The microtonal theory of going where your whims take you
If you've spent any time in the world of alternative tuning systems — scales that don't use the familiar 12 equal semitones of a standard piano — you may have stumbled across the name Budjarn Lambeth. Based in New South Wales, Australia, Lambeth is a self-described amateur hobbyist who has nonetheless produced an extraordinary volume of original music theory, invented scales, and wiki contributions over the past few years. His work lives primarily on the Xenharmonic Wiki, the main collaborative encyclopedia for microtonal and alternative tuning theory.
This article is an introduction to his ideas for musicians who are comfortable with standard theory — you know your intervals, your modes, your chord functions — but haven't yet fallen down the microtonal rabbit hole. Lambeth's work is a great entry point because, while it can get technically dense, many of his core ideas are driven by aesthetic intuition and a genuine love of sound exploration rather than pure mathematics.
Who Is Budjarn Lambeth?
Lambeth describes himself as an "improviser-composer" and scalesmith — someone who invents new musical scales. His original microtonal music is hosted on YouTube, and he contributes extensively to the Xenharmonic Wiki, where he has helped organize, document, and expand the community's collective knowledge about alternative tuning.
His interests span several areas: he invents new theoretical frameworks, constructs original scales and temperaments, and advocates for a more playful, exploratory approach to tuning. He has a recurring "hot take" on the Xenharmonic Wiki that the community should take itself less seriously and have more fun — and his work embodies that ethos. He named a series of temperaments after characters from Guardians of the Galaxy Vol. 3. He named one of his own scales "the fishcrackers scale." He is clearly not trying to impress anyone with academic gravitas.
Yet the ideas themselves are often genuinely clever, and some have started to circulate more widely in the microtonal community.
A Quick Primer: What Is Microtonal Music?
Before diving in, a brief orientation. Standard Western music uses 12 equal divisions of the octave (12-EDO). Every semitone is exactly the same size — 100 cents, where 1200 cents equals one octave.
Microtonal music uses scales with different numbers of divisions, or divisions of intervals other than the octave, or just intonation (tuning intervals using simple whole-number ratios like 3/2 for a perfect fifth or 5/4 for a major third). The field is enormous and the Xenharmonic Wiki documents thousands of alternative tuning systems.
If you want to get oriented in this world, the wiki's page on equal-step tunings and just intonation are good starting points.
Lambeth's Original Theoretical Ideas
Structural Beating
One of Lambeth's more philosophically interesting proposals is a concept he calls structural beating.
In standard acoustic physics, "beating" refers to the wavering sound you hear when two notes are slightly out of tune with each other — the two waveforms periodically fall in and out of phase, producing a pulsing effect. Lambeth hypothesizes that something analogous might happen at a much larger structural scale with certain kinds of scales.
Here's the idea in plain terms. Most scales repeat at the octave — the note an octave above any given pitch sounds like "the same note, but higher." Your ears perceive the octave as an interval of equivalence. In standard 12-EDO, every octave is exactly 1200 cents.
But what if you built a scale where the repeating interval was not the octave? For example, equal divisions of a minor seventh (7/4, approximately 969 cents) or a minor ninth (16/9, approximately 996 cents)? These scales repeat at a different interval than where your ear expects repetition. Lambeth suggests this creates a kind of macro-level "beating" or phasing effect: as the scale ascends or descends, the scale's built-in repetition point gradually drifts in and out of sync with the octave, creating the impression that the scale is constantly shifting and evolving even though it's mathematically periodic.
He describes this as a potentially desirable property — "the composer gets something from nothing." A single repeating scale starts to feel like it never quite repeats.
Whether or not you find the psychoacoustic theory convincing, it's a fascinating design principle for scale construction.
Polytriadicism
Polytriadicism is one of Lambeth's most immediately practical ideas for composers.
The concept is simple: rather than tuning an entire ensemble to one scale, you tune different instruments (or instrument groups) to different triads — three-note subsets — drawn from a shared larger tuning system. The consonances within each instrument's triad are clear and easy to navigate. The interaction between different instruments, playing different triads simultaneously, generates the harmonic complexity of the larger system.
Think of it a little like how a string quartet in standard Western music might voice a chord: each instrument only plays one note, but together they create something richer than any one instrument could on its own. Polytriadicism extends this idea to the tuning system itself.
Lambeth notes this is especially useful for approaching complex microtonal temperaments that don't have obvious small, consonant scales, or for navigating large just intonation sets that might otherwise feel overwhelming. It's also a tool for xenrhythmic (alternative rhythm) composition, where each triad can "label" a different rhythmic layer, making complex polyrhythms easier for listeners to follow.
