His guides to 15edo, 22edo, 29edo, 37edo, and to the oneirotonic scale
If you spend enough time in the corners of the internet where microtonal music lives, you will eventually stumble across a wiki user called Unque, also known on YouTube as Uncreative Name. He describes himself as “a music theorist, composer, performer, mathematician, worldbuilder, and linguist,” and if his extensive body of wiki writing is anything to go by, that description is not an exaggeration. He is perhaps best known within the xenharmonic community as a vocal advocate for tuning systems that don’t get much mainstream attention even within microtonal circles — and for having written some of the most thorough, composer-facing composition theory guides on the Xenharmonic Wiki.
This article is an attempt to introduce his work to musicians who are comfortable with standard Western music theory — modes, chord progressions, voice leading, functional harmony — but who have little or no background in microtonality. We’ll walk through the tuning systems Unque has written about, explain what makes each one interesting according to his compositional framework, and try to give you a sense of what it would actually feel like to write music in these systems.
Fair warning: this is a long article. Unque’s work is detailed and technical, and doing it justice requires some patience. Grab a coffee.
Who Is Unque?
Unque came to xenharmonic music through an interest in non-Western music traditions, particularly the Arabic Maqamat — the modal system used in Arabic classical music, which features “neutral” intervals that fall roughly halfway between the major and minor versions of a given interval. When he encountered these neutral seconds, thirds, and sixths, he became curious about how they worked, and that curiosity led him down a rabbit hole that took him through the harmonic series, Just Intonation, and eventually to Equal Divisions of the Octave.
His YouTube channel, Uncreative Name, hosts a small but growing catalog of original compositions in various microtonal tuning systems, including pieces written in 15-EDO, 17-EDO, 18-EDO, 19-EDO, 22-EDO, 26-EDO, 27-EDO, 29-EDO, 31-EDO, 37-EDO, and even 2.3.7 Just Intonation. His compositions are not academic exercises — they are genuine pieces of music with titles like “Isles of Despair,” “Methane Lamentation,” and “The Nachtlandian Somersault,” suggesting a composer with a real aesthetic personality and a sense of humor.
But his most significant contribution to the xenharmonic community is probably not his music itself — it is his written composition theory. On the Xenharmonic Wiki, he has produced extensive practical guides to writing music in 15-EDO, 22-EDO, 29-EDO, and 37-EDO, with additional theoretical work on scales, chords, voice leading, and modulation. These guides are distinctive because they approach each tuning system not as a collection of approximations to Just Intonation ratios, but as a compositional world with its own internal logic — its own scales, its own chords, its own notions of tension and resolution.
A Quick Primer: What Is an EDO?
Before we dive into Unque’s work, let’s make sure we’re on the same page about the basic vocabulary.
Standard Western music uses 12-tone Equal Temperament, which divides the octave into 12 equal semitones. An Equal Division of the Octave (EDO) is simply a tuning system that divides the octave into some other number of equal steps. 19-EDO uses 19 equal steps, 31-EDO uses 31, and so on. Some EDOs are very close to 12-EDO in their interval structure; others are radically different.
When Unque writes about 15-EDO, for example, he is describing a system where the octave is divided into 15 equal steps, each about 80 cents wide (compared to the 100-cent semitone of 12-EDO). This means that the “perfect fifth” in 15-EDO — the interval we hear as stable and resonant in standard tuning — lands at 720 cents rather than the 702 cents of a just fifth or the 700 cents of a 12-EDO fifth. That difference of 18–20 cents might seem small, but it has profound effects on how harmony works.
There are also non-octave tuning systems, like 30-EDT, where the period of repetition is the tritave (the 3:1 frequency ratio, an octave plus a fifth) rather than the octave. We’ll touch on that briefly when we discuss Unque’s advocacy for that system.
Unque’s “Tuning Propaganda”: An Overview
On his Xenharmonic Wiki user page, Unque lists several tuning systems under the heading “Tuning Propaganda” — a self-aware acknowledgment that he is making an argument, not just presenting neutral information. The systems he advocates for most strongly are 15-EDO, 30-EDT, 29-EDO, 36-EDO, 41-EDO, and 43-EDO. For each, he offers a brief rationale, and for several of them he has written full composition theory guides. Let’s work through them.
15-EDO: The Beautiful Alien
Unque describes 15-EDO as the first tuning system he “truly fell in love with” on his xenharmonic journey. His reasoning is telling: where systems like 17-EDO, 19-EDO, and 31-EDO felt like “simple extensions to the familiar,” 15-EDO offered something genuinely alien. And crucially, it was alien in a way that was musically useful, not just theoretically interesting.
What Makes 15-EDO Special?
