Your guide to 36edo, the sixth-tone system
If you’ve ever bent a guitar string and thought “that note sounds more right than the fretted pitch” — you’ve already felt the pull of notes that live outside the piano keys. Today we’re going to explore a tuning system called 36edo (36 equal divisions of the octave), also known as sixth-tone equal temperament, that is in many ways the most musician-friendly entry point into the world of microtonality.
First, the Quick Jargon Glossary
Before anything else, let’s set up some terminology so the rest of this article makes sense:
EDO stands for “Equal Divisions of the Octave.” Our familiar Western tuning system divides the octave into 12 equal slices — hence it’s called 12edo (or 12-TET, 12-ET — all the same thing). A cent is a unit of musical interval size: there are 100 cents per semitone, and 1200 cents in an octave. So a quartertone is 50 cents, a minor third is 300 cents, and so on.
Just intonation (JI) refers to intervals tuned to pure whole-number frequency ratios — the kind of intervals that appear naturally in the overtone series of a vibrating string. For instance, a perfect fifth is the ratio 3:2. When we play fifths on a guitar or piano, they’re close to pure but not exactly — because 12edo tempers (slightly mistuning) intervals to make all 12 keys equally usable.
Harmonics: when a string vibrates, it doesn’t just produce one frequency. It simultaneously produces integer multiples of the fundamental — the 2nd harmonic (an octave up), the 3rd (a perfect fifth above that), the 4th (another octave), the 5th (a major third), the 6th, the 7th, and so on. The 7th harmonic produces an interval that has no standard name in Western music, because 12edo can’t represent it accurately. It sits about 31 cents flat of our minor seventh — a different note entirely, not just an “out of tune” version of one.
What Is 36edo?
36edo divides the octave into 36 equal steps of about 33.3 cents each — exactly one third of a semitone. This step is called a sixth-tone (since it’s one sixth of a whole tone), and the Xenharmonic Wiki humorously proposes calling it a “quark” — drawing an analogy to particle physics, where just as protons are made of three quarks, a semitone is made of three sixth-tones.
36 is divisible by 12, which means 12edo is entirely contained within 36edo. Every note you already know — every piano key, every guitar fret — is already present in 36edo. What 36edo adds is two new notes between each adjacent pair of 12edo notes: one a third of a semitone above, and one a third of a semitone below.
A useful way to visualise this: imagine every note on the piano gains two neighbouring “shadow” versions, one slightly higher and one slightly lower. These shadow notes are the new colours that 36edo adds to the palette.
The Easiest Entry Point into Microtonality
For musicians with a strong background in conventional music theory, 36edo is arguably the gentlest possible introduction to the world beyond 12 notes. This is worth saying upfront, because “microtonal” can sound intimidating — conjuring images of impenetrable theory, unplayable instruments, and music that sounds simply out of tune.
36edo sidesteps most of those obstacles:
Every note you already know is still there. No familiar interval is removed or significantly altered. Your existing ear training, your knowledge of chords and scales, your intuitions about tension and resolution — all of it carries over intact.
All the new intervals sound like inflected versions of familiar ones, not alien pitches. The sixth-tone (33 cents) is narrow enough that a “blue A” sounds like a recognisable, expressive variation of A — not like a note that has nothing to do with A. This is a meaningful psychological difference from quarter-tone systems, where the 50-cent step often sounds genuinely disorienting to 12edo ears.
Standard notation extends simply. The ups and downs notation system adds a caret (^) or “v” to indicate a sixth-tone up or down — so ^A means “A raised by one sixth-tone.” If you can read standard notation, you’re already 90% of the way there.
It maps directly onto music you already know and love. The blue notes of blues, the expressive flat sevenths of jazz, the characteristic intervals of Indonesian gamelan — these sounds are already in 36edo, now precisely defined and named. More on this below.
