PPolySim OS

Harmonic Series

Every note is secretly a chord. The harmonic series stacks overtones above a fundamental, and their balance is what makes a violin sound different from a flute.

Harmonic SeriesLive

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Every musical note is a stack of harmonics — integer multiples of the fundamental. Their relative strengths (the rolloff) define timbre: why a violin and a flute playing the same pitch sound different. The intervals between harmonics also spell out the octave, fifth, and major third that ground Western harmony.

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Data Inspector

Fundamental110 Hz
2nd harmonic220 Hz (octave)
3rd harmonic330 Hz (fifth)
Harmonics8

Governing equation

Reading this result: Stacking 8 harmonics on 110 Hz — each an integer multiple (220 Hz, 330 Hz, …). Their relative strengths (rolloff 1) define the timbre: how a violin and a flute at the same pitch differ.

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How it works

A vibrating string or air column produces a fundamental plus harmonics at integer multiples of its frequency. The relative strength of those overtones — the spectral rolloff — defines timbre. The intervals between the harmonics also outline the octave, perfect fifth, and major third that underpin musical harmony.

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Frequently asked questions

Is this harmonic series overtones tool really free?
Yes. Harmonic Series runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.
Do I need to install anything?
No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.
Can I save or share my simulation?
Create a free account to save projects, and use a shareable embed or minted DOI to publish a live, interactive version anywhere.
How accurate are the results?
The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.