27-equal temperament (27edo): a curated garden of new musical colours

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If you’ve ever bent a guitar string and thought “I wish I could just live there,” or if you’ve ever felt like the 12 notes of the piano were leaving something delicious just out of reach, then 27edo might be the tuning system that changes your musical life.

This guide assumes you know your way around chords, intervals, and basic music theory. It does not assume you know anything about microtonality. Let’s fix that.

What Does “27edo” Even Mean?

EDO stands for “Equal Divisions of the Octave.” Standard Western music uses 12edo — 12 equally spaced notes per octave, the familiar piano layout. 27edo simply does the same thing but with 27 notes instead of 12. Each step is about 44.4 cents wide — for comparison, a standard semitone is 100 cents. So each step in 27edo is less than half a semitone.

You still have an octave (2:1 ratio, identical to standard tuning). You still have something recognizable as a perfect fifth. You still have major chords and minor chords. But you also have a whole palette of new flavors that 12edo simply cannot express.

Think of it like this: 12edo gives you a box of 12 crayons. 27edo gives you 27, including colors that the 12-crayon box doesn’t even have names for yet.

Why 27 Specifically? Isn’t That an Awkward Number?

It’s actually a beautifully logical one. 27 = ³³, meaning 27edo contains both 3edo and 9edo as perfect subsets. But beyond the math, 27edo earns its keep by being one of the most harmonically interesting tuning systems in this size range, for reasons we’ll dig into below.

The Harmonic Series: Why Tuning Systems Even Exist

To understand what makes 27edo special, you need a quick word about the harmonic series. When any note rings out, it produces not just one pitch but a whole stack of overtones at mathematically simple frequency ratios above the fundamental: 2:1 (octave), 3:2 (perfect fifth), 4:3 (perfect fourth), 5:4 (major third), 6:5 (minor third), 7:4 (the “harmonic seventh”), and so on. The more closely a tuning system approximates these simple ratios, the more consonant and resonant its chords tend to sound.

12edo does a decent job with the octave, fifth, fourth, and major/minor thirds, but it handles the 7th harmonic (7:4) extremely poorly — it’s off by 31 cents, nearly a third of a semitone. 27edo approaches several harmonics differently: they are all tuned a bit sharp of just, but many important harmonic relationships — particularly those between the harmonics — come out very clean.

The Intervals: What New Colors Does 27edo Give You?

Here’s where things get exciting for a practicing musician.

The fifth: 27edo’s perfect fifth lands at 711 cents, about 9 cents sharp of the just 3:2 (702 cents). This is audible but not jarring — it gives the tuning a slightly tense, forward-leaning quality. You can think of this as a “superpythagorean” fifth, meaning it sits on the other side of pure from the slightly flat fifths of meantone temperaments like the one underlying standard tuning.

The major third: Here’s a big one. 27edo’s major third is exactly 400 cents — the same as 12edo. That’s 14 cents sharp of the just 5:4 major third (386 cents). This means your familiar major chord will sound the same shade of brightness you’re used to. However, it also means that 27edo is the natural territory for a different kind of major third: the supermajor thirdat 444 cents, approximating the 9:7 ratio. If you’ve ever heard a chord and thought it sounded “ancient” or “open” in a way that’s hard to explain, that interval might be why.

The new thirds: Between and around the standard minor and major thirds, 27edo offers three additional flavors:

  • The subminor third at 267 cents (approximating 7:6) — darker and more dissonant than a standard minor third, with a strongly “blue note” character
  • The neutral third at 356 cents (approximating 16:13) — right between major and minor, the sound of a lot of Middle Eastern and maqam music
  • The supermajor third at 444 cents (approximating 9:7) — brighter and more open than a major third

This gives 27edo five distinct flavors of third: subminor, minor, neutral, major, and supermajor. This is not a theoretical nicety — these are genuinely usable, musically expressive intervals, each with its own emotional character.