In 15-EDO, the “perfect fifth” — the interval we hear as the stable backbone of Western harmony — is 720 cents. This is about 18 cents sharper than a just fifth, which is a very large deviation. (For comparison, the fifth in 12-EDO is only 2 cents flat from just.) This means that the Circle of Fifths, which underpins so much of Western harmonic thinking, is substantially damaged in 15-EDO. The system does not provide a convincing approximation of the 3:2 frequency ratio.
What 15-EDO does provide is an excellent major third at 400 cents — exactly the same as in 12-EDO, which itself is a decent approximation of the just major third at 386 cents. It also provides a very good minor third at 320 cents, a good approximation of the just 6:5 ratio at 316 cents. And it contains 5-EDO as a subset, which gives it an internal symmetry that 12-EDO lacks.
But perhaps most importantly for Unque’s compositional approach, 15-EDO supports Porcupine temperament and Blackwood temperament, two very different ways of organizing the tuning’s melodic and harmonic resources.
The Intervals of 15-EDO
Unque’s composition theory guide for 15-EDO begins with a careful survey of the tuning’s intervals and what JI ratios they might represent. This is complicated by the fact that 15-EDO has several competing interpretive frameworks, and Unque is admirably honest about the controversy.
The most contested interval is the “fifth” at 9 steps (720 cents). Unque notes that some people hear this as representing 3:2, others prefer the interpretation 50:33, and still others prefer 97:64. He presents these perspectives fairly without trying to resolve the argument definitively, instead letting compositional practice guide the choice.
He also notes that 15-EDO can be interpreted as a “dual-9 system,” meaning it has two intervals that can plausibly function as whole tones: 2 steps (160 cents, close to 10:9) and 3 steps (240 cents, close to 8:7). This “dual whole tone” property is actually a feature rather than a bug in Unque’s view, as it allows for a near-perfect correspondence between two different versions of the 3L 2M 2s scale (more on this below).
He also discusses the connection to the Carlos Alpha scale, a non-octave tuning developed by composer Wendy Carlos, though he is skeptical of this connection in practice, noting its poor accuracy and the lack of clear compositional equivalence.
One genuinely useful observation is Unque’s identification of 15-EDO’s two tritones — one at 6 steps (480 cents) and one at 7 steps (560 cents) — as potential consonances that approximate the 11th harmonic. These tritones are about a quartertone away from the familiar semioctave tritone of 12-EDO, but within 15-EDO’s harmonic framework, they can function as stable-enough sonorities, particularly in contexts informed by 11-limit harmony.
Notation in 15-EDO
Because 15-EDO doesn’t have a clean diatonic fifth, notating it is genuinely tricky. Unque discusses four possible notation systems, each privileging a different scale as the set of “natural” notes:
Blackwood notation is based on the Blackwood Decatonic scale, a 10-note scale that divides the octave into five equal major thirds, each subdivided into two steps. This is perhaps the most characteristic scale of 15-EDO.
Porcupine notation is based on Porcupine temperament, which generates scales by stacking intervals of about 160 cents. In 15-EDO, this gives us a 7-note scale as the “diatonic,” though it sounds quite different from standard diatonic music.
Kleismic notation is based on Kleismic temperament, which generates scales by stacking minor thirds.
Nicetone notation is based on a scale that closely resembles the familiar Zarlino diatonic, made by alternating major and minor thirds. Unque uses this when writing in the 3L 2M 2s scale.
The choice between these systems isn’t just cosmetic — it reflects genuine differences in how the music is organized and heard.
Chords in 15-EDO: The Porcupine Framework
One of the most useful sections of Unque’s 15-EDO guide is his chord taxonomy for Porcupine-based scales. In the Porcupine scales, chords are built by stacking intervals of 4, 5, and 6 steps, giving a 3x3 matrix of chord types that Unque compares to Major, Minor, and Suspended chords in common practice Western music.
The naming system he develops is wonderfully practical: each chord gets a Greek-prefix abbreviation (Pat, Met, etc.) and a number indicating the scale degree at the top. The Major triad (5+4 steps, approximately 4:5:6) is “Pat 3,” the Minor triad (4+5 steps) is “Pat 2,” the Quartal chord (6+6 steps) is “Met 4,” and so on.
Crucially, Unque notes that every chord in this system is either symmetrical (the same interval pattern read forwards and backwards) or “Delta-Rational” (DR) — meaning it can be inverted to yield a chord with a simple JI interpretation. No chord has both properties. This is a nontrivial structural observation about 15-EDO’s harmonic geometry.
