The Swing Generator

NOV 01, 2025

But what is swing? I’m not talking about the jazz style — not big-band swing or shuffle feel — but the underlying motion that makes any rhythm feel alive. Every answer I’ve ever heard to that question is either too vague (“you just feel it”) or just plain wrong (“it’s triplets”). I’ve been chasing that question for years, and I finally found an incredibly powerful formula. It’s simple, repeatable, and correlates perfectly to my sense of which rhythms are alive and which are dead.

I started my search by studying rhythms that are known for their swing — polyrhythms. I began with the simplest one: three beats against two. I played a continuous loop, tapping three times with my right hand for every two times with my left.

How did I do it? I imagined a loop of six pulses. One hand taps every other pulse (three hits per loop), the other taps every third pulse (two hits per loop). Because both start together on the first pulse, the whole thing lines up perfectly. Six was the smallest number divisible by both two and three.

Then I listened. Both hands tapping, perfectly even, perfectly aligned mathematically. Did it swing? Surprisingly, no. I thought this was supposed to be the gold standard of groove — and it sounded mechanical. Like two metronomes ticking away, which is exactly what it was.

Then I did something magical. I combined the hits of both hands into a single rhythm and played that new pattern with just my right hand:

R – R R R –

Then, with my left hand, I played the silences:

R L R R R L

Suddenly, it swung.

That’s when I stumbled onto something powerful. When I treated the silent beats as active parts of the rhythm — not gaps, but voices of their own — the groove came alive. The moment each side stopped being predictable, the rhythm started to swing.

The same thing happened with the next polyrhythms in line — 4:3, 5:2, 5:3, 5:4. Dead when played on one hand, alive and dancing when the other hand filled in the spaces. Each time, the moment I gave the silence its own shape, the groove came to life.

By the time I reached 5:4, I realized it required twenty sub-pulses to complete a single cycle. That’s a lot to keep track of, and the loop starts feeling more like math than music. Anything beyond that only gets longer and less practical. Was that it? Five or six possible swinging rhythms in the world? It didn’t seem right. There had to be more — and there are. Lots more.

To find out what really made a rhythm swing, I decided to start from the ground up. I built every possible rhythm, one pulse at a time. Two-pulse loops, three-pulse loops, four, five, six — testing them all systematically. I wrote them out as simple right- and left-hand taps, making sure every pulse was covered by one hand or the other, but never both.

Then I listened. The short loops — two, three, even five pulses — sounded flat, like machines. But at six pulses something new appeared. R L L R R L. It swung. That was the first time the groove truly came alive.

From that point on I could see a pattern forming — there seemed to be a hidden rule underneath it all, an algorithm that could tell me, before even playing, whether a rhythm would swing.

The rule turned out to be simple: no hand can be steady. If either hand plays a repeating sequence, the groove collapses. Swing only appears when both hands stay in motion, constantly shifting their relationships. When each hand keeps breaking its own habits, the music breathes. The groove becomes a living system where neither side ever settles, yet the overall pulse stays rock solid.

The Cluster Rule

Swing collapses when one hand moves in big, predictable blocks or gaps. A cluster is any uninterrupted sequence of two or more hits by the same hand. If a hand repeats the same-sized cluster or the same-sized gap at regular points in the loop, that hand has become steady, and the rhythm fails the test.

For example: R R R L L R might look asymmetric, but it fails because the left hand’s hits are perfectly nested inside the right hand’s repeating pattern of hits and rests. It sounds like two blocks simply handing control back and forth. Using the cluster rule, the formula matches what I hear and correctly classifies it as not swinging.

When I listed out every possible combination of right- and left-hand hits in a six-pulse loop, something fascinating happened. The classic 3:2 polyrhythm appeared automatically — it was simply one of the options. And sure enough, it passed the no-steady-hand test perfectly. Each hand stayed unstable, and the groove swung hard. But it wasn’t alone. Other patterns showed up that felt just as alive, like L R R L L R. These weren’t recognized polyrhythms at all — just asymmetric loops that happened to satisfy the same rule. That’s when I realized polyrhythms were only a tiny subset of all possible swinging rhythms. The real secret wasn’t ratio — it was the balance of instability itself.

Instead of using the standard polyrhythm formula, which only produces a handful of usable swing patterns, I now had a method that uncovered an enormous range of unique and practical grooves. Once I started applying the rule to longer loops, the possibilities exploded.

I don’t present this as a universal law of rhythm — just a generator. A systematic approach to uncover a great number of grooves that feel alive and swing. Using the system, one can discover all the standard polyrhythms and so much more. The math behind it is simple, and the results speak for themselves.

The Numbers Behind the Discovery

To see how far the rule really reaches, I mapped out every possible 6-pulse loop where each pulse belongs to either the right or left hand, but never both. Then I applied the no-steady-hand rule and the cluster rule mechanically. The result is a clean yes-or-no outcome for every pattern.

All 6-Pulse Rhythms

24 Swing, 40 Don’t Swing

R R R R R R → NO R R R R R L → NO R R R R L R → NO R R R R L L → NO R R R L R R → NO R R R L R L → YES R R R L L R → NO R R R L L L → NO R R L R R R → NO R R L R R L → NO R R L R L R → YES R R L R L L → YES R R L L R R → NO R R L L R L → YES R R L L L R → NO R R L L L L → NO R L R R R R → NO R L R R R L → YES R L R R L R → NO R L R R L L → YES R L R L R R → YES R L R L R L → NO R L R L L R → YES R L R L L L → YES R L L R R R → NO R L L R R L → YES R L L R L R → YES R L L R L L → NO R L L L R R → NO R L L L R L → YES R L L L L R → NO R L L L L L → NO L R R R R R → NO L R R R R L → NO L R R R L R → YES L R R R L L → NO L R R L R R → NO L R R L R L → YES L R R L L R → YES L R R L L L → NO L R L R R R → YES L R L R R L → YES L R L R L R → NO L R L R L L → YES L R L L R R → YES L R L L R L → NO L R L L L R → YES L R L L L L → NO L L R R R R → NO L L R R R L → NO L L R R L R → YES L L R R L L → NO L L R L R R → YES L L R L R L → YES L L R L L R → NO L L R L L L → NO L L L R R R → NO L L L R R L → NO L L L R L R → YES L L L R L L → NO L L L L R R → NO L L L L R L → NO L L L L L R → NO L L L L L L → NO Sanity Checks

The fill-the-silences 3:2 feel: R L R R R L → YES (#18) The block pattern: R R R R L L → NO (#4 – fails the cluster rule: one long R block followed by an L block, no interaction) The perfectly alternating machine: R L R L R L → NO (#22 – both hands perfectly predictable) “Some say swing comes from micro-timings or human deviation — the subtle delays, accents, and orchestrations that make real music feel human. I agree those details matter, but they’re icing on the cake. What I’m describing is the core skeleton — the bare topology of hits and rests that determines whether a rhythm even can swing.”

Micro-timing can deepen a living groove, but it can’t resurrect a dead one. All the nuance in the world won’t make R L R L swing.

Swing is the sound of two living forces sharing one pulse. When neither side is steady, the rhythm breathes — and that breath is the groove.