14-equal temperament (14edo): the neutral scale with three types of thirds, but no major or minor

What if the piano had 14 keys per octave instead of 12?

First Things First: What Is an EDO?

Before we dive into 14, let’s make sure we’re on the same page about the acronym. EDO stands for Equal Division of the Octave — and you’ve been using one your whole musical life. Standard Western tuning is 12edo: the octave is divided into 12 equal steps of 100 cents each. Every semitone is identical in size, which is why you can transpose freely and why a piano can play in any key without retuning.

14edo does the same thing, but with 14 equal steps instead of 12. Each step is about 85.7 cents — noticeably smaller than a semitone (100 cents), but larger than a quarter-tone (50 cents). The octave still doubles in frequency, but you carve it up differently on the way there.

This is the heart of microtonality: using a different number of divisions (or different-sized divisions) to get a different palette of intervals. Just as 12edo is a choice — one that was historically standardized, not divinely ordained — 14edo is another valid choice, with its own character and its own set of musical possibilities.

How Does 14edo Compare to 12edo at a Glance?

The first thing musicians usually notice: the fifth is flat. At 685.7 cents versus 12edo’s 700, it’s about 14 cents narrow. That’s a significant deviation — compare it to just intonation’s pure 5th at 702 cents, and 14edo’s fifth is nearly 16 cents flat. This gives 14edo a somewhat unusual, tense quality in any music that relies on stacked fifths or circle-of-fifths progressions.

But that same “flaw” is where the interest begins.

Three Kinds of Thirds — That’s the Whole Deal

Here is the most musically exciting fact about 14edo: it has three distinct types of thirds and three distinct types of sixths, compared to 12edo’s two of each (major and minor).

In 12edo, your options for a third are:

Minor third: 300 cents (3 semitones)
Major third: 400 cents (4 semitones)

In 14edo, your options expand to:

Subminor third: 257 cents (3 steps) — darker than a minor third, approximating the 7/6 ratio from the overtone series
Neutral third: 343 cents (4 steps) — a true middle-ground third, neither major nor minor
Supermajor third: 429 cents (5 steps) — brighter than a major third, approximating 9/7

This is a genuinely radical expansion of harmonic colour. In jazz, when you voice a chord as major vs. minor, you’re choosing between two shades. In 14edo, you have three shades for the same interval class — and they each have distinct emotional characters.

The neutral third in particular is worth dwelling on. At 343 cents, it appears in maqam music, in blues inflections, in the “in-between” note that vocalists sometimes slide through. In 14edo, it’s not a blue note or a bend — it’s a discrete, stable pitch. Harmonies built on neutral thirds have a floating, ambiguous quality that’s neither the brightness of a major chord nor the heaviness of a minor chord.

The Fifth Problem (and Why It Doesn’t Matter as Much as You Think)

In conventional harmony, the perfect fifth (3/2 in just intonation, 700 cents in 12edo) is the backbone of tonal music — it’s what powers the circle of fifths, root movement in chord progressions, and the stability of a power chord. 14edo’s fifth, at 685.7 cents, doesn’t stack cleanly. In 12edo, 12 perfect fifths almost exactly circle back to the octave (the tiny discrepancy is the Pythagorean comma, which is what equal temperament “fixes”). In 14edo, stacking fifths does not give you a useful circle — it just wanders off.

What 14edo gives you instead is a circle of fifths based on 7edo — a seven-note system where the steps are all identical (two 14edo steps each). In fact, 7edo is literally contained inside 14edo as a subset: every other note of 14edo gives you exactly the seven-note whole-tone-ish scale of 7edo. The 14edo Xen Wiki page describes this as two interleaved circles of seven fifths, neither of which connects to the other.

This means that if you try to map familiar tonal functions onto 14edo (I chord, IV chord, V chord moving by fifth), you’ll find that the usual voice-leading and resolution logic doesn’t hold. The dominant-to-tonic pull is dramatically weakened. But this isn’t a bug — it’s an invitation to explore a completely different logic of harmonic motion.

The Omnidiatonic Scale: A New “Major Scale” for 14edo

One of the most practical entry points into 14edo for musicians with a classical or popular theory background is the omnidiatonic scale — a 7-note scale within 14edo that can substitute for the standard major scale and still support recognizable triadic harmony.

This scale is “omnidiatonic” because it works similarly to the diatonic major scale in terms of structure, but the chords it generates are different. The two main chords it produces are the 6:7:9 chord (a subminor triad approximation) and the 14:18:21 chord (a chord with a subminor fifth and a subminor third above it). There’s also a neutral chord that sits in between. These are genuinely usable as consonances — not dissonant crunches — once your ear adjusts.

For composers and improvisers, this is the most approachable place to start with 14edo: treat it as a scale with a different palette of thirds and see what chord progressions emerge. The logic is unfamiliar, but the idea of “here’s a scale, here are its chords, here’s how they move” is exactly the same as learning a new mode in 12edo.

The Beep[9] Scale: 14edo’s Most Characteristic Sound

If the omnidiatonic scale is the gentle entry point, the Beep[9] scale is where 14edo gets truly alien — and truly interesting.

“Beep” is a regular temperament (a way of systematically mapping just intonation intervals onto a scale), and 14edo is actually the largest EDO that naturally supports it. Beep[9] gives you a 9-note scale within 14edo — an “enneatonic” scale — that has some remarkable properties.