Scales in 15-EDO
Unque documents several important scales in 15-EDO:
7L 1s is perhaps the most popular scale in the system. It has 7 large steps and 1 small step, and its 8 modes have been named after sea creatures by William Lynch: Octopus, Mantis, Dolphin, Crab, Tuna, Salmon, Starfish, and Whale. The scale is notable for being more versatile than its near-uniformity would suggest — despite most steps being the same size, the different modes have quite different harmonic characters.
5L 5s is a 10-note scale that is a mode of limited transposition — meaning some of its modes are exact transpositions of each other. It has two modes: a Bright mode and a Dark mode. This symmetry makes it particularly useful for modulation, and Unque uses it as a “superstructure” from which multiple 7-note scales can be derived.
4L 3s is a 7-note scale that Unque describes as an important structural scale. Its large step is 3 steps of 15-EDO rather than 2, giving its modes more contrast with each other than the previous scales. The seven modes are named by Ayceman after figures from the Elder Scrolls lore: Nerevarine, Vivecan, Lorkhanic, Sothic, Kagrenacan, Almalexian, and Dagothic.
3L 2M 2s is the closest thing 15-EDO has to a “diatonic” scale. It is made by alternating major and minor thirds (5 and 4 steps respectively), and its step pattern resembles that of the Zarlino scale — the historically important just-intonation diatonic that Renaissance theorists like Ptolemy and Zarlino described. It comes in left-hand and right-hand versions depending on which interval you stack first.
Functional Harmony in 15-EDO
Unque’s treatment of functional harmony in 15-EDO is one of the more practically useful sections of his guide. He makes several key observations:
Despite the damaged Circle of Fifths, chords in 15-EDO still have a tendency to rotate around it — though the pull is weaker than in more accurate tunings. Voice leading is, in Unque’s view, “the single most important element of 15-EDO harmony,” because it provides consistent direction in the absence of strong harmonic gravity.
He provides two concrete chord progression examples. The first uses the right-hand C Ionian mode of 3L 2M 2s and arrives at the progression C — F — em — G (I — IV — iii — V), using voice leading to compensate for the inaccurate fifths. The second uses the C Starfish mode of 7L 1s and arrives at C — am — B — hb° (I — vii — VIII — vi°), using a combination of voice leading, circle of fifths movement, and tension-and-release.
Superstructures and Modulation
One of the most distinctive ideas in Unque’s 15-EDO guide is his concept of “superstructures” — larger scales that contain multiple smaller constituent structures, allowing for smooth modulation between different keys or modal centers.
His primary example uses the 5L 5s scale as a superstructure containing the 3L 2M 2s scale as a constituent. Because 5L 5s is a mode of limited transposition, it contains the Ionian mode of 3L 2M 2s on both the first degree © and the eighth degree (A#), even though C Ionian and A# Ionian don’t share any notes. By using 5L 5s as the overarching structure, a composer can modulate smoothly between these two keys without passing through any intermediate scales.
This idea has a clear parallel in how Maqam music uses Jins transitions — small melodic cells that link different modal centers — and it’s notable that Unque explicitly makes this comparison, circling back to the Arabic music that first got him interested in microtonality.
30-EDT: The Stretched Octave
Unque’s advocacy for 30-EDT (Equal Divisions of the Tritave) is brief but interesting. 30-EDT divides the tritave — the 3:1 frequency ratio, which is an octave plus a perfect fifth — into 30 equal steps rather than dividing the octave.
The most obvious application Unque notes is as a “stretched” version of 19-EDO. Because 19-EDO has a consistent tendency to tune all prime harmonics flat (meaning all its intervals are slightly narrower than their just-intonation counterparts), stretching the octave to the tritave compensates for this flatness in a principled way.
But Unque also advocates for 30-EDT on its own terms as a tritave-equivalent system. He argues that the semi-tritave — the interval at the midpoint of the tritave — is “relatively consonant” and “a very intuitive size for a period” because it falls precisely halfway between the perfect fifth and the octave, the two most common spans for a scale. This makes it a natural reference point for melodic organization in a way that the semi-octave (the tritone) is not.
29-EDO: The Xenharmonic Beginner’s Best Friend
Unque’s most extensive composition theory writing is devoted to 29-EDO, and it’s not hard to see why. He argues, somewhat provocatively, that 29-EDO should replace the more commonly recommended introductory microtonal systems — 17-EDO, 24-EDO, and 31-EDO — as the gateway drug for musicians transitioning from 12-tone thinking.
His argument has several prongs, and it’s worth taking each seriously.
The Case for 29-EDO as an Introduction
Accurate fifths and a familiar Circle. 29-EDO’s perfect fifth is 703.448 cents, compared to the just 701.955 cents — an error of less than 1.5 cents. This is better than 12-EDO’s fifth (700 cents, about 2 cents flat) and much better than 15-EDO (18 cents sharp) or 22-EDO (about 7 cents sharp). The result is that the Circle of Fifths in 29-EDO feels genuinely familiar. The diatonic scale sounds recognizably diatonic, and musicians can orient themselves using the same harmonic landmarks they know from 12-EDO.
