22edo/Intervals
This page goes over each of the steps of 22edo in detail, as is done in the documentation for various other equal temperaments on various websites. The notation used is ups and downs notation.
Function names are derived from Aura's function names. Standard super-/sub- terminology is restored; this section will not cover treble-down harmony.
Intervals of 22edo
1\22
Degree: b2
Interval: ^1, m2
Category: Dissonance
Function: Supergradient (leads past tonic)
This is the edostep of 22edo. It serves as the 5-limit chromatic semitone 25/24, the 11-limit quartertone 33/32, and the syntonic comma 81/80. Additionally, it is the minor second and is thus the accidental in a pentatonic system. This is close to the most dissonant interval there is when played harmonically, as modeled by the harmonic entropy system, and functions as a "diesis", representing a small difference between qualities. Significantly, alongside 25/24 it is also 49/48, the interval separating 8/7 and 7/6. Therefore, 22edo uses the same interval as the chroma for 5-limit and chthonic harmony. As a generator, it generates the escapade temperament against the octave and the hemipaj temperament against the tritone.
While it can be called a quartertone, the term "quartertone" often implies the use of the semisharp accidental, which is not used in 22edo as the chromatic semitone spans 3 steps.
2\22
Degree: ^b2
Interval: vA1, ^m2
Category: Dissonance
Function: Supervicinant (supertonic) / Supercollocant (leading tone)
This is perhaps the true "semitone" of 22edo, being exactly half of a whole tone. However, it does not appear as either of the two types of semitones found in mosdiatonic at all, requiring other scales or accidentals to be used to utilize it. As implied later on in #Chromatic subsets, this interval separates qualities that share a degree of "stability", such as the supermajor from the nearminor third, or the nearmajor from the subminor. This is also the generator for the important pajara temperament against the semioctave, and its most common step size. This interval represents 17/16 and 16/15; in fact, the harmonic series segment 14:15:16:17:18 collapses to a chain of four 2\22 steps, and consequently 12:13:14:15:16:17:18 is a fragment (2-3-2-2-2-2) of the pajara[10] scale spanning a perfect fifth.
As mentioned in the section on functional harmony, this interval serves as 22edo's leading tone, being close to the 5-limit (and specifically 12edo) leading tone used in common practice. The fact that the leading tone differs from any interval of mosdiatonic ends up adding a large degree of distortion and complexity to 22edo's functional harmony.
2\22 does not, however, have a well-established corresponding accidental; most accidentals mentioned are either one step (^ and v) or three steps (# and b). An alteration by this interval may be notated as down-sharp or double-up, or using the HEJI third-tone accidentals.
2\22 is also the step size of 11edo, a subset of every other note of 22edo.
3\22
Degree: v2
Interval: A1, vM2
Category: Dissonance (9-odd-limit consonance*)
Function: Supervicinant (supertonic) (Quill)
While this interval is 10/9 (a 9-odd-limit consonance) in function, it is considerably narrowed from what the just tuning would be, so it is better to consider its primary interpretation 11/10 and consider it a dissonance. (One may consider its function as 10/9 to not be 10/9 per-se but rather "(4/3)/(6/5)", treating it as a spacer interval separating key tuning targets.) It is the chromatic semitone of 22edo, separating MOSdiatonic major and minor intervals from one another. It is larger than the diatonic semitone, which is different from 12edo where they are the same size and opposite a meantone system where the diatonic semitone is larger.
This interval may be called the quill, as it represents 10/9, 11/10, and 12/11; as a result of this, it splits the nearminor second in two and the perfect fourth in three and generates porcupine temperament (or its semioctave counterpart, hedgehog). Outside of being a chromatic semitone, it functions as the scale step of porcupine's MOSes and contrasts with 9/8 in scales such as zarlino. Its flat tuning means the difference between Pythagorean and 5-limit tuning is exaggerated, rather than tempered out, and is thus much more easily usable for a system of interval quality than in just intonation.
4\22
Degree: 2
Interval: M2
Category: Secondary consonance
Function: Supervicinant (supertonic, whole tone) / Subvaricant
As a degree, the supermajor second serves as the second step of the MOS major and minor scales. As an interval, it also separates the perfect fourth and perfect fifth, and is therefore an important structural interval. It represents 9/8 and 8/7, and is therefore within the 9-odd-limit used as the standard of consonance on this page. In chthonic harmony, it serves as the minor unilatus, corresponding to the subvaricant function. Being wider than the 12edo major second also allows this interval to be used in more consonant chords without crowding. This builds the MOS diatonic scale, and divides the supermajor third into two equal parts and the augmented fourth (down fifth, ~16/11) into three, generating machine temperament (another 11edo-based temperament). Against the semioctave, however, it generates astrology temperament.
