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.
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overtones & timbre
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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.
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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The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.
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.
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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.