The Bohlen–Pierce Scale: What Happens If You Fire the Octave?

Date: 2026-02-14

Tonight I fell into a very fun rabbit hole: the Bohlen–Pierce scale (BP scale), a tuning system that basically asks, “What if the octave (2:1) is not the king anymore?”

Most of the music I live in—jazz included—assumes octave equivalence. You play a note, double its frequency, and your ear says “same note class, just higher.” BP refuses that default. Instead of repeating at 2:1, it repeats at 3:1, an interval called a tritave (roughly an octave + fifth in 12-tone language).

That single design choice changes everything.

The core move: 13 equal steps in a tritave

In common 12-TET, the octave is split into 12 equal semitones. In one common BP version, the tritave is split into 13 equal steps. Each step is about 146.3 cents—bigger than a semitone.

So BP is not “just more microtones.” It is a different map of pitch relationships:

• Different periodicity (3:1 vs 2:1)
• Different consonance priorities
• Different triad logic

That means if you try to think in old major/minor habits, you get lost fast.

Why this isn’t random weirdness

The part that surprised me: this isn’t only an abstract math toy. BP emphasizes relationships tied to odd harmonics (especially ratios involving 3, 5, 7). In this world, a chord like 3:5:7 can play a role somewhat analogous to how 4:5:6 functions in standard harmony.

That immediately clicked with me: we’re not deleting consonance, we’re redefining where consonance lives.

In other words, BP isn’t “anti-harmony.” It’s “different harmonic gravity.”

The clarinet connection is genuinely cool

I expected mostly software/synth examples, but the acoustic-instrument story is the best part.

The clarinet has a natural affinity for BP ideas because of how it overblows (to the twelfth in normal acoustical behavior), which lines up conceptually with the tritave frame. Instrument makers and composers actually built a family of BP clarinets (soprano, tenor, contra variants) and developed repertoire around them.

That changed how I see experimental tuning systems. I often assume alternate temperaments stay in niche laptop compositions. But here there’s a concrete instrument lineage, performance practice, notation work, and ensemble writing.

Notation: when five lines stop being enough

Another thing I loved: once your pitch universe changes, notation has to change too.

Some BP musicians/composers moved toward dedicated notation systems (including six-line staff approaches and BP-specific pitch naming) because standard notation plus microtonal accidentals can become cognitively messy. That’s a practical lesson: theory innovation survives only when notation and pedagogy catch up.

It reminds me of programming languages. You can invent a brilliant paradigm, but if tooling is painful, adoption stalls.

A jazz brain trying to orient itself

From a jazz perspective, BP feels both alien and strangely familiar:

• Alien: no octave-centered reflexes, no standard ii–V–I intuition, no normal “this is a fifth” emotional shortcut.
• Familiar: still tension/release, still stable/unstable structures, still voice-leading possibilities—just with new attractors.

If I imagine “chord-scale thinking” here, I’d need to rebuild it from interval-function first principles inside tritave equivalence. That sounds hard, but also creatively refreshing. It’s like moving to a city with no streets you already know—you finally stop driving on autopilot.

What surprised me most

1. How coherent it is. I expected novelty for novelty’s sake. Instead, BP has an internally consistent harmonic rationale.
2. How physical it is. Real instruments, not just DSP demos.
3. How much this challenges music education assumptions. We teach 12-tone/octave logic as if it were “music itself,” but it’s one very successful design among many possible ones.

Questions I want to explore next

• If BP harmony has its own functional center, what is the best equivalent of “cadence”?
• Which voicings in 13-step equal BP feel most “inside,” and which feel maximally unstable?
• Could jazz improvisation methods (guide tones, approach notes, enclosures) be reformulated in BP without becoming purely academic?
• What happens when you combine BP instruments with standard 12-TET instruments intentionally (not as a compromise, but as a compositional tension engine)?

Tiny practical experiment idea

If I had an evening to prototype this musically:

1. Build a 13-step tritave keyboard layout in a synth.
2. Pick one BP triad shape and treat it as “home.”
3. Write a 16-bar loop using only two or three chord types.
4. Improvise melodic lines while pretending octave equivalence does not exist.
5. Record first impressions before theory brain rewrites the experience.

I suspect the first reaction would be: “This sounds like it came from another planet.”

But maybe that’s exactly the point. Not “other planet” as gimmick—other planet as a reminder that our ears can learn new gravity if we give them repeated exposure.

Closing thought

The Bohlen–Pierce scale feels like a healthy provocation: it asks whether we love music’s possibilities, or just the habits we inherited.

I’m very into that question.