Distinct, unambiguous interordinals. The term “interordinal” refers to intervals that fall between the standard diatonic interval categories — between major second and minor third, between major third and perfect fourth, between perfect fifth and minor sixth, and between major sixth and minor seventh. In 12-EDO, these regions are empty. In 29-EDO, each region contains exactly one interval, and each of those intervals is clearly distinct from its neighbors. Unque names these four interordinals the Chthonic, the Naiadic, the Cocytic, and the Ouranic.
This is significant for beginners because it means that 29-EDO offers genuine microtonality — sounds that are impossible in 12-EDO — while still being navigable using familiar Circle-of-Fifths logic. You can place these unfamiliar intervals onto a structure you already understand.
A highly divisible perfect fourth. In 29-EDO, the perfect fourth falls at 12 steps. The number 12 is divisible by 2, 3, 4, and 6, which means that the fourth can be cleanly divided into equal parts in multiple ways. This supports Porcupine temperament, Tesseract temperament, Negri temperament, Semaphore temperament, and other systems that use the fourth as a structural interval.
Access to supersets. For composers interested in very high accuracy, 29-EDO’s fifth is the optimal tuning for Parapyth temperament, and multiples of 29-EDO (particularly 87-EDO) support Rodan temperament, an extremely efficient system for extending the harmonic series.
The Intervals of 29-EDO
Unque provides a thorough interval table for 29-EDO that is worth examining carefully. The key feature is the presence of four interordinal intervals alongside the familiar diatonic categories:
The Chthonic (6 steps, ~248 cents) falls between the major second and minor third. Two Chthonics make a perfect fourth — this bisection property makes it particularly useful harmonically.
The Naiadic (11 steps, ~455 cents) falls between the major third and perfect fourth. Two Naiadics make a major sixth.
The Cocytic (18 steps, ~745 cents) falls between the perfect fifth and minor sixth. Two Cocytics reduce to a minor third.
The Ouranic (23 steps, ~952 cents) falls between the major sixth and minor seventh. Two Ouranic intervals reduce to a perfect fifth.
These pairs — Chthonic/Naiadic and Cocytic/Ouranic — are related by octave inversion, and they slot into the harmonic fabric of 29-EDO in ways that Unque explores at length in his guides.
He also discusses Extraclassical Tonality in 29-EDO — a harmonic system based on the “arto” and “tendo” thirds, which differ from the standard major and minor thirds by a diesis (1 step of 29-EDO). These thirds create a distinctly microtonal sound and can be used to introduce genuinely alien harmonic colors into an otherwise conventional progression.
Addressing the Critics: Harmonic Approximations
One frequent criticism of 29-EDO is that it doesn’t approximate the higher prime harmonics (5, 7, 11, 13) very accurately. Unque’s response to this is clever and worth understanding.
He argues that while the individual primes may have significant error, the ratios between those primes are tuned quite well, because the errors on primes 5, 7, 11, and 13 all point in the same direction and are of roughly the same magnitude. This means their difference tones — the frequencies produced by the interaction of two tones, which your ear uses to assess consonance — are well-tuned.
He formalizes this by working out 29-EDO’s accurate subgroup: rather than 2.3.5.7.11.13 (the standard 13-limit), the system works well in 2.3.7/5.11/5.13/5.29.37. This is an unusual subgroup that includes primes 29 and 37, which happen to be approximated well by the chromatic semitone and the arto third respectively. It’s a genuinely insightful piece of harmonic analysis.
Chords of 29-EDO
The chord taxonomy for 29-EDO is extensive. Unque organizes chords into several families:
Tertian triads — built by stacking two thirds — come in a dizzying variety, because the diesis (1 step) can be added to or subtracted from any of the standard thirds to produce new chord types. The standard Major and Minor triads are present, but so are Tendo, Upminor, Downmajor, Arto, and various Wolf and Augmented variants. Each of these has its own character and its own typical scale contexts.
Chthonic triads — built by stacking intervals that add up to a perfect fourth rather than a perfect fifth — are an unusual harmonic resource that 29-EDO offers. The “perfect” Chthonic triad (6+6 steps) is particularly characteristic, and Unque notes it as the primary consonance of the 5L 4s scale.
Quartal inversions — built from stacked fourths — are familiar from jazz and 20th-century classical music, but in 29-EDO they come in additional varieties thanks to the upfourth and downfourth.
