Stack enough sine waves and you can build any tone. Additive synthesis assembles rich waveforms one harmonic at a time — the sound design behind classic synths.
Additive SynthesisLive
building tone from sine waves
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Any periodic waveform is a sum of sine harmonics — the basis of additive synthesis. A sawtooth needs every harmonic falling as 1/k; a square only odd harmonics; a triangle odