How I Would Explain Recursion To A Musician

After nearly a decade of building software systems for startups and contributing to projects used by enterprise companies, I’ve learned that the best explanations don’t come from textbooks. They come from connecting what someone already knows to what they need to learn.

Recently, I revisited a conversation I had with a talented musician who was diving into programming. When we reached the topic of recursion, I watched his eyes glaze over at the typical "a function that calls itself" explanation. That's when I realised: musicians already understand recursion. They just call it something else.

The Musical Foundation

Every musician knows the power of repetition with variation. Think about Pachelbel's Canon, where the same harmonic progression repeats endlessly, each time with new melodic layers. Or consider how a jazz musician takes a theme, plays it, then plays variations that reference the original theme, building complexity through controlled repetition.

Johann Pachelbel, Canon in D (score image from PianoTV.net, Canon in D Piano Tutorial). Accessed June 27, 2025.

This is recursion in its purest form: a pattern that references itself while moving toward a resolution.

The Conductor's Recursion

Imagine you're performing a piece where the composer has written: "Repeat this passage, but each time, play it softer than before. Stop when you can barely hear the notes."

Here's what's happening:

• The recursive call: The instruction to repeat the passage

• The changing state: Each repetition is softer than the last

• The base case: Stop when the volume reaches near silence

• The resolution: The music naturally fades to its conclusion

This is exactly how recursion works in code. Let me show you with a simple example:

function playPassage(volume) {
    if (volume <= 0) {
        // Base case: too quiet to continue
        return "Silence"
    }

    // Play the current passage
    performMusic(volume)

    // Recursive call: play again, but softer
    return playPassage(volume - 10)
}

The Fractal Nature of Musical Structure

Here's where it gets beautiful. Music itself is recursive at multiple levels. A symphony has movements, movements have sections, sections have phrases, phrases have motifs. Each level contains and references the patterns of the levels around it.

"Classical Forms" Tina Christie Flute, Tina Christie, https://tinachristieflute.com. Accessed 27 June, 2025.

Consider how a fugue works. Bach takes a simple subject (theme) and weaves it through different voices, each entry calling back to the original while creating something entirely new. The subject appears, then appears again in a different voice, then again transformed, until the entire piece resolves.

This is recursive thinking: solving a complex musical problem by breaking it into smaller, similar problems.

The Stack Overflow of Music

Every musician has experienced the musical equivalent of a stack overflow error. It happens when you get caught in a practice loop, playing the same difficult passage over and over without progress, until your muscle memory breaks down and you can't play anything correctly.

In programming, this happens when we forget the base case. The function keeps calling itself forever until the system runs out of memory. In music, it happens when we practice without intention, repeating without moving toward resolution.

The solution in both cases is the same: define clear stopping conditions and ensure each iteration moves us closer to our goal.

Practical Recursion: The Musical Tree

Think about how a melody develops. A composer starts with a simple phrase, then creates variations: inversions, augmentations, diminutions. Each variation references the original but adds something new.

This is exactly how recursive algorithms work with data structures like trees. Each node contains data and references to smaller versions of the same structure. When we traverse a musical tree of variations, we're using recursive thinking: "Process this variation, then process all its sub-variations the same way."

Why This Matters Beyond Code

Understanding recursion through music isn't just about making programming concepts accessible. It's about recognising that the patterns we use to create software mirror the patterns humans have used to create art for centuries.

When I'm architecting systems for large enterprises, I often think like a composer. How can I break this complex problem into smaller, self-similar pieces? How can I create patterns that reference themselves while building toward a resolution? How can I ensure my "performance" doesn't get stuck in an infinite loop?

The Resolution

Recursion isn't just a programming technique. It's a way of thinking about problems that musicians, artists, and creators have used intuitively for generations. By connecting it to musical concepts, we're not simplifying recursion; we're revealing its deeper elegance.

The next time you encounter a recursive problem, think like a musician. What's your theme? How will it develop? Where will it resolve? And most importantly, how will you know when to stop?

Because in both music and code, the most beautiful solutions are often the ones that know exactly when to end.