It is also often seen as significant to have this interval as a degree in a diatonic scale, as it allows the chord built on the fifth to itself contain a fifth; this is why, for instance, minor tonality does not just simply use Phrygian, instead altering the seventh to acquire an upwards leading tone similar to major.
Tuning-wise, it is significantly sharp of a whole tone and significantly flat of 8/7, meaning that 22edo like other septimal porcupine edos doesn't have a particularly good approximation to the meantone or 12edo whole tone; this makes it sound especially strange to some listeners.
It is the largest interval that could be considered a "step" in 22edo, as opposed to a "skip".
5\22
Degree: b3
Interval: m3
Category: Secondary consonance
Function: Subvaricant / Mediant
The smallest of the four types of thirds in the system, it is the subminor third, representing 7/6, and one of the two to correspond to 12edo's minor quality. It is found in the MOS diatonic scale, making it easily accessible when using a chain of fifths (superpyth temperament) and it also functions as the major version of a chthonic (especially in the 10-form, where it is not primarily a third at all) in the chord 6:7:8, and hence it can be seen as sharing the subvaricant and mediant functions. A triad with this third has a stable, dark quality. (In the metaphor used by Kite's color notation, this is zo (blue, a color associated with "bluesy" sounds and intervals of the 7th harmonic).)
This acts as a scale step in pentic, which can be considered the primary scale of superpyth temperament (as the small diatonic semitone is much better considered as an inflection in its own right). When pentic is extended into pajara, an occurrence of 5\22 splits into a semitone and a nearmajor second.
As a generator, this generates orwell temperament, a way of organizing the entire 11-limit; at its core, it evenly divides the 11/8 diminished fifth in two. Against the semioctave, it generates doublewide temperament.
6\22
Degree: ^b3
Interval: ^m3
Category: Imperfect consonance
Function: Mediant
The next smallest third, it has the nearminor quality, which represents 6/5. However, it is very sharp for an approximation to 6/5, being about as far from 11/9. This is a consequence of porcupine temperament, and indirectly of the lack of neutral thirds in 22edo. Therefore, it is best considered from a structural perspective, rather than a perspective revolving around tuning accuracy, where it serves as the complement to the nearmajor third and builds triads with an unstable, dark quality. (In the metaphor used by Kite's color notation, this is gu (green, a "cool, shaded" color like the interval's dark quality).) It does not appear in superpyth temperament, and must instead be arrived at with a very complex scale or with another system such as porcupine or pajara. As a result of doublewide temperament, a 5:6:7 chord is bounded by a perfect semioctave, but the distinction between the two intervals making it up helps solidify its harmonic identity. Stated equivalently, the nearminor third is as sharp of 300c as the subminor third is flat.
This interval replaces 5\22 in the zarlino/5-limit counterpart of pentic.
As a generator, this generates orgone temperament, another 11edo temperament which finds 16/11 at two steps and 7/4 at three steps. It may be alternated with the nearmajor third to instead generate the zarlino scale. It functions as an alternative generator for doublewide against the semioctave; alternating the two yields a 4-note scale that closes at the octave and may be considered a kind of diminished seventh chord.
7\22
Degree: v3
Interval: vM3
Category: Imperfect consonance
Function: Mediant
This interval, the nearmajor third, represents the interval 5/4. 5/4 is a significant structural interval as it represents the octave-reduced 5th harmonic in just intonation, and so may be stacked with other "prime" intervals to reach other intervals in just intonation. However, in a scale-based and edo-based context, this significance decreases somewhat, only leading to its strong consonance (behind 3/2, 4/3, and debatably 5/3 if the tuning is accepted).
It appears as part of the isoharmonic chord 4:5:6, which may be familiar as the 5-limit major chord approximated by 12edo. However, it is very important to note that this interval is only one of two qualities of major third in 22edo - that it does not appear in superpyth diatonic does not mean the latter scale lacks a major third. This interval builds a triad with a stable, bright quality. (In the metaphor used by Kite's color notation, this is yo (yellow, like warmth and sunshine).) Tuning-wise, it is slightly flat of the just 5/4 major third, which is enough to sufficiently affect its distinctiveness from the nearminor third. Additionally, a nearminor chord built on this degree may function as a substitute for a tonic nearmajor chord.
