The secretly awesome tuning for microtonal jazz: 37edo (37-equal temperament)

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How 37edo provides gorgeous upper chord extensions — both the xenharmonic and familiar ones

Before we dive into 37 specifically, let’s make sure we’re on the same page about the basics.

“EDO” stands for Equal Divisions of the Octave. The tuning system you already know — standard Western tuning — is 12-EDO: the octave is cut into 12 equal slices, each one a semitone. Every semitone is exactly 100 cents wide (there are 1200 cents in an octave).

Equal temperament on the Xenharmonic Wiki is the broader concept here: you pick a number, divide the octave that many ways, and every step is the same size. 19-EDO, 22-EDO, 31-EDO — these are all common microtonal alternatives that composers and adventurous guitarists have explored for decades.

37-EDO takes the octave and slices it into 37 equal parts. Each step is about 32.4 cents wide — roughly a third of a semitone. That’s pretty tiny. You’d have to play three steps of 37-EDO to travel roughly the same distance as one semitone on a standard piano.

Why 37? That Seems Random.

Fair question. The honest answer is: not every EDO is created equal, and musicians and theorists explore them specifically because of which natural intervals they approximate well.

In just intonation — the “pure” tuning system based on simple mathematical ratios — the notes of the harmonic series are given precise frequency ratios. The perfect fifth is 3/2, the major third is 5/4, the harmonic seventh is 7/4, and so on. Standard 12-EDO approximates these ratios, but with varying amounts of error: the fifth is almost perfect, the major third is noticeably sharp, and the harmonic seventh (7/4, that bluesy flat seventh) is so wrong that 12-EDO essentially ignores it.

37-EDO has a completely different set of strengths. Here’s what it gets remarkably right:

  • The 11th harmonic (11/8, a sort of “super tritone” about halfway between a perfect fourth and a tritone) is virtually exact — only 0.03 cents off. That’s basically perfect.
  • The 13th harmonic (13/8, a kind of exotic major sixth) is only 2.7 cents off — well within the threshold most ears would notice.
  • The 7th harmonic (7/4) is about 4.1 cents off — quite good.
  • The 5th harmonic (5/4, the major third) is only 2.9 cents off — better than 12-EDO’s ~14 cents error.

What 37-EDO does not do well is approximate the 3rd harmonic — the perfect fifth. At about 11.6 cents sharp, it’s noticeably off. This is actually the key personality of 37-EDO: it thrives in a world where the perfect fifth takes a back seat, and weirder, higher harmonics take center stage.

This makes it, in the language of microtonal theory, a strong no-threes system — meaning it really shines when you avoid building harmony around fifths and fourths, and instead lean into chords built from the 5th, 7th, 11th, and 13th harmonics.

So What Does It Actually Sound Like?

Think about a chord like 8:10:11:13:14. In 12-EDO, you can’t really play this — the 11th and 13th harmonics simply don’t exist in that system. In 37-EDO, all of those harmonics are approximated beautifully, and that chord — which has no perfect fifth in it at all — can ring with an almost supernatural clarity.

If you’ve ever heard music that sounds “not quite Western but not quite Eastern either,” harmonically fresh and strange but somehow still consonant, there’s a good chance it was leaning on these higher harmonics. 37-EDO is a particularly well-suited vehicle for exactly that sound.

The Fifth Situation: Two Flavors

Here’s something fascinating about 37-EDO that musicians with a theory background will appreciate: it has two usable fifths.

The perfect fifth in just intonation is 702 cents. In 37-EDO:

  • 22 steps = 713.5 cents — this is the “sharp fifth,” about 11.6 cents sharp of pure. It produces a bright, tense, almost Pythagorean sound.
  • 21 steps = 681.1 cents — this is the “flat fifth,” about 21 cents flat of pure. It’s so flat that it generates a completely different kind of scale.

The sharp fifth (22\37) generates what’s called a superpythagorean diatonic scale — all the interval names you know (major third, minor third, etc.) still exist, but they’re in unexpected places. The major third comes out to about 454 cents (wider than a just 5/4 at 386 cents) and the minor third is only about 259 cents (narrower than a standard minor third of 300 cents). This is the world of Archy and Oceanfront temperaments, where 7/6 and 9/7 serve as the “minor” and “major” thirds.

The flat fifth (21\37) generates an antidiatonic or mavila scale — the step pattern looks like a diatonic scale but with major and minor flipped. What would be a “major” key sounds distinctly “minor” and vice versa. It’s deeply strange and beautiful, beloved by xenharmonic composers for its otherworldly lilt.

This dual-fifth nature makes 37-EDO a rich toolkit. Depending on which fifth you choose as your generator, you’re essentially choosing between two completely different musical worlds — and you can explore both within the same tuning system.

Temperaments Supported by 37-EDO

If you’ve gotten into music theory deeply enough to understand that different modal systems and chord progressions arise from different structural “generators,” you’ll find the concept of regular temperaments fascinating. Here are some of the temperaments 37-EDO supports well:

Porcupine temperament is arguably 37-EDO’s most famous application. The generator here is a flat minor whole tone — about 162 cents, which is 5 steps of 37-EDO. Stack three of these generators and you get a perfect fourth; stack two and you get a minor third (6/5). This gives you a completely different way of organizing a seven-note scale: instead of the familiar WWHWWWH pattern, porcupine’s scales have a beautiful symmetry — three equal tetrachords stacked within the octave. The scales feel modal and ancient, but the harmony is distinctly modern and xenharmonic.