People with absolute (perfect) pitch — who can find xenharmonic music genuinely disorienting because their pitch memory is so tightly calibrated to 12edo — are reported to cope better with 36edo than with most other microtonal systems, because the new notes are close enough to familiar pitches to be categorised as inflections rather than as completely foreign sounds.
Red Notes and Blue Notes: A New Colour for Every Pitch
A particularly intuitive way of thinking about 36edo’s new notes uses colour. Since 36edo places two new notes between every pair of adjacent semitones:
- The note a sixth-tone below any 12edo note can be called a “blue note” — it’s slightly flat, darker, more “down.”
- The note a sixth-tone above any 12edo note can be called a “red note” — it’s slightly sharp, brighter, more “up.”
Every interval you already know now exists in three versions: the standard version, the blue version (a sixth-tone flatter), and the red version (a sixth-tone sharper). A blue minor third sounds distinctly different from a standard minor third, but it still sounds like a minor third — just shifted in a direction that has no name in conventional notation. A red major seventh has a biting, leaning quality that a standard major seventh doesn’t quite have.
This colour metaphor makes 36edo very navigable for a conventionally trained musician. Instead of memorising a completely new set of 36 pitches, you’re expanding a system you already know — adding two new shades to every existing colour.
Three Pianos, Three Guitars: Playing 36edo on Standard Instruments
Here’s the part that might surprise you most: you don’t necessarily need any special instrument to start exploring 36edo. Because every note in 36edo is either a standard 12edo note, or a standard note raised or lowered by exactly one sixth-tone, the entire 36-note system can be covered by three ordinary 12edo instruments, each tuned approximately 33 cents apart from the others.
A pianist could sit at three pianos, one tuned normally, one tuned 33 cents sharp, and one tuned 33 cents flat. A guitarist could use three guitars with slightly different open tunings. All 36 pitches are then available across the ensemble.
This is not a new idea. Henri Pousseur’s Prospection (1952–53) for three detuned pianos is an early example, and more recently Francium’s Playing Children (2022) takes exactly the same approach. Nick Vuci’s Fantasy for Sixth-Tone Harmonium (2022) and Miroslav Beinhauer’s Pieces For Sixth-Tone Harmonium (2024) have explored purpose-built single-instrument approaches.
For solo electronic experimentation, a MIDI controller with pitch bend or a DAW with microtonal pitch-shifting can get you there immediately. The Lumatone isomorphic keyboard supports 36edo with a dedicated mapping. And the Xenharmonic Wiki’s 36edo page lists tuning files compatible with common software synthesisers.
Quarter-Tones vs. Sixth-Tones: Two Different Harmonic Worlds
The most well-known microtonal system is 24edo, which adds a note exactly halfway between each 12edo semitone — the quartertone. Quarter-tones have been used by composers including Charles Ives, Alois Hába, and Karlheinz Stockhausen, and they’re fundamental to Arabic and Persian music. So what’s the difference, and why would you choose sixth-tones over quartertones?
The answer comes down to which harmonic gaps each system fills.
12edo does a good job with harmonics 2, 3, and 6 (the octave, fifth, and their compounds), and a reasonable job with harmonic 5 (the major third, though 14 cents sharp). The harmonics it handles worst are the 7th and the 11th. Both sit awkwardly between the notes of 12edo — the 7th harmonic is about 31 cents flat of our minor seventh, and the 11th harmonic lands almost exactly midway between our perfect fourth and tritone. These are two distinct harmonic gaps, and 24edo and 36edo each fill a different one of them.
24edo — quartertones — primarily closes the gap on the 11th harmonic. The 11th harmonic (octave-reduced) sits at about 551 cents — almost exactly halfway between the perfect fourth (500 cents) and the tritone (600 cents). 12edo can only offer 500 or 600 cents; 24edo adds 550 cents, which lands within 1 cent of the pure 11th harmonic. This is why quartertones appear so naturally in Arabic maqam and Turkish makam music: those traditions make extensive use of neutral intervals — neutral seconds (~150 cents) and neutral thirds (~350 cents) — which correspond to 11-limit harmonics. When an Arabic musician plays what we’d call a “three-quarter-tone step,” they’re navigating this harmonic territory. The quartertone system is the right tool for that world.
