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.