Extraclassical tetrads — four-note chords using arto and tendo thirds — fill a role in 29-EDO somewhat like seventh chords in standard harmony, capping a perfect fifth with an additional microtonal layer.
MOS Scales of 29-EDO
Moment of Symmetry (MOS) scales are scales generated by repeatedly stacking a single interval until the resulting set of pitches has only two distinct step sizes. They are the backbone of a great deal of xenharmonic scale theory, and 29-EDO is particularly rich in them because 29 is a prime number — meaning every interval in the system can serve as a generator, producing a different MOS scale.
Unque documents the following MOS scales in 29-EDO:
5L 2s — the standard diatonic, generated by the Circle of Fifths. In 29-EDO, this sounds nearly identical to the familiar diatonic, with the notable exception that the tritone comes in two clearly distinct sizes. The seven modes carry the familiar names: Lydian, Ionian, Mixolydian, Dorian, Aeolian, Phrygian, Locrian.
5L 7s — a 12-note extension of the diatonic, created by continuing the chain of fifths in both directions. The resulting modes are called “grave” (extended upward) and “acute” (extended downward) versions of the seven diatonic modes, creating a rich 12-mode system.
4L 3s — Unque describes this as a version of the Harmonic Minor scale unique to 29-EDO. Because the augmented second in 29-EDO is precisely three steps larger than a major second, distributing that interval evenly across the three semitones of the Harmonic Minor reduces it to a two-step-variety scale. The modes are named Nerevarine, Vivecan, Lorkhanic, Sothic, Kagrenacan, Almalexian, and Dagothic — again borrowed from Elder Scrolls lore, matching the names used in 15-EDO.
4L 5s — a 9-note scale that plays the role of the Diminished scale in 29-EDO. Its modes are named after Greek geographical features (Roi, Steno, Limni, Telma, Krini, Elos, Mychos, Akti, Dini) by Lilly Flores.
3L 5s — an 8-note Augmented scale, analogous to the Tcherepnin scale of 12-EDO. Its modes are named after chess pieces (King, Queen, Marshall, Cardinal, Rook, Bishop, Knight, Pawn) by R-4981.
3L 4s — the “neutral scale,” generated by stacking submajor sevenths. This scale is significantly more alien than the previous ones, using harmony based on up- and downfifths rather than standard perfect fifths. Its modes are named by Andrew Heathwaite: Dril, Gil, Kleeth, Bish, Fish, Jwl, Led.
5L 1s — the whole tone scale, which in 29-EDO has six distinct modes rather than the single mode of 12-EDO’s whole tone scale. Mode names are given by Lilly Flores: Erev, Oplen, Layla, Shemesh, Boqer, Tsohorayim.
7L 1s — an 8-note scale exploiting the divisibility of 29-EDO’s perfect fourth. Splitting the fourth into three steps (downmajor second + upminor third) and extending the pattern gives an octatonic scale with sea-creature mode names from Willian Lynch: Octopus, Mantis, Dolphin, Crab, Tuna, Salmon, Starfish, Whale.
5L 4s — a 9-note scale splitting the fourth into two parts, producing a scale with abundant interordinal intervals. Mode names from Inthar: Cristacan, Pican, Stellerian, Podocian, Nucifragan, Coracian, Frugilegian, Temnurial, Pyrrhian.
Beyond MOS: Other Scales of 29-EDO
Unque also documents several scales that aren’t strictly MOS scales but have their own compositional value:
3L 2M 2s (also called Blackdye in 29-EDO) — the same scale type that appears in 15-EDO and 22-EDO, generated by alternating wide and narrow neutral thirds. It comes in left-hand and right-hand versions and occupies an interesting position between the diatonic and the neutral 3L 4s scale.
5L 2M 3s — a 10-note extension of 3L 2M 2s, also called Blackdye. This scale adds a dietic step into each large step of the underlying 3L 2M 2s scale, unifying the two chiralities and producing ten modes (five grave, five acute).
2L 3M 2s — a scale generated by alternating arto and tendo thirds, designed around extraclassical tonality.
Chromatic Genus scales — based on the ancient Greek Chromatic Genus, which divides the perfect fourth into a minor third and two semitones. Unque provides three variants (neutral, arto, and Pythagorean chromatic) with full modal tables.
Functional Harmony in 29-EDO
Unque’s treatment of functional harmony in 29-EDO is more sophisticated than his 15-EDO treatment, reflecting the greater harmonic complexity of the system.
He identifies three types of leading tones: the diesis (1 step, ~41 cents), the semitone (2 steps, ~83 cents), and the chroma (3 steps, ~124 cents). The semitone is the strongest of the three — narrow enough to create real tension, but wide enough to be heard as a distinct interval rather than a slight tuning inflection.