36edo — sixth-tones — primarily closes the gap on the 7th harmonic. The 7th harmonic (the septimal seventh, ratio 7:4) sits at about 969 cents — nearly a third of a semitone flat of our standard minor seventh at 1000 cents. Neither 12edo nor 24edo gets within 19 cents of this ratio. 36edo places a note at 966.7 cents, only about 2 cents from the pure ratio — an exceptionally precise approximation. This is the harmonic that blues singers reach for, that barbershop quartets lock into on their dominant seventh chords, that jazz brass players favour when they have room to bend. Sixth-tones put it precisely on the map.
So these are complementary systems, each suited to a different harmonic territory, not competing alternatives. If your interest is in Arabic maqam, Turkish makam, or the 11-limit world more broadly, quartertones are the more natural choice. If your interest is in blues, jazz, septimal harmony, and the emotionally raw sound world of 7-limit just intonation, sixth-tones fit better.
The picture for Middle Eastern music is more nuanced than a simple quartertones-win verdict. Arabic maqam music uses neutral intervals — neutral seconds (~150 cents) and neutral thirds (~350 cents) — that 24edo approximates well with its 150-cent and 350-cent steps. For Arabic music specifically, 24edo is the better fit.
Persian music, however, is a different story. Persian intervals include a step closer to 60–70 cents (sometimes called a “Persian quartertone” or koron) rather than the 50-cent quartertone of Arabic tradition. 36edo’s 67-cent step actually approximates this more closely than 24edo’s 50-cent step does, making 36edo a reasonable fixed-pitch approximation for Persian music. Turkish makam music is yet another case — its microtonal system is often approximated using 53edo, which captures the specific interval sizes of Turkish theory more accurately than either 24edo or 36edo.
It’s worth noting that in all three of these traditions, equal-temperament approximations are only ever a scaffold for fixed-pitch instruments like keyboards. In practice, singers and instrumentalists in Arabic, Persian, and Turkish music deviate expressively from any fixed grid, inflecting pitches fluidly according to the demands of the maqam or dastgah. The equal temperament is a map, not the territory.
The 7th Harmonic: The Interval 12edo Can’t Play
In standard tuning, the ratio 7:4 — the “harmonic seventh” or “septimal seventh” — sits about 31 cents flat of our minor seventh (B♭ in the key of C). That’s nearly a third of a semitone lower. It’s a real pitch that you hear in the natural overtone series of any vibrating string, and it’s an interval that players of flexible-pitch instruments gravitate toward instinctively.
Here’s the remarkable thing: blue notes in blues and jazz are, at least in part, this very interval. Empirical research on early blues recordings has found that the “blue seventh” — that expressive, soulful flat seventh that singers and guitarists reach for — clusters very close to the 7:4 ratio. Analysis of classic blues performances has found that the flat seventh blue note sits at approximately 979 cents, corresponding closely to the just intonation ratio 7/4 at 968.8 cents. Similarly, the 7:4 harmonic seventh is heard in the barbershop quartet’s characteristic “harmonic seventh chord,” which also appears to have African American origins.
36edo places a note at 966.7 cents — only about 2 cents away from the pure 7:4 ratio. That’s exceptionally close, well within the threshold of perception. By contrast, our standard minor seventh in 12edo sits at 1000 cents, a whopping 31 cents sharp of the natural harmonic.
This means that 36edo can accurately represent the sound that blues singers and jazz instrumentalists have been intuitively reaching for. It puts that note on the scale, giving it a fixed home.
