One of the most rewarding entry points into microtonal music for musicians
This article assumes you understand chords, scales, intervals, and basic functional harmony. What it won’t assume is that you know anything about microtonality. Let’s start from scratch.
What is 15edo?
15 equal divisions of the octave means exactly what it sounds like: the octave is cut into 15 perfectly equal steps, instead of the usual 12. Each step is 80 cents — compared to the 100-cent semitones we’re used to. That’s a noticeably smaller step, and it means you have 3 extra notes per octave to work with compared to 12-TET.
One handy way to think about 15edo is as three interleaved copies of 5-tone equal temperament (5edo), a pentatonic tuning you can think of as similar to the black keys on a piano. Those three copies sit side by side but don’t connect to each other through perfect fifths — which has some interesting consequences we’ll get to shortly.
Why Would Anyone Use This?
Fair question. Here are the main reasons musicians are drawn to 15edo:
First, it still has recognizable major and minor triads. This might sound like a low bar, but it’s actually a big deal. Many equal temperaments near this size — 13edo, 14edo, 16edo — produce triads that are too warped to feel like “major” or “minor” in any intuitive sense. 15edo is one of the smallest tunings where those chords still feel grounded and familiar, which was noted by theorists like Ivor Darreg and Easley Blackwood Jr.
Second, it approximates some higher harmonics better than 12-TET does. Specifically, the 7th harmonic (the interval 7/4, a slightly flat minor seventh) and the 11th harmonic (a kind of “super-fourth” about a quarter-tone sharp) are both well-represented in 15edo. This means chords that use these intervals — which sound strikingly consonant once your ear adjusts — are directly available. 15edo is in fact considered the smallest tuning that makes the 11th harmonic usable while still having a workable perfect fifth.
Third, it’s weird enough to be interesting. The familiar is in there, but it’s been rearranged in ways that open up entirely new harmonic territory.
The Fifth Situation
Here’s where things get a little different from what you’re used to. In 12-TET, the circle of fifths passes through all 12 notes before looping back. In 15edo, the perfect fifth (720 cents, noticeably wider than the 702-cent just fifth we’re accustomed to) only cycles through 5 notes before it closes. That means you get three separate, disconnected circles of fifths — each containing only 5 notes.
The practical consequence: there is no conventional diatonic scale in 15edo. The familiar 7-note do-re-mi-fa-sol-la-ti arrangement, built by stacking fifths, simply doesn’t exist here in its usual form. E and F collapse to the same pitch. B and C do too. That 12-TET staple, the half-step voice leading that drives so much tonal music, is gone.
This sounds alarming if you’re used to traditional harmony, but it’s actually an invitation to explore different organizing principles. Think of it less as “broken 12-TET” and more as a completely different tonal universe with its own internal logic.
The Scales Worth Knowing
Since the diatonic scale doesn’t work the same way, 15edo has its own preferred scales. Two are especially important:
The Blackwood Decatonic Scale
Named after Easley Blackwood Jr., the blackwood temperament gives 15edo its most famous scale: a 10-note scale (5 large steps + 5 small steps, alternating, written as 2 1 2 1 2 1 2 1 2 1 in 15edo steps). Because 15 = 3 × 5, this scale neatly maps onto three interlocking pentatonic cycles, and every single note of the scale can serve as the root of a 7-limit chord — meaning you get rich, somewhat jazz-flavored harmony available from every scale degree. Blackwood explored this extensively in his 1980 Twelve Microtonal Etudes, Op. 28 and his Suite for Guitar in 15-note Equal Tuning, Op. 33, the latter performed on a specially fretted acoustic guitar.
The Porcupine Scale
Porcupine temperament is generated not by the fifth but by a small step of about 160 cents (2 steps of 15edo). Stack six of those generators and you get a 7-note scale: 3 2 2 2 2 2 2 in 15edo steps. This scale has a flowing, slightly exotic character and contains both major and minor triads. It’s been called the “natural” diatonic of 15edo by many composers who work in this system. Herman Miller’s Mizarian Porcupine Overture (1999) is so associated with this scale that the temperament was named after the piece.
The Zarlino Scale
The Zarlino diatonic (3 2 1 3 2 3 1 in steps) is 15edo’s closest approximation to a traditional just major scale. It sounds familiar but with a distinctive quality — slightly warmer in some places, slightly strange in others. It’s a useful bridge for musicians coming from a classical background.