The harmonic seventh: At 978 cents (approximating 7:4), 27edo’s “harmonic seventh” — also called the septimal minor seventh — is one of its most valuable resources. This interval is what makes dominant seventh chords in blues music feel so “right” even when technically out of tune with standard pitch. 27edo gives you direct, deliberate access to it.

The 13th harmonic: 27edo approximates the 13th harmonic (the interval 13:8 above the root) particularly well — it’s only about 4 cents off. That “neutral sixth” at 844 cents has an eerie, floating quality and appears in the harmonic series of naturally played brass instruments.

The Comma Magic: Why Certain Things Just Work

Commas are tiny intervals that temperaments “temper out” — essentially decide to treat as zero. When a comma is tempered out, two things that are theoretically slightly different become the same note, which simplifies the harmonic structure enormously. 27edo tempers out several useful commas:

64/63 (the septimal comma): This means the harmonic seventh (7:4) can be divided exactly into two perfect fourths (4:3 + 4:3). In practical terms, a chord built on the harmonic seventh resolves into fourths beautifully. This is the same relationship you find in 5edo, 17edo, and 22edo. It makes the “jazz seventh” feel acoustically inevitable rather than slightly compromised.

128/125 (the lesser diesis): Three major thirds (5:4) stack up to exactly one octave. Musically, this means augmented triads are symmetrical and modulating by major thirds returns you to your starting point — just like in 12edo and its cousins.

245/243 (the sensamagic comma): This ties together the intervals of 9:7 and a chain of four fifths, which is what makes superpyth temperament work — more on that in a moment.

The SoundCloud description from Sacred Skeleton’s 27edo Guitar Explorations puts it well from a musician’s perspective: these comma relationships mean “27edo has a broad palette of harmonic resources, and it’s not too difficult to find chords that sound smooth and strong, and it’s easy to connect one to another via simple scale structures.”

The Scales: What Do You Actually Play?

27edo supports several distinct scale systems, each with its own character.

Superpyth: This is the most immediately approachable scale family in 27edo. The superpyth diatonic scale (5L 2s, generated by the 711-cent fifth) looks and functions much like a standard major scale, but the major third is wide (444 cents, the supermajor third) and the minor third is narrow (267 cents, the subminor third). Standard diatonic logic — scales, modes, chord progressions — all transfer. You’re still thinking in terms of “do re mi fa sol la ti do,” but the intervals between the notes are slightly wider on top and narrower on the bottom, giving everything a bold, almost medieval feeling. Igliashon Jones’s Superpythagorean Waltz is a lovely entry point for hearing this.

27edo is sometimes described as “the superpythagorean counterpart of 19edo.” Just as 19edo is the definitive meantone system (where the fifth is slightly flat and three fourths reach a near-perfect minor third), 27edo is the system where the fifth is slightly sharp and three fourths reach a near-perfect 7:6 subminor third. If you know and love 19edo, 27edo is its philosophical mirror image.

Augene: Built on a period of 400 cents (one third of the octave), this temperament gives you augmented-scale logic — three symmetrical “poles” dividing the octave equally. Augmented chord progressions feel natural here. The scale Augene[12] in particular works beautifully in 27edo and has been used in pieces by Igliashon Jones and Joel Taylor.

Tetracot: Generated by stacking 177-cent “small major seconds,” tetracot creates a seven-note scale (6L 1s, the “archeotonic”) that sounds quite unlike anything in standard music — alien and flowing. Dustin Schallert has recorded several pieces using tetracot in 27edo.

Myna: One of the more exotic options, myna explicitly names and uses all five third-types described above: subminor, minor, neutral, major, and supermajor. If you want to make the most of 27edo’s harmonic diversity, myna is worth exploring.