Related to this, 36edo also accurately represents:
- 7/6 (the “subminor third” or septimal minor third, ~267 cents) — 8 steps of 36edo = 266.7 cents
- 9/7 (the “supermajor third”, ~435 cents) — 13 steps of 36edo = 433.3 cents
- 7/5 (the septimal tritone, ~583 cents) — 17 steps of 36edo = 566.7 cents
- 12/7 (the “supermajor sixth”, ~933 cents) — 28 steps of 36edo = 933.3 cents
All of these intervals are derived from the 7th harmonic and are part of the sound world of blues, jazz, and a number of world music traditions.
The Good News for Conventional Intervals
You might be wondering: if 36edo adds all these new notes, does it make the familiar ones worse? The answer is mostly no. The perfect fifth (3:2 = 702 cents) is represented as 700 cents — exactly the same as in 12edo. The perfect fourth, octave, major second, minor third, major third — all are inherited from 12edo and are exactly as accurate (or as slightly impure) as they are in standard tuning.
Where 36edo does not improve on 12edo is the 5th harmonic — the major third (5:4 = 386 cents). The nearest step in 36edo is 12 steps = 400 cents, same as in standard tuning, still 14 cents sharp of pure. But for music where the sound of the seventh harmonic matters — blues, jazz, certain folk traditions, and experimental harmony — 36edo is hard to beat at its size.
Metallic Harmony: A New Kind of Chord
One of the most compelling harmonic applications of 36edo is what the xenharmonic community calls metallic harmony — a system of building chords from sevenths rather than thirds.
In conventional Western harmony, chords are built by stacking thirds: a major triad is root + major third + perfect fifth. In metallic harmony, the interval 7/4 (the harmonic seventh, ~969 cents) takes the role that the fifth plays in conventional harmony — it’s treated as the primary structural interval, and chords are built using it as the main ingredient.
For instance, the chord formed by the frequency ratios 4:7:13 — root, harmonic seventh, and a thirteenth harmonic — has a cold, metallic, resonant quality quite unlike anything in standard Western harmony. It’s not dissonant in the conventional sense; it’s actually very pure from a harmonic standpoint. It just sounds unusual, because these are intervals our standard tuning system normally can’t represent.
36edo is one of the few practical tuning systems where metallic harmony works well, precisely because of its accurate 7th harmonic. The Xenharmonic Wiki notes that 36edo is an ideal tuning for metallic harmony at its size, making it one of the most harmonically rich practical microtonal systems available without requiring an unwieldy number of notes.
World Music Connections
36edo is more cosmopolitan than it might first appear. Beyond blues and jazz, it intersects meaningfully with several world music traditions:
Indonesian gamelan pelog: 9edo (every 4th step of 36edo) approximates the pelog scale structure, meaning gamelan-flavoured music adapts reasonably well into the 36edo framework.
Slendro: The other main gamelan scale can also be approximated within 36edo in several ways.
Arabic, Persian, and Turkish music: The picture here is more nuanced than a simple “quartertones win” verdict. Arabic maqam music uses neutral intervals — neutral seconds around 150 cents, neutral thirds around 350 cents — that align closely with 24edo’s steps, making 24edo the better fit for Arabic music. Persian music is a different story: Persian intervals include a step closer to 60–70 cents (the koron) rather than the 50-cent quartertone of Arabic tradition, and 36edo’s 67-cent step approximates this more closely than 24edo’s 50-cent step. Turkish makam is yet another case, most accurately modelled by 53edo. In all three traditions, however, equal temperament approximations are a convenience for fixed-pitch instruments only — performing musicians inflect pitches expressively and do not play in strict equal temperament regardless of which grid is used as a reference.
What 36edo Doesn’t Do Well
Any honest guide has to address the tradeoffs clearly. 36edo has some significant limitations, and understanding them will help you decide whether it’s the right tool for your musical goals.