He also discusses the 14th-century theorist Marchetto da Padova’s use of interordinal intervals as counterpoint dissonances, noting that the Chthonic and Ouranic intervals function as useful counterpoint tensions in 29-EDO in a way that parallels Marchetto’s medieval practice.
His worked example — a chord progression in C Vivecan (the Harmonic Minor mode of 4L 3s on C) — is particularly illuminating. The Vivecan mode doesn’t contain a perfect fifth over the root; it has an upfifth instead. This creates an unusual tonal center, and Unque’s solution is to use harmonic patterns to “convince” the listener that the upfifth is more resolved than the downfifths found on the other scale degrees. The resulting progression is C ^min ^5 — ^F ^min v5 — D ^min v5 — vA vct ^4, a chord progression that uses a combination of voice leading and circle-of-fifths movement to create genuine functional harmony in a thoroughly microtonal context.
Mode, Key, and Scale Transitions
The final section of Unque’s 29-EDO guide deals with three distinct kinds of harmonic movement: changing the perceived root within a single scale (re-rooting), changing to a transposed version of the same scale (moving transposition), and modulating to a different scale entirely.
His example for re-rooting uses the Blackdye scale (5L 2M 3s), showing how to move from Grave Ionian on C to Grave Mixolydian on G using a sequence of smooth voice leading moves that gradually introduce the new tonic without any jarring leaps.
His example for moving transposition uses the neutral 3L 4s scale, showing how to move from Kleeth mode on C to Kleeth mode on B by exploiting the circle of submajor thirds (C — vE — ^G — B), which defines the scale’s generator. This is an elegant piece of modulation theory — using the very interval that generates the scale as the vehicle for moving between transpositions of it.
22-EDO: The 11-Limit Playground
22-EDO is one of the most celebrated systems in the xenharmonic world. It is arguably the smallest EDO to support the full 11-limit — meaning it approximates all the harmonic ratios involving prime numbers up to 11 with reasonable accuracy. It is also the intersection of several beloved temperaments: Superpyth, Porcupine, Orwell, and Magic.
Unque notes that fans of 15-EDO will likely be drawn to 22-EDO, because the latter is quite useful as an extension of the former that provides more accurate interval representations.
The Intervals of 22-EDO
22-EDO’s perfect fifth is about 709 cents — significantly sharper than just (702 cents) and substantially sharper than 12-EDO (700 cents). This sharpness has the same consequence as in 15-EDO: suspended chords feel less tense and more restful, while standard tertian triads feel tenser and more energetic. Western music translated into 22-EDO without adjustment will sound strange.
Unque’s interval table for 22-EDO includes two notation systems: Superpyth Notation, based on the standard Circle of Fifths (where the fifth generates the notation), and Pajara Notation, which uses ten nominals instead of the traditional seven. He uses Greek letters for the Pajara nominals (α through ι) to avoid confusion with the standard Latin letters of Superpyth notation.
The thirds of 22-EDO are particularly interesting. There are four kinds: subminor (5 steps, representing 7:6), minor (6 steps, representing 6:5 and 11:9), major (7 steps, representing 5:4), and supermajor (8 steps, representing 9:7). Unque notes that the minor third at 6 steps is contentious — it’s quite sharp for a minor third but not sharp enough to be a neutral third, so it doesn’t cleanly represent either 6:5 or 11:9.
Scales in 22-EDO
Unque’s scale coverage for 22-EDO is similarly thorough:
5L 2s in 22-EDO uses the Superpyth diatonic, which represents the 2.3.7 subgroup of Just Intonation. The modes have standard names (Lydian through Locrian) but behave quite differently from Meantone diatonic music due to the sharper fifth.
3L 2M 2s in 22-EDO represents the 5-limit Zarlino diatonic, generated by alternating 6-step and 7-step thirds. Unque notes that this scale is much closer to familiar common-practice harmony than the Superpyth diatonic.
5L 2m 3s (Blackdye in 22-EDO) is a 10-note extension of 3L 2M 2s, just as in 29-EDO. It can be notated in either Superpyth or Pajara, and Unque provides full mode tables for both.
2L 8s is described as “another characteristic scale of 22-EDO,” independently discovered by Paul Erlich, Gene Ward Smith, and Olivier Messiaen (who described its 12-EDO analog). It is a mode of limited transposition with fivefold symmetry, and it forms the basis for Pajara Notation. Unque categorizes its five modes using Erlich’s “Static/Dynamic Major/Minor” framework.
4L 5s in 22-EDO is closely associated with Orwell temperament.
3L 4s in 22-EDO is associated with Magic temperament and uses Marvel triads (augmented triads with a specific tuning) as its primary consonances.