As a generator of a scale, it may function as an alternative generator for astrology temperament, or against the octave as a generator for magic temperament.
8\22
Degree: 3
Interval: M3
Category: Secondary consonance
Function: Mediant, superobstant
This is the final of four qualities of third, and it represents the interval 9/7, approximating it to about one cent of error. As a result of being sandwiched between 4/3 and 5/4, it is the least stable of the thirds, while simultaneously the brightest, as evidenced by its special "superobstant" function. It produces a triad with an unstable, bright quality (in the metaphor used by Kite's color notation, this is ru (red, alarming or inflamed, "hot" or "spicy").) This is the major third found in the superpyth diatonic scale, and is often used to illustrate the difference in the diatonic scale's tuning between 22edo and other systems such as 19edo. As a degree, it has the mediant function, and a subminor chord built on this degree may function as a substitute for a tonic supermajor chord.
The temperament it generates, sentry (an 11edo temperament where two 9/7s stack to 5/3) represents one of the major structural equivalences used in both octave- and tritave-equivalent harmony, the sensamagic temperament. This means that 22edo can function as a tritave-based system (if the 7 cents of detuning on the 3/1 is acceptable) that supports the same scale used in the Bohlen-Pierce system (about 8.2edo), however if this is done it is best to avoid the octave entirely or use a timbre (such as a square wave) that doesn't align at the octave.
In Aura's function system, the superobstant functions as a disruptive, dissonant interval in chords and melodies.
9\22
Degree: 4
Interval: P4
Category: Perfect consonance
Function: Subdominant (serviant)
The perfect fourth (4/3) serves a rather similar role to how it does in 12edo, being separated from the tritone by a semitone and generating the edo's MOS diatonic scale. However, it is tuned flatly and merges with the complex 7-limit interval 21/16, which is separated from it by the archytas comma in just intonation. (The tempering out of the archytas comma defines superpyth temperament.) In functional harmony, it tends to lead towards the nearmajor third, rather than the supermajor third, and it appears as the seventh of a nearmajor dominant chord, equivalent to a harmonic seventh chord in this system, serving that leading function. It is also the bounding interval of a tetrachord, and therefore important to building scales, and of a chthonic triad. Because it is a perfect consonance, and because it appears on six of the seven degrees of MOS diatonic, it is called a "perfect fourth", rather than its perhaps more systematic diatonic name of a "minor fifth".
Additionally, it may serve a role in 5/3-based harmony as the complement of 5/4, with 9/7 acting as a "neutral" interval in the middle.
10\22
Degree: b5, ^4
Interval: d5, ^4
Category: Dissonance
Function: Subient
This interval represents 11/8 and 15/11, and may be found in a number of different ways by various temperaments. By itself, it generates an 11edo-based temperament called joan, and is one of two prime harmonics to exist in 11edo. Against the semioctave, it generates hemipaj temperament. In functional harmony, it functions as a supermajor counterpart of the perfect fourth's role as a tendency tone towards the nearmajor third (and thus can replace the perfect fourth in certain scales), and can be considered to be the "near" counterpart of the perfect fourth itself, occurring in the harmonic series over a power of 2. This is the wolf fourth, found between D-G or A-D in the zarlino scale. The fact that the near fourth is simultaneously 11/8 results in the conflation of many 11-limit intervals with nearmajor or nearminor counterparts. For instance, 11/9 is the nearminor third, and 12/11 is the nearmajor second; meanwhile, 33/32 is tuned the same way as the interval separating nearmajor from supermajor degrees.
11\22
Degree: ^b5, v#4
Interval: d5, ^4
Category: Dissonance (7-odd-limit consonance*)
Function: Antitonic
The tritone is the single interval of 22edo shared with 12edo (besides the octave and unison), and perfectly divides the octave in two. It represents the intervals 7/5 and 10/7 simultaneously, and while it does not do a good job at approximating either, it still inherits structural properties from the overall 7-limit nature of 22edo that make it recognizable as those intervals. While it is a 7-odd-limit consonance, it suffers from the same issue as the nearmajor second - in this case, the semioctave is particularly dissonant in and of itself, regardless of just interpretation. However, when contextualized correctly (such as in a 4:5:6:7 chord), it can function as a secondary consonance as 7/5 normally would, making its role a lot more functional and contextual than a normal 7/5 would be. This overall makes it, surprisingly for an interval which isn't even xenharmonic, one of the most important intervals to understand in 22edo, as it ends up coming up a lot when engaging with the 7- and 11-limit.