The 5th harmonic (pure major thirds) is just as compromised as in 12edo. The just major third, 5/4, sits at 386 cents. 12edo approximates it at 400 cents — 14 cents sharp, a discrepancy that bothers anyone trained in Renaissance polyphony or who has played in a well-tuned string quartet. 36edo offers exactly the same approximation: 12 steps = 400 cents, no improvement whatsoever. The lush, beating-free thirds of barbershop harmony, of meantone keyboard music, of Baroque intonation practice — none of that is better served by 36edo than by ordinary 12edo. For pure thirds, you need a system like 31edo (major third only 0.8 cents flat of pure) or 53edo (within 1 cent), both of which handle 5-limit harmony far more accurately.
The 11th harmonic is genuinely inaccessible. As discussed in the quarter-tones section, the 11th harmonic (octave-reduced to ~551 cents) falls almost exactly between two steps of 36edo — 16 steps at 533 cents and 17 steps at 567 cents, both more than 15 cents away from the pure value. The relative error is close to 50%, meaning 36edo is about as wrong as it’s possible to be about this harmonic. It cannot meaningfully represent neutral intervals, undecimal music, or the characteristic sound of 11-limit just intonation. If the 11th harmonic matters to you, 24edo is far better. So is 72edo, which is a superset of 36edo and adds accurate representations of both the 5th and 11th harmonics — at the cost of being a considerably larger and more complex system to work in.
The 13th harmonic is only moderately well approximated. 36edo gets within about 7 cents of the 13th harmonic (octave-reduced to ~840 cents). That’s usable in some contexts, but noticeably rough in music where 13-limit intervals are prominently featured. Systems like 72edo or 94edo serve the 13th harmonic far better.
It does not help with vocal or string ensemble intonation for conventional repertoire. If you’re a choral conductor or string quartet coach working to improve intonation in standard repertoire, 36edo is not the framework you need. A cappella intonation naturally gravitates toward 5-limit just intonation — pure thirds and fifths — and 36edo offers no improvement there. Thinking directly in terms of just intonation, or using a system like 53edo, is more relevant for those purposes.
The complexity jump from 12edo is real, even if smaller than with other systems. 36edo is the easiest microtonal system for 12edo musicians — but “easiest” is relative. Writing, notating, rehearsing, and performing acoustic ensemble music that genuinely exploits 36edo’s resources is still considerably more demanding than working in 12edo. The accessibility argument is strongest for composers and electronic producers working in a DAW, and somewhat weaker for acoustic ensemble contexts where every performer needs to internalise the new pitches.
It’s a specialist tool, not a general upgrade. Unlike 72edo — which approximates the 2nd through 13th harmonics well and could be argued to be a broadly superior tuning system — 36edo excels in one specific dimension (the 7th harmonic) while making no progress on others (the 5th and 11th). That focus is a strength if your musical goals align with it, and a significant limitation if they don’t.
In summary: if your musical interest lies in blues harmony, jazz, septimal chord structures, or metallic harmony, 36edo does its job extraordinarily well and is one of the most accessible routes into that territory. If your interests centre on pure thirds, neutral intervals, or broader harmonic coverage, you’ll want to look at other systems.
Where to Start
If you want to explore 36edo:
- The Xenharmonic Wiki’s 36edo article is comprehensive and includes scales, notation guides, tuning files, and a list of recorded music.
- The Metallic harmony article explains the seventh-based chord system in more detail.
- The Xenharmonic Wiki’s just intonation primer is a good place to build your understanding of harmonic ratios.
- Software like Surge XT or Scala can load 36edo tuning files and let you experiment in a DAW immediately.
- For a deeper dive into the blue note connection, the empirical research paper by Cutting (2018) in Empirical Musicology Review, “Microtonal Analysis of Blue Notes and the Blues Scale,” is freely accessible online and very readable.
The world outside 12 equal temperament is vast — but 36edo is one of the most natural, musically grounded, and practically accessible gateways into it. It starts where you already are, and takes you somewhere genuinely new.
Sources: Xenharmonic Wiki — 36edo; Xenharmonic Wiki — Metallic harmony; Cutting, J. (2018), “Microtonal Analysis of Blue Notes and the Blues Scale,” Empirical Musicology Review; Wikipedia — Blue note.
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