3L 7s is a 10-note scale extending 3L 4s, discussed at length in a paper by Komorsky, with modes named after the ten Sefirot of the Kabbalah: Malkuth, Yesod, Hod, Netzach, Tiferet, Gevurah, Chesed, Binah, Chokmah, Keter.
Chords of 22-EDO
The chord table for 22-EDO is one of the most impressive in Unque’s guides. Having four types of thirds rather than two, 22-EDO has a genuinely rich array of triads. Unque lists them systematically with both Superpyth and Pajara notation, JI interpretations, and the scales in which each chord typically appears.
Some highlights: the Marvel triad (7+7 steps, representing 16:20:25) appears in both 2L 8s and 3L 4s and is the primary consonance of Magic temperament. The Sensamagic triad (8+8 steps, representing 11:14:18) appears in 11-EDO-generated contexts. The Orwell Diminished triad (5+5 steps) is the characteristic chord of Orwell temperament.
There are also four distinct types of diminished triads but only two types of augmented triads — a consequence of the Marvel comma being tempered out in 22-EDO.
Functional Harmony in 22-EDO
Unque’s functional harmony treatment for 22-EDO mirrors his approach in 15-EDO: identify the leading tones, identify the tense intervals that resolve by contrary motion, and build progressions from back to front.
In Superpyth 22-EDO, the sharp fifth means that quartal harmony is actually more consonant than tertian harmony — the opposite of the situation in Meantone tunings. This leads to the main tonic chord in C Ionian (Superpyth) being Csus4 rather than C major.
His example progression — Csus4 — Eow — Fsus4 — Gsaj — is built using Orwell Diminished and Supermajor triads as tension chords, exploiting the leading tone between E and F and the strong pull of the Supermajor chord over the fifth degree. Notably, the Fsus4 and Eow chords introduce B♭, which contrasts with the B♮ found in the Gsaj chord, creating an extra layer of harmonic color.
37-EDO: The Structural Extension
37-EDO is described by Unque as “another 11-limit system with a sharp diatonic fifth” and a supporter of Porcupine temperament — characteristics it shares with both 15-EDO and 22-EDO. Being 15 + 22, it is quite literally a structural combination of the two systems, and Unque notes that fans of both will likely be drawn to it.
His composition theory page for 37-EDO is currently under construction (as of the latest version of the document) and contains only an interval table and a brief notation section. But the interval table is already interesting.
37-EDO has an unusual property: it has two different mappings for the 3:2 perfect fifth — one “diatonic” fifth at 22 steps (about 714 cents) and one “antidiatonic” fifth at 21 steps (about 681 cents). This harmonic ambiguity, combined with its accurate higher-prime approximations, makes 37-EDO a genuinely complex system. Unque uses a “+” to indicate interpretations using the diatonic 3-limit and “–” for those using the antidiatonic 3-limit.
The interval table for 37-EDO also introduces some new temperament names: Sycamore, Passion, Cubical, Didacus, Gorgo/Shoe, Barbados, Cuthbert, Orgone, Beatles, Wuerschmidt, Lambeth, Ammonite, Ultrapyth, Undecimation, and Emka. The “Lambeth” temperament, generated by the interval 14/11, is named after the area of London — a detail that suggests this might be a mild in-joke about the wiki user’s location.
41-EDO and 43-EDO: Larger Systems
Unque does not have full composition theory guides for 41-EDO or 43-EDO, but his brief advocacy for each on his user page is worth summarizing.
41-EDO
41-EDO is noted for its exceptional harmonic accuracy — Unque claims that the first fifteen harmonics are “practically indistinguishable from JI.” Its edostep serves as an all-purpose formal comma, representing several important comma identifications simultaneously.
Its perfect fifth maps to 24 steps — a highly divisible number — supporting the Neutral, Slendric, Tetracot, and Miracletemperaments. Instruments like the Kite Guitar have made 41-EDO more practically accessible than its size might suggest.
41-EDO is also notable for being the unique intersection of Magic, Sensamagic, and Pentacircle temperaments — a combination of relationships that makes it, in Unque’s view, “a perfect choice for composers who want to access strong low-complexity JI-like sound while retaining all the benefits of an equal temperament sequence.”
43-EDO
43-EDO is large enough that even “rank-2 thinking” — organizing music around two generating intervals — becomes difficult. Unque’s approach is to treat it as a Septimal Meantone system with an additional undecimal chroma (~45/44 to ~100/99) providing access to 11-limit intervals.
Because the diatonic chromatic semitone is three of these undecimal chromata, any interval in 43-EDO can be notated with no more than one accidental of each kind — a practical notational convenience.
43-EDO also supports an interesting structural property: the wholetone can be altered into a “down-wholetone” such that three of them make a perfect fourth rather than an augmented fourth. This creates a structure resembling Porcupine temperament but without the classical minor third.