Didacus / Hemiwürschmidt temperament uses a generator of about 194.6 cents (6 steps of 37-EDO), which approximates the interval 28/25. This is a sophisticated no-threes temperament: two generators reach 5/4, and five generators reach 7/4. The harmonic world here revolves around chords like 4:5:7 and 8:10:11:14, all of which 37-EDO approximates well.

Ultrapyth uses the sharp fifth (22\37 = 713.5 cents) as its generator, and maps the “major third” not to 5/4 but to 13/10 (about 454 cents). This is a fascinating bitten-into-the-apple moment: familiar diatonic scales still structurally exist, but the major triad sounds like nothing you’ve heard before — 10:13:15 instead of 4:5:6. The Xenharmonic Wiki describes 37-EDO as a good tuning of both Oceanfront and Ultrapyth.

The Interval Palette

One of the most exciting things about 37-EDO for musicians is the sheer variety of intervals available. Here’s a brief tour:

  • 32.4 cents (1 step): About a third of a semitone. Useful as an inflection — like a very sharp leading tone or a microtonal comma shift.
  • 162 cents (5 steps): A flat whole tone, the porcupine generator. Somewhere between a whole step and a minor second in feel.
  • 259.5 cents (8 steps): Maps to 7/6, the “subminor third” — that characteristic bluesy, tightly wound third used in septimal harmony.
  • 389.2 cents (12 steps): Your familiar major third (5/4), approximated beautifully.
  • 454.1 cents (14 steps): The major third in ultrapyth — 13/10, unusually wide and bright.
  • 551.4 cents (17 steps): The 11th harmonic (11/8) — right between a perfect fourth and a tritone, rendered almost perfectly.
  • 648.6 cents (20 steps): The 11th subharmonic (16/11) — the complement of 11/8.
  • 713.5 cents (22 steps): The sharp fifth (3/2 approximation).
  • 875.7 cents (27 steps): Maps to 5/3, a nice just major sixth.
  • 973 cents (30 steps): Maps to 7/4, the harmonic seventh — that quintessentially blues interval, here rendered with only 4 cents of error.

Scales to Try

If you want to start composing or improvising in 37-EDO, here are a few starting points:

Porcupine[7] — a seven-note scale with step pattern 5 5 5 7 5 5 5 (in steps of 37-EDO). Three equal tetrachords separated by small “linking” steps. Modal, symmetric, beautiful.

Porcupine[15] — an expanded fifteen-note version: 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2. This gives you a chromatic-scale-like palette, but organized around porcupine’s logic rather than 12-EDO’s.

Oceanfront[7] — built from the sharp fifth generator, giving you a heptatonic scale that’s structurally like a major scale but where “major triads” are 10:13:15. The step patterns (like 7 1 7 7 7 1 7) have a distinctly pentatonic flavor with passing tones.

Beatles[7] — step pattern 4 7 4 7 4 7 4, generated by 11 steps (356.8 cents, approximating 16/13). A seven-note scale with an unusual, haunting symmetry.

All of these MOS (Moment of Symmetry) scales are the xenharmonic equivalent of the diatonic scale — the most natural, structurally coherent scales generated by a single interval.

How to Actually Play in 37-EDO

Getting 37-EDO into your ears and fingers is more accessible than you might think:

  • Synthesizers & DAWs: Any synth with microtonal tuning support (Surge XT, u-he Hive, ZynAddSubFX, and many others) can load a Scala tuning file for 37-EDO. Scala files for virtually every EDO are freely available online.
  • Guitar: Refretted guitars for unusual EDOs exist, or you can use a fretless guitar or slide guitar with a drone and approximate intervals by ear. There’s also a dedicated fretting system for 37-EDO using a skip-fret approach.
  • The Lumatone keyboard: This isomorphic keyboard can be mapped to 37-EDO and is increasingly popular in the xenharmonic community.
  • Ear training: Start by just listening. The music list on the 37-EDO Xenharmonic Wiki page is extensive, with dozens of freely available compositions by composers like Ray Perlner, Francium, Claudi Meneghin, and many others. Listen to the porcupine-based pieces first — they’ll give your ear the most familiar foothold.

Why Bother?

You might be thinking: this all sounds fascinating but also complicated. Why not just write more songs in 12-EDO?

Here’s a thought: every scale system you already know felt complicated before it was familiar. The circle of fifths, modal theory, secondary dominants — these are all just mental maps. 37-EDO offers you new maps to entirely new territory. The harmonic colors available — those 11th and 13th harmonics ringing pure and clear, the antidiatonic flip of mavila, the symmetric tetrachords of porcupine — genuinely cannot be approximated in 12-EDO. They are a different kind of music.

Joe Monzo, one of the early theorists who documented 37-EDO extensively, noted that it offers particularly compelling possibilities for jazz, where harmonic color often matters more than strict adherence to the fifth-based backbone of Western harmony. If you love jazz, blues, or experimental music, 37-EDO has a lot to say to you.

Further Reading

Happy exploring. The rabbit hole is deep, but the sounds waiting at the bottom are unlike anything in the standard twelve.



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