Also notably, this interval is not the augmented fourth or diminished fifth, and as a result it does not exist in MOS diatonic, requiring a standard dominant resolution to go outside the MOS diatonic scale (it does, however, show up in superpyth chromatic). The fact that it is regardless a perfect tritone allows for tritone subsitution to still work in 22edo to some extent, as a chord a tritone away from a dominant tetrad will still contain the same notes, even if spelled differently. As a degree, it functions as an unstable structural anchor, contrasting with the stable structural anchor of the perfect fifth, with the antitonic function. This appears as the augmented fourth and diminished fifth in zarlino diatonic, however, and is the only interval other than the octave to appear on every note in pajara.
Against the octave, it generates 2edo, which is a trivial equal temperament wherein only the tritone itself and the unison/octave exist. However, it acts as the period for many of 22edo's other temperaments, allowing 5/4 and 7/4 to be conflated into a single step on the generator chain and simplifying harmony (this is jubilismic temperament).
12\22
Degree: v5, #4
Interval: v5, A4
Category: Dissonance
Function: Imponent
This interval is the wolf fifth, and is the main reason why zarlino is often discarded as a scale in favor of mosdiatonic. However, in porcupine systems such as 22edo, it actually takes on the value of 16/11, an important 11-limit interval found in 11edo and generated in 22edo by stacking two nearminor thirds or three whole tones. Additionally, unlike the perfect fifth, it has the power of two in the numerator, rather than the denominator, suggesting use as the interval between an 11-limit fourth (11/8) and the octave. While it and its otonal counterpart are not found in pajara[10], they are in pajara[12].
This serves as a generator of joan, like 10\22.
13\22
Degree: 5
Interval: P5
Category: Perfect consonance
Function: Dominant
This interval is the perfect fifth, the next most consonant interval (octave-reduced) after the octave itself, representing the ratio 3/2. Because of its extreme simplicity, it is an important interval to have in scales, which is part of why the pajara and diatonic scales are particularly prominent (despite taking a really long time to reach 5/4, MOS diatonic is still one of the most widely used scales in 22edo). This interval stacks (octave-reduced) to a whole tone, equivalent to 8/7 under superpyth temperament, and can function as a generator of pajara itself, or of superpyth like the perfect fourth. Like in 12edo, a chord built on this interval creates a tension that resolves to the tonic, and the perfect fifth is the bounding interval of most tertian triads themselves. Because it is a perfect consonance, and because it appears on six of the seven degrees of MOS diatonic, it is called a "perfect fifth", rather than its perhaps more systematic diatonic name of a "major fifth".
Tuning-wise, its tuning is slightly sharp of just intonation - enough to be noticeable to some people, but nowhere near enough to make it lose its identity. It is at essentially the optimal tuning for pajara temperament - any sharper and the nearmajor and nearminor thirds lose their distinction from one another, and any flatter and the harmonic seventh loses its identity to some extent.
14\22
Degree: b6
Interval: m6
Category: Secondary consonance
Function: Subobstant, submediant
This interval has a few different identities: firstly, it is the octave complement of the supermajor third (as the subminor sixth, 14/9) and therefore appears as a degree when halving a descending 5/3, or the step between 6/5 and the octave, representing the descending form of sentry's generator chain. However, it also appears when two nearmajor thirds are stacked upon one another, producing a "near augmented" triad closed by a 9/7. Finally, it is an alternative generator for hedgehog temperament, being a quill raised by a perfect tritone. It is the most complex of the 9-odd-limit intervals found in 22edo, and therefore occupies a similar sort of space to 8/5 in 12edo, being significantly discordant due to its proximity to the perfect fifth and giving augmented chords their characteristic "spacey" quality. However note that unlike in 12edo's augmented chords, this interval does not evenly split the octave into three, and as a result augmented chords are perhaps not as "basic" of a chord type in 22edo, in any form. Additionally, unlike its complement 9/7, it only has one LCJI interval nearby as opposed to two, making it a bit more stable of a note to place in a chord, especially if the perfect fifth is avoided nearby.
