Diatonic scale.  This provides the scale with three new modes in addition to the seven already present.  Due to the commatic step, this scale does not distinguish the left-hand from the right-hand variants.

While there is no singular generator sequence used to create this scale, it can be thought of as two pentatonic scales offset by a neutral second, which is coincidentally the amount by which a sharp or flat alters a note; this makes the scale easy to notate as a pentatonic scale and its sharp/flat counterpart.  This splits the modes into five "grave" modes and five "acute" modes, where the grave modes place the root on the flattened pentatonic, and the acute modes place the root on the sharpened one.

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| Dorian

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| Mixolydian

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| Ionian

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! Gens Up

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! Notes

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| 3

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| 1

| Dorian

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| 0

| Contains the Wolf fourth (vF)

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Where disambiguation is needed between the modes of 5L 7s and 5L 2M 2s, the former can be described as "chromatic," and the latter as "blackdye."

The [[2L 8s]] scale is another characteristic scale of 22edo, which was discovered independently by [[Paul Erlich]], [[Gene Ward Smith]], and [[wikipedia:Olivier_Messiaen|Olivier Messiaen]] (though the latter theorist documented [https://ianring.com/musictheory/scales/3055 the scale's analog in 12edo] rather than in 22).

Erlich divides four of the five unique rotations into a 2x2 grid, categorized by how many thirds it contains (one third is "static," two is "dynamic,") and which type of third falls on the fourth degree of the scale (major or minor).  The brightest mode does not appear to have been considered by Erlich, due to lacking a perfect fifth above the root.

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! Step pattern

! Notes

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| LssssLssss

| Contains the wolf fifth (^G)

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| sLssssLsss

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| ssLssssLss

| Static Major

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| 2

| sssLssssLs

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The [[4L&nbsp;5s]] scale is another quite useful scale available in 22edo <s>and a perfect example of 22edo being better than 31</s>; it is closely associated with [[Orwell]] temperament, and as such is best utilized alongside Orwell Chords for functional harmony (see below).

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| LsLsLssLs

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| 5

| C - C♯ - E♭ - D♯ - G♭ - F♯ - ^A♭ - A - A♯ - C

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| sLsLsLssL

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| sLssLsLsL

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|+ style="font-size: 105%;" |Modes of 3L 4s

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! Step Pattern

!Notes

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| Gil

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| C - vD♯ - vE - vF - ^G - ^A♭ - B - C

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| C - D♭ - vE - vF - ^G - ^A♭ - B - C

|Contains the up- and down-leading tones, making it easy to root melodically.

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| C - D♭ - vE - vF - ^G - ^A♭ - ^B𝄫 - C

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| 1

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| C - D♭ - E𝄫 - vF - vG♭ - ^A♭ - ^B𝄫 - C

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22edo provides a number of ways to construct and notate chords; while I cannot provide a comprehensive list of every possible chord available in 22edo, I will discuss and generalize the forms that I find to be most important for 22edo's structure.

Having four types of thirds rather than two, 22edo has a more colorful array of tertian triads than common practice music does.  The 5-limit Major and Minor triads can be approximated using 6\22 and 7\22 as the thirds, and the 7-limit triads can be approximated using 5\22 and 8\22.

{| class="wikitable sortable"

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! Name

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| 1/(21:18:14)

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| c^ow

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| 30:35:42

| 1/(7:6:5)

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| 1/(42:35:30)

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|Minor Wolf

|C - E♭ - vG

|5\22 + 7\22

|24:28:35

|1/(35:30:24)

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|Major Wolf

|C v

|7\22 + 5\22

|24:30:35

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| C - vE - ^G

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| E+/C

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| 11:14:18

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|Sensa (1st inv.)

|7:9:11

|1/(14:11:9)

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|Sensa (2nd inv.)

|9:11:14

|1/(11:9:7)

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In diatonic tunings with a sharp-tempered 3/2, such as the [[Superpyth]] diatonic found in 22edo, quartal harmony is often more concordant than tertian harmony; as such, musicians interested in using Superpyth should familiarize themselves with the Quartal Triad and its inversions.

{| class="wikitable"

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! Formula

! 7-limit JI

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| C - F - B♭

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| 16:21:24

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Useful harmonic progressions may arise in a number of ways depending on the scale being used and depending on what chord the composer wishes to tonicize.  Here, I will document some examples of how functional harmonic progressions may be created in the different scales of 22edo, with concepts that can be extended to apply to any scale.

Note that I will be constructing these chord progressions from back to front; this means that we will start with the resolution, then find the dominant chord, and then find a subdominant to precede it.

Just like in common-practice music theory, chords in 22edo have a tendency to rotate about the Circle of Fifths.  This means that in Diatonic music and other scales that contain 13\22, the chord built off of that note will be useful as a dominant.

Finally, it is important to notice certain tense intervals that have a tendency to voice lead by contrary motion to certain other intervals.  Specifically, the semioctave has a tendency to resolve either inwards or outwards to yield a perfect fourth/fifth; additionally, the subminor third may resolve outwards to a major third, and the supermajor third may resolve inwards to a minor third.

The C Ionian scale in Superpyth is a perfect showcase of how common-practice harmony differs from that of 22edo; specifically, quartal harmony tends to provide a more resolved sound than tertian harmony does, due to the sharp fifth exaggerating the size of the chroma.  Thus, our progression can resolve quite nicely to the tonic chord, Csus4 or G⁴/C.

A supermajor triad can be found over the fifth degree of the Ionian mode, which is much tenser than the major triad found in Meantone tunings due to the major seventh (the third of the V chord) being significantly sharper; this increases the strength of the pull towards the tonic, as well as destabilizes the V chord, making it clear that this is not a place of rest and thus negating the need for a dominant seventh over that chord.  This allows us to restrict our progression to three-part harmony rather than switching between three- and four-part harmony as is often done in common-practice progressions.

[[File:Isus4 - iiiow - IVsus4 - Vsaj.mp3|thumb|The Csus4 - e^ow - Fsus4 - Gsaj chord progression]]

Thus, our four-chord progression is Csus4 - e^ow - Fsus4 - Gsaj.  This series of chords uses a combination of voice leading, tension-and-release paradigms, and circle of fifths movement to provide a dynamic and functional harmonic progression.

[[Category:Approaches to tuning systems]]