How Chords Work
Major and minor triads exist in 15edo, but they’re slightly different from what you know. The major third is the same size as in 12-TET (400 cents, 5 steps), but the fifth is wider (720 cents, 9 steps). Some composers describe the result as “shimmery” or “pungent” — the wide fifth gives triads a bright, slightly tense quality even when fully resolved.
Where 15edo really opens up is in its 7-limit chords. The interval 7/4 (about 969 cents, or 12 steps) is well approximated, meaning you can build chords that include this “subminor seventh” — an interval that sits between a minor seventh and a major sixth, and which has an unusually consonant, locked-in quality once you’re used to it. Chords like 4:5:6:7 (a major triad with an added 7th harmonic on top) sound remarkably stable and resolved in 15edo in a way they simply don’t in 12-TET.
There’s also the concept of metallic harmony — a harmonic approach that treats 7/4 as its primary consonance (rather than the major third), building triads out of sevenths instead of thirds. 15edo is one of the recommended tunings for this approach, which produces chords with a characteristic cool, metallic quality.
Chord Naming: A Brief Note
Because the standard sharp/flat system was designed around the circle of fifths, and 15edo’s fifths only cycle through 5 notes, you need different notation tools. The community has developed ups and downs notation, which uses carets (^) and v-shapes to indicate raising or lowering by one step. In this system, a familiar-sounding minor chord becomes C–^E♭–G (a “C upminor” chord, written C^m), because the regular C–E♭–G is actually closer to a sus2. The “real” major chord with a 5/4 major third is C–vE–G, called “C down” or Cv.
This notation takes some getting used to, but it’s logical once you internalize it, and it means every 15edo chord can be described unambiguously.
15edo on Guitar
One reason 15edo is particularly popular among adventurous guitarists is that the instrument actually becomes more symmetrical in this tuning. On a standard 12-TET guitar, strings are tuned in fourths except for the B string, which breaks the pattern. In 15edo, you can tune all six strings a perfect fourth apart and span exactly two octaves from the lowest to highest string — because the perfect fourth in 15edo comes from 5edo, and five of them close perfectly. That means all chord shapes look the same anywhere on the neck, and minor arpeggios are vertically stacked in a particularly convenient way. Ron Sword’s Pentadecaphonic Scales for Guitar is the definitive reference for this approach, cataloguing over 300 scale and temperament examples with chord-scale progressions.
Composers and Music to Listen To
Easley Blackwood’s Suite for Guitar in 15-note Equal Tuning, Op. 33 is the canonical starting point — it sounds strange but coherent, like tonal music from a parallel universe. Blackwood himself believed 15edo “is likely to bring about a considerable enrichment of both classical and popular repertoire in a variety of styles.”
For something more contemporary, Sevish’s track “Fifteen” from his album Golden Hour (2010) is an accessible pop/electronic piece that shows off how musical 15edo can sound without being overwhelming. His later “Moonopolis” and “So Thankful” (the latter in the Blackwood[10] scale) are also excellent.
Herman Miller’s Mizarian Porcupine Overture (1999) is the piece that defined porcupine temperament as a compositional language. Cryptic Ruse’s A Year Without Breath (2022) is a full 11-piece album in 15edo worth exploring if you want a deeper dive.
Claudi Meneghin has composed extensively in 15edo including canons, fugues, chaconnes, and organ works — a uniquely baroque approach to a very xenharmonic tuning.
Is 15edo Right for You?
If you’re looking for a microtonal system that’s genuinely foreign to 12-TET without being completely unnavigable, 15edo is an excellent choice. It’s small enough to feel manageable (only 3 more notes than you’re used to per octave), it has recognizable triads as anchor points, and it opens up harmonic territory — particularly around the 7th and 11th harmonics — that simply doesn’t exist in conventional tuning.
The catch is that you need to let go of the diatonic scale as your organizing principle. The “scales you already know” don’t transfer cleanly. But if you’re willing to learn the Porcupine or Blackwood scales on their own terms, you’ll find a fully coherent harmonic world waiting on the other side.
The Xenharmonic Wiki’s 15edo page is the most comprehensive reference available for going deeper, covering intervals, temperaments, notation systems, instrument layouts, and a large catalog of composed music. The 15edo/Music page lists dozens of recordings across styles. And for the theoretical underpinning of why some of these chords feel so resolved, the porcupine temperament and blackwood temperament articles are worth reading once you’ve had a chance to listen first.
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