In this framework, the generator (the interval you stack to build the scale) is 3 steps of 14edo, or about 257 cents. Think of it like a third-based spiral rather than a fifth-based one. The result is a scale where there are six consonant interval classes rather than the usual two “perfect” consonances (4th and 5th) you know from diatonic music. In Beep[9]:

The Perfect 3rd⁹ (3 steps, ~257¢) stands in for the role of the perfect fourth — it’s the stable anchor interval
The Perfect 4th⁹ (5 steps, ~429¢) approximates a major third, but functions as a stable perfect interval
The Perfect 5th⁹ (6 steps, ~514¢) approximates a perfect fourth — recognizable as “open”
The Perfect 6th⁹ (8 steps, ~686¢) approximates a fifth
The Perfect 7th⁹ (9 steps, ~771¢) takes the role of a subminor sixth
The Perfect 8th⁹ (11 steps, ~943¢) is the highest consonance

The dissonances are the steps in between, and — just like the tritone in diatonic music — there are three of them (at 4, 7, and 10 steps), each creating tension that resolves to an adjacent consonance.

Melodically, Beep[9] modes are described as very similar to diatonic modes — just with more notes and two “mediants” (middle-degree notes between the tonic and dominant) instead of one. If you know how dorian or mixolydian feel, the Beep[9] modes will give you an analogous experience in a completely foreign harmonic world.

For best results with these tetrads, bell-like or organ-style timbres work better than heavily distorted guitar — the timbres of an instrument influence how its harmonics interact with the tuning system, and 14edo’s intervals are most consonant with inharmonic or mellow tones.

Notation: How Do You Write This Down?

This is a practical concern if you want to work with 14edo more seriously. There are a few approaches:

Ups and Downs Notation is probably the most widely used system for EDOs like 14. It extends standard notation by adding arrows (^ for “up one step,” v for “down one step”) to existing note names. Because 7edo is embedded in 14edo, the seven natural note names (C, D, E, F, G, A, B) map onto every other step of 14edo. The in-between notes get an up or down arrow:

C = 0 steps
^C / vD = 1 step (up-C or down-D)
D = 2 steps
^D / vE = 3 steps
E = 4 steps
and so on…

For chords, the ups and downs system also dispenses with the words “major” and “minor” entirely — since every interval is “perfect” (there’s only one size of each), you just describe alterations in terms of ups and downs. For example, C–E–G is just “C” (a perfect triad), while C–vE–G is “C down” (a triad with a lowered — subminor — third).

Ivor Darreg’s notation, described in the attached wiki source, takes a different approach: since 14edo contains two interlocking sets of 7 notes that never share a fifth relationship with each other, he proposed naming the second set with asterisks: F*, C*, G*, D*, A*, E*, B*. This makes the structure of the system more visually explicit.

Who’s Actually Making Music in 14edo?

You might wonder: is this just theory, or are people actually composing and performing in 14edo? Quite a lot of people, as it turns out.

Some highlights from the Music in 14edo page:

Sevish — one of the best-known xenharmonic composers, has released 14edo works including “Detached and Distant” (2012) and “Sleep Deprived Cooked Alive” (2015). His music bridges electronic beats and careful microtonal harmony in an accessible way.
Xotla — released several 14edo tracks on Bandcamp, including “Orbital Motive” and “Chiral”, with a lush, organic electronic sound.
NullPointerException Music — a prolific xenharmonic composer with multiple 14edo albums.
Francium — made a modern rendering of an actual 1926 jazz piano piece (“Bluin’ The Black Keys” by Arthur Schutt) in 14edo, demonstrating that some familiar jazz vocabulary can be recast in the tuning.
Budjarn Lambeth — composed Fennec Temple in 14edo, a piece for synthesized woodwinds.
Cryptic Ruse — an experimental rock/metal band that has used 14edo alongside other microtonal systems.

The variety here is striking: jazz reimaginings, ambient electronic music, metal, classical structures. 14edo is weird enough to be clearly xenharmonic, but accessible enough that its harmonic logic doesn’t require you to abandon everything you know about music.

Practical Tips If You Want to Try 14edo

In a DAW: Software like Bitwig Studio has built-in microtuning support. Surge XT (free) and many other synths accept Scala tuning files or MTS-ESP (MIDI Tuning Standard). You can find 14edo Scala files or generate them with Scale Workshop, a free browser-based tool.

On guitar: Refrettable guitars or fanned-fret microtonal guitars can be set up for 14edo. A book specifically dedicated to this is Tetradecaphonic Scales for Guitar by Ron Sword (2009), which covers scales, chord-scales, notation, and theory for 14edo on guitar.

On keyboard: Lumatone mappings for 14edo are available — the Lumatone is an isomorphic keyboard designed for alternative tunings.

Starting point: The easiest musical entry point is probably the omnidiatonic scale. Pick any 7 consecutive steps from the table above that spell out the omnidiatonic pattern, treat it like a major scale, and experiment with the three types of thirds as chord tones. Your ears will adapt faster than you expect.

Why Bother?

Fair question. The honest answer is: because it sounds unlike anything you’ve heard before, and because the constraints of a new tuning system force you to think about harmony and melody in fresh ways.

In 12edo, you’ve absorbed thousands of hours of music that’s conditioned your expectations — what resolves, what tensions, what feels like “home.” In 14edo, those expectations don’t apply in the same way. The narrow fifth doesn’t pull toward resolution the way a 12edo fifth does. The three types of thirds offer shades of colour that 12edo can only approximate with bends and blue notes. The tritone — at exactly 600 cents — is the same as in 12edo, which creates an interesting anchor point.

Musicians who work with 14edo often describe it as expanding their harmonic vocabulary rather than replacing it. You’re not abandoning what you know; you’re discovering that the map of musical possibility is much larger than the one most of us were handed.

The Microtone Fox

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