15\22
Degree: ^b6
Interval: ^m6
Category: Primary consonance
Function: Submediant
This interval is the nearminor sixth, 8/5. Its most significant characteristic which sets it apart from its octave complement is that it leads down to the perfect fifth 3/2; this property gives it the unstable, dark sound befitting of a nearminor interval and makes it rather significant when it comes to harmony in modes such as Aeolian where standard leading tones going up to the octave are absent. It also appears in augmented chords where one of the major thirds is supermajor (which notably form the main "invertible" form of augmented chord). Functions as the descending generator of magic, reaching a perfect fourth after 5 steps rather than a perfect fifth.
16\22
Degree: v6
Interval: vM6
Category: Primary consonance
Function: Submediant
The nearmajor sixth represents 5/3 functionally, however its usability when considering 5/3 to be a consonance in its own right is somewhat limited. This is reflected by the combination of the existence of the sensamagic structure and the accuracy of 9/7, making this interval closer to a submajor than a proper nearmajor. Regardless, it still has the role of 5/3 in harmony, appearing especially in inversions of tertian chords and acting as the bounding interval of chords in naiadic harmony, such as 3:4:5. The open, stable, bright sound of this interval is fitting with the previously established quality of the nearmajor third.
This is also the mosdiatonic augmented fifth, being built by stacking two 9/7s as previously mentioned, which bridges 5/3-based and 3/2-based harmony in a way not found in 12edo.
17\22
Degree: 6
Interval: M6
Category: Secondary consonance
Function: Submediant, varicant
This interval serves as the "minor" counterpart to 7/4 as a varicant or antilatus, appearing over a nearminor third in a chord built with a tritone between the second and fourth notes and serving as a useful harmonic counterpart to chords like 4:5:6:7. Additionally, it is the supermajor sixth, representing 12/7, and therefore having the "alarmed", bright sound of supermajor, being nestled in between 5/3 and 7/4 the same way the supermajor third is jammed in between 5/4 and 4/3. It's a slightly different sound, but it still overall achieves its function, albeit with more functional relevance in the 10-form.
18\22
Degree: b7
Interval: m7
Category: Secondary consonance
Function: Varicant, subvicinant
This is the 7th harmonic (the subminor 7th, 7/4), one of the main "features" of 22edo. It is unusually sharply approximated due to 22edo's archy temperament, but it still functions as the 7th harmonic regardless. It is, alongside the 11th harmonic, found in 11edo, making 11edo itself a 2.7.11(.17) system. It mainly features in the MOS diatonic scale as the minor seventh. The nearmajor chord with this seventh added is 4:5:6:7, the harmonic seventh chord. I have chosen to notate this chord with an unmarked "7" symbol, as it functions as a dominant tetrad in nearmajor and collapses to the standard dominant chord in 12edo. Additionally, the supermajor chord with this seventh is the dominant chord in MOS diatonic. Additionally, the ratios between this and other intervals form the intervals of the 7-limit.
Archy is one of the four main simple archetypes for the 2.3.7 subgroup, with the others (in increasing order of structural complexity) being semaphore, slendric, and buzzard.
19\22
Degree: ^b7
Interval: ^m7
Category: Dissonance (9-odd-limit consonance*)
Function: Subvicinant
This is the octave-complement of the quill, and as such functions as a generator of porcupine temperament, reaching 3/2 instead of 4/3. It is the nearminor seventh, representing 11/6, 20/11, and 9/5. While the latter makes it technically fall under the 9-odd-limit similar to the quill, it is similarly detuned enough that its identity as an interval in and of itself largely depends on other intervals, even more so since an interval this wide generally doesn't fall between steps in two otherwise corresponding chords. It serves as an alternative minor seventh for dominant seventh chords, especially working for the supermajor version resolving to nearmajor, as it is separated from the supermajor third by a tritone.
20\22
Degree: v7
Interval: vM7
Category: Dissonance*
Function: Subvicinant, subcollocant (leading tone)
The nearmajor seventh, it appears as a leading tone in the major scales leading up to the octave. It may be useful to alter other seventh notes to this in certain situations. However, many more scales can have such an alteration done to them, due to the existence of the supermajor seventh (for example, you can use a "harmonic supermajor" alongside the harmonic nearminor and subminor, which is a kind of scale that only really makes sense in systems like 22edo). As a degree, this forms the third of the V dominant chord when it is a nearmajor chord (and is why dominant chords generally want to be nearmajor in the first place). Appears in a nearmajor seventh chord, where it may be used as a functional consonance in certain situations. It may be seen as a 15/8 interval.