Finally, Unque notes 43-EDO’s accurate tuning of Bleu temperament, which divides the perfect fifth into five equal parts.
The 5L 3s (Oneirotonic) Scale: A Case Study in Scale Theory
One of Unque’s more self-contained theoretical contributions is his work on the 5L 3s scale, which he calls the “Oneirotonic” scale. This scale has 5 large steps and 3 small steps per octave — it can be found in several EDOs, including 13-EDO (the “basic” or balanced version), 18-EDO, 21-EDO, and others.
Unque’s theoretical approach to 5L 3s is distinctive because the scale’s generator (3 steps above the root in the basic 13-EDO tuning) falls an odd number of steps above the root. This means the scale cannot be split into two intervals of the same category — unlike the diatonic 5L 2s, which can be split into a major and minor third to give the major/minor chord dichotomy. As a result, Oneirotonic does not have a major/minor dichotomy; instead, its chord structure has a three-waydistinction.
He identifies two primary approaches to chords in the Oneirotonic scale:
Tertiary triads (built from major and minor thirds) come in three types that occur in the scale: Major, Minor, and Diminished. The Augmented triad does not naturally occur but can be extrapolated. In hard tunings of the scale, the Major triad resembles 10:13:15 and the Diminished triad resembles 6:7:8 — genuinely consonant sonorities. In soft tunings (closer to equal-step scales), the tritones approach the semioctave and the chords become less stable.
Genspan triads (built by splitting the perfect fifth into a third and a fourth) come in four types. In soft tunings, these are the more consonant option — the Fourth genspan (P4 + m3) resembles 6:8:9, and the Third genspan (M3 + d4) resembles 4:5:6. In hard tunings, these become less stable as the intervals stretch away from their JI targets.
This “switching of places” between tertiary and genspan chords as you move between soft and hard tunings is a fascinating structural property that Unque compares to the analogous behavior of tertian and suspended chords in the diatonic scale.
The eight modes of the Oneirotonic scale are named after locations in the Dreamlands from H.P. Lovecraft’s fiction: Dylathian, Ilarnekian, Celephaïsian, Ultharian, Mnarian, Kadathian, Hlanithian, and Sarnathian. The natural major mode is Ilarnekian; the harmonic minor mode is Celephaïsian; the natural minor mode is Ultharian; the natural diminished mode is Hlanithian.
What Unque’s Work Tells Us
Reading through Unque’s guides, several recurring themes emerge that tell us something important about his compositional philosophy.
He prioritizes compositional utility over theoretical elegance. When he advocates for 29-EDO, he’s not primarily arguing that it approximates JI better than the alternatives — he’s arguing that it gives composers more useful musical resources. When he dismisses the Carlos Alpha interpretation of 15-EDO, it’s because he finds it compositionally unproductive, not because it’s theoretically wrong.
He takes notation seriously. Multiple notation systems appear in his guides, and he is careful to explain which one he’s using and why. This reflects an understanding that notation is not neutral — the way you write down a scale shapes how you think about it and how you hear it.
He is interested in voice leading as a universal principle. Across all his guides, voice leading — the smooth movement of individual voices from one chord to the next — emerges as the most fundamental principle of harmonic organization. This is particularly important in tuning systems with damaged or absent Circles of Fifths, where the automatic gravitational pull of standard harmonic progressions is reduced or absent.
He is genuinely playful. Mode names borrowed from Elder Scrolls lore, Lovecraftian Dreamlands geography, sea creatures, and chess pieces; a self-described “exotempering troll” and “spewer of recreational mathematics”; chord progressions worked out in 14th-century counterpoint frameworks. This is someone who clearly loves the material and approaches it with genuine delight.
Where to Find Unque’s Work
All of Unque’s composition theory writing is available on the Xenharmonic Wiki:
- 15-EDO Composition Theory
- 22-EDO Composition Theory
- 29-EDO Composition Theory
- 37-EDO Composition Theory (under construction)
- 5L 3s Tonal Theory (under construction)
His music is on YouTube at @uncreativename2190, and his broader profile — including links to worldbuilding projects and other theoretical work — is on the Xenharmonic Wiki User:Unque page.
If you’re a musician curious about microtonality, his guides are an excellent entry point, particularly the 29-EDO guide, which was written with beginners specifically in mind. You’ll need some patience for the notation — the accidentals pile up quickly in a 29-note system — but the underlying musical ideas are grounded in exactly the same voice-leading and harmonic logic that traditional music theory teaches. Unque has simply extended that logic into stranger, more colorful territory.
And once you’ve heard those Chthonic thirds resolve, you may find it difficult to go back.
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