What Does It Sound Like? Listening Recommendations

The best way to internalize 27edo is simply to listen. Here are some approachable entry points:

  • Sacred Skeleton — 27edo Guitar Explorations (SoundCloud): Four tracks ranging from doom metal to post-rock. An excellent demonstration that this tuning can be visceral and physical, not just theoretical.
  • Igliashon Jones — Superpythagorean Waltz (YouTube): A charming, dance-like piece that shows how naturally diatonic-style music can work in 27edo.
  • Brendan Byrnes — Sunspots: Byrnes is a guitarist who has built custom 27edo instruments and has a large body of work in the system.
  • Bryan Deister — 27edo waltz and 27edo improv (2025): More recent recordings that show the tuning being used in a relaxed, improvisational context.
  • Francium — “Router-Pseudoscientist”: Available on Spotify and Bandcamp, this was a 2025 entry in the Temperament of the Month Club challenge.

For a beginner’s video walkthrough, search YouTube for “basic Dave 27 EDO” — it’s a friendly, musically focused tour through the intervals.

How Do I Actually Play It?

This is the practical question. There are several good answers depending on your setup.

Software (easiest entry point): Scale Workshop (by Sevish, free in your browser) lets you build a 27edo scale and play it on a virtual keyboard immediately. Bitwig Studio has a built-in Micro-Pitch device. Surge XT is a free synthesizer with excellent microtuning support. Any DAW that accepts .tun or .scl files can be retuned.

Lumatone keyboard: The Lumatone is an isomorphic MIDI keyboard that can be mapped to any tuning. Several 27edo layouts are documented on the Xenharmonic Wiki, making this probably the most ergonomic physical option.

Guitar: A dedicated 27edo guitar requires 27 frets per octave, which results in frets very close together higher on the neck. Brendan Byrnes owns and plays one. A more accessible alternative is a skip-fretted guitar, which keeps a subset of 27edo notes but with more comfortable fret spacing.

Is 27edo “Consistent”?

This is a technical property that matters in practice. A tuning is consistent in a given odd limit if, whenever you add up intervals to reach a target ratio, you always arrive at the same number of steps — the result doesn’t vary depending on your path. 27edo is consistent up to the 9-odd-limit and distinctly consistent up to the 7-odd-limit. What this means practically: any chord built from ratios up to 9 in the harmonic series will behave predictably and unambiguously. You won’t get contradictory fingerings for the same chord.

The Bigger Picture: Where Does 27edo Fit in Microtonal Space?

If you’re familiar with 12edo and maybe experimenting with other tunings, here’s a rough map:

  • 19edo is the “gentle” cousin — meantone fifths, near-pure major thirds, a warm and singable sound. Great first step into microtonality.
  • 22edo emphasizes septimal (7-limit) harmony aggressively. Sharp and edgy.
  • 27edo sits between these worlds. Its fifth is sharp like 22edo’s, but it has more notes and more nuance. It has a wide, bold, slightly archaic feeling in its diatonic scales, but extraordinary harmonic depth when you start using its full resources.
  • 31edo is the other major player in this neighborhood — more notes, smoother approximations, and a long history in Western music theory going back to Christiaan Huygens. If you want near-just chords, 31edo is often the recommendation. If you want bold character and gritty septimal color, 27edo makes a strong case.

A Final Word

27edo is not a beginner-friendly tuning in the sense of being easy to stumble into. But it is surprisingly intuitive once you let go of the expectation that everything needs to sound like 12edo. As Sacred Skeleton wrote after recording four albums of improvised 27edo guitar: “Despite its large size, I find it surprisingly intuitive.”

What 27edo offers is a set of harmonic colors that simply do not exist in standard tuning: the open, archaic ache of the 9:7 supermajor third, the dark soul of the 7:6 subminor third, the floating ambiguity of the 16:13 neutral third, and the warm gravity of the 7:4 harmonic seventh. These aren’t exotic curiosities — they’re intervals that the human ear responds to deeply, because they come from the harmonic series itself.

The 12 notes we have aren’t the only notes there are. They’re just the ones we decided to build pianos around.

There are 15 more.

Further Reading and Resources

This article draws on the Xenharmonic Wiki article on 27edo, Sacred Skeleton’s liner notes for 27edo Guitar Explorations (SoundCloud, 2022), and a YouTube video overview by Basic Dave.

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