21\22
Degree: 7
Interval: M7
Category: Dissonance
Function: Subgradient
This is the largest interval in 22edo smaller than the octave, and acts as a "supergradient", leading past the octave towards the subgradient the next octave up or being used in chromatic, melodic situations as a scale degree. It is also the supermajor seventh, appearing in the MOS form of the major scale and representing the octave-complements of the various interpretations of the quarter tone. It is also the prime harmonic 31/16, although the only structure in which this really becomes relevant is escapade, where it serves as the generator.
22\22, 0\22
Degree: 8
Interval: P8
Category: Perfect consonance (equivalence)
Function: Tonic
The octave is the interval of equivalence, in 22edo as in most edos in practice. While it is not universal (tritave tunings exist), it is the interval that much of 22edo's structure is defined around and it is the interval between notes that sound equivalent on most instruments. It is a perfect consonance. It is equivalent via itself to the unison, serving as a degree as the "tonic", the home point which functional harmony is built around - the chord on the tonic determines the key of the music. It is also the only just intonation interval represented exactly in 22edo (or in any equal temperament defined as an equal division of the octave).
Chromatic subsets
In 22edo, multiple qualities may be combined together into a compound system. In 12edo, there is little reason to do this, because there are only two qualities available, so the scale combining them (the 12edo chromatic scale, or some other large scale like ├─┴┴┴┴─┴┴┴─┴┤ 2 1 1 1 2 1 1 2 1) is not particularly engaging from either a tonal or modal perspective. However, in 22edo, there are four different qualities, from which two may be selected to share characteristics.
The standard chromatic scales combine nearmajor+nearminor and supermajor+subminor, which lead to somewhat of the same problem as 12edo chromatic; they are opposing pairs of qualities. However, if we make an asymmetric chromatic scale, with (for instance) supermajor and nearminor, we get a scale with the trait they have in common: being "unstable". Alternatively, you could get a generally "dark" system by combining subminor and nearminor qualities.
The following are a few examples of these kinds of scales, including diatonic and chromatic variations. (Note that in tonal music, these become less distinct from standard counterparts, as degrees are already expected to be altered between different qualities depending on context.)
Nearminor (harmonic): P1 - SM2 - nm3 - P4 - P5 - nm6 - NM7 - P8 (├───┴─┴──┴───┴─┴────┴─┤ 4 2 3 4 2 5 2)
Subminor (harmonic): P1 - SM2 - sm3 - P4 - P5 - sm6 - NM7 - P8 (├───┴┴───┴───┴┴─────┴─┤ 4 1 4 4 1 6 2)
Compound minor (harmonic + natural): P1 - SM2 - sm3 - nm3 - P4 - P5 - sm6 - nm6 - NM7 - P8 (├───┴┴┴──┴───┴┴┴────┴─┤ 4 1 1 3 4 1 1 5 2)
Supermajor (harmonic): P1 - SM2 - SM3 - P4 - P5 - SM6 - NM7 - P8 (├───┴───┴┴───┴───┴──┴─┤ 4 4 1 4 4 3 2)
Compound unstable (harmonic + natural): P1 - SM2 - nm3 - SM3 - P4 - P5 - nm6 - SM6 - nm7 - NM7 - P8 (├───┴─┴─┴┴───┴─┴─┴─┴┴─┤ 4 2 2 1 4 2 2 2 1 2)
Aberrismic scales may also be leveraged for this purpose.
Consonant vs. tense suspended chords
The wider supermajor second and contrast with the supermajor third actually makes suspended chords somewhat of a point of resolution, rather than a point of tension like in 12edo. It's reasonable to have a suspended chord that doesn't resolve, perhaps making the term "suspended" inaccurate. These suspended chords can function like arto and tendo chords, with a 1-2-4-5 chord structure being plausible, or can be used in modal harmony as a form of "mode-agnostic" anchor point. The sus4 chord in particular is composed of the three octave-reduced perfect consonances, and thus can also be considered the most basic polychordal scale (perhaps a/the "dichordal" scale). The consonance of the supermajor second is additionally what allows chthonic harmony to function. However, suspensions that function more like 12edo ones in leading into the MOS diatonic intervals and being more tense can still be found with the nearmajor sus2 and wolf sus4, which lose some of the structural elegance of standard Pythagorean suspensions in favor of a more tense, crowded sound that can easily resolve to even the rather tense supermajor triad.
