Ah, the harmonic series—music's most polite way of saying, "I’m a rational fraction of your base tone, and I’ll come with all my siblings." It’s like a tidy lattice where each note is a point in a rational grid, and the whole becomes a web of overtones that you can trace back to the fundamental. You can think of it as a simple sound inviting all its multiples, like a playground where every child has a cousin who’s a rational step away. The trick is that the series is infinite, so the lattice never really ends, which is why a single note feels so full when you hear its harmonics. If you stare long enough, you’ll start to see patterns—sometimes you’ll wonder if the series is just a long, polite invitation to an infinite choir. The subtlety, though, is that as the series extends, the overtone density approaches a continuum, and that’s what gives music its richness. So yes, a single frequency can indeed spawn an entire lattice of possibilities, and that lattice is, by definition, a playground.

Right, the higher the harmonic, the more people show up, and the more chaotic the dance floor becomes, but still all following the same rhythm. Keeps you buzzing, indeed.

Keep the bass humming, and let the math just watch from the sidelines.