Equalizer Subgroups
This is perhaps Lambeth's most idiosyncratic and distinctive theoretical contribution: the equalizer subgroup.
Some background: in microtonal theory, a "subgroup" is a set of prime numbers whose ratios you're working with. The standard 5-limit subgroup, for example, means you're working with ratios built from the primes 2, 3, and 5 — the familiar harmonic language of most Western music. The 7-limit adds the prime 7, giving you intervals like the 7/4 harmonic seventh. Higher primes produce more exotic intervals.
Lambeth divides the harmonic series into three categories:
Structural harmonics (primes 2, 3, 4, 5): These provide stability, tonal gravity, and a warm bath of consonance. They're the foundation.
Assertive harmonics (harmonics 5 through 12): These have "strong personalities." When you include them in a tuning, they dominate the sound and define its flavor. The major third (5/4), the harmonic seventh (7/4), the neutral third (11/8) — these all have very recognizable, strong characters.
Ethereal harmonics (13 and above): These are subtler. They influence the sound but tend to fade into the background, adding consonances and dissonances that aren't immediately identifiable on their own but have a cumulative effect.
An equalizer subgroup deliberately excludes the assertive harmonics (5 through 12), keeping only some structural harmonics and at least three ethereal ones. The analogy Lambeth draws is to an audio equalizer: by cutting the mids and boosting the lows and highs, you create space for textures that would otherwise be masked.
The hope is that the subtle flavors of those higher harmonics — harmonics 13, 17, 19, 23, and beyond — can shine through without being overwhelmed by the more "opinionated" character of the middle harmonics.
It's a genuinely unusual compositional philosophy, and one that doesn't have much precedent in mainstream microtonal theory. Lambeth has invented several temperaments explicitly designed around this concept, including the Fifigeist temperament (subgroup 2.3.5.13.17.19).
Substitute Harmonics
The substitute harmonic framework is a technique for deliberately "fudging" a tuning system into unfamiliar territory.
The idea: take a simple, well-known harmonic — say, the 3rd harmonic (the perfect fifth, approximately 702 cents) — and replace it with a more complex harmonic that closely approximates it. For example, the 767th harmonic, when reduced to within the octave, sits very close to the perfect fifth at around 700 cents. If you substitute the 3rd harmonic with the 767th, you've technically converted a standard 5-limit tuning system into a much more exotic one built on the subgroup 2.5.767 — while sounding superficially similar.
Lambeth has developed a collection of temperaments using this technique. The ones using sharper substitutes (harmonics slightly above the ones being replaced) are named after sharp weapons: Daggerminished, Pajaraxe. Those using flattersubstitutes are named after flat, desert regions: Sahara. A family of "narrowed compton" temperaments, which substitute the 5th harmonic, are named with "-com" or "-come" endings: Dotcom, Sitcom, Romcom, Telecom, Intercom, and so on.
Beyond the entertaining naming conventions, this framework offers a practical tool for composers who want to explore unusual harmonic colors that sit just outside the standard sonic vocabulary.
Quasipelog Theory
Quasipelog theory is a framework Lambeth developed in late 2025 for approaching 16-EDO (sixteen equal divisions of the octave) and related tunings.
The name is a nod to Pelog, one of the two principal tuning systems in Javanese and Balinese gamelan music. Pelog scales have a characteristic sound — a mix of small and large steps that create a mood unlike anything in Western music. 16-EDO supports a temperament called Mavila, whose scales have a similar melodic flavor to Pelog.
Lambeth defines four essential scale types within quasipelog theory, all derived from Mavila's MOS scales (MOS, or "Moment of Symmetry," scales are a family of well-structured scales that recur throughout microtonal theory):
- Quasipelog minor: a 5-tone scale
- Quasipelog major: another 5-tone scale with a different modal character
- Quasipelog heptatonic: a 7-tone scale
- Quasipelog chromatic: a 16-tone scale derived from stacking fifths
He also specifies a timbre philosophy: instruments with purely harmonic overtones (like a standard synthesizer sawtooth wave, or a guitar) are to be avoided in quasipelog music. Instead, he recommends metallophones, bells, inharmonic synth timbres, thin woodwind sounds, or sine waves. This mirrors real gamelan practice, where metallic inharmonic instruments are essential to the characteristic sound.
This is an important and often overlooked point in microtonal composition: the relationship between scale and timbre matters enormously. A scale that sounds beautiful on bells may sound jarring on a guitar, and vice versa.
Selected Scales
Lambeth has invented a very large number of scales — the list on his wiki page runs to well over 100 named scales. Here are three that illustrate different aspects of his approach.
The Antipental Blues Scale
The antipental blues scale is a six-note, octave-repeating scale designed to sound melodically similar to the familiar minor blues scale from 12-EDO, but with entirely different harmonic content.
Where the standard blues scale uses intervals built on the 5th harmonic (the familiar major third, perfect fifth, etc.), the antipental blues scale avoids the 5th harmonic entirely. Instead, its harmonic content comes from the subgroup 2.3.7.11 — intervals like 7/6 (a subminor third, about 267 cents), 11/8 (a "tritone" that sits halfway between a perfect fourth and tritone, about 551 cents), and 7/4 (the harmonic seventh, about 969 cents).
In just intonation, the scale's notes are: 7/6, 4/3, 11/8, 3/2, 7/4, 2/1.
You get the same kind of pentatonic-adjacent melodic motion you'd use to play a blues solo, but the underlying harmonic relationships are completely alien to standard Western practice. It's a clever way to give familiar melodic shapes an unfamiliar sonic texture. Lambeth's recommended tuning for the scale is the POTE (Pure Octave Tenney-Euclidean) tuning of Orwell temperament in 22 tones.
The Firedance Scale
The firedance scale is a five-note scale and an example of Lambeth's more intuitive, ear-first approach to scale construction.
It was built by starting from 5-EDO — five equal divisions of the octave, producing a perfectly even pentatonic scale — and then adjusting individual notes up or down by single steps of 15-EDO until the scale "sounded good." The final scale lives in what's called zeta-stretched 15-EDO, also known as 47zpi (the 47th zeta peak index), where the octave itself is slightly compressed according to a mathematical process called the optimal octave stretch.
The scale's intervals are approximately: 239¢, 558¢, 717¢, 957¢, 1196¢.
What's interesting is that although Lambeth designed this scale entirely by ear, it turns out to closely approximate a primodal over-7 scale — a scale drawn from harmonics 64, 77, 84, 98, and 112 of the harmonic series. The numbers 239, 717, and 957 are all decent approximations of intervals built on the 7th harmonic (8/7 ≈ 231¢, 3/2 ≈ 702¢, 7/4 ≈ 969¢). The ear, apparently, finds these harmonic relationships even when the brain isn't consciously looking for them.
The Moon Dust Scale
The moon dust scale is one of Lambeth's more ambitious recent inventions. It's a 16-tone just intonation scale with a period of 16/1 — that is, it repeats not at the octave but at the quadruple octave, four octaves above the tonic.
Its intervals span an enormous range: 17/14, 19/14, 3/2, 9/4, 19/8, 11/4, 7/2, 4/1, 9/2, 11/2, 6/1, 9/1, 19/2, 11/1, 57/4, 16/1.
You can see the mix of familiar ratios (3/2 is just a perfect fifth; 4/1 is two octaves) with genuinely exotic ones (19/14 is an interval you will essentially never encounter in standard music theory). Lambeth describes it as having "distinctly dynamic melodic steps with interspersed bendy little steps and big stark leaps."
The scale was inspired by a chord shared by fellow microtonal composer Maeve Gutierrez on the Xenharmonic Alliance Discord server. Lambeth transposed part of the chord down an octave, added a few structural notes, and used Scale Workshop (a free browser-based tool for microtonal scale design) to fill in the remaining notes by ear.
According to Lambeth, it sounds particularly nice when approximated in 24-EDO, 30-EDO, 31-EDO, or 72-EDO — standard and near-standard tuning systems that are much more accessible for performers.
The Batch 89 Temperaments
Lambeth's Batch 89 temperaments are a beautiful example of his approach to creative concept-making. These are four temperaments, first documented in 2023, each dedicated to one of the members of Batch 89 from Guardians of the Galaxy Vol. 3 — the group of genetically engineered animals who form the emotional heart of that film.
Each temperament tempers four harmonics: the 2nd harmonic (because each character had two creators), the 89th harmonic (representing their shared trauma), and two additional harmonics determined by converting the character's name to numbers using the A1Z26 cipher (where A=1, B=2, and so on).
- Floor (the rabbit): 2.3.11.89 subgroup
- Teefs (the walrus): 2.5.11.89 subgroup
- Lylla (the otter): 2.3.31.89 subgroup
- Rocket (the raccoon): 2.9⁺.9⁻.89 subgroup (a "dual harmonic 9" temperament)
Beyond the charming concept, these are real working temperaments with useable MOS scales. Lambeth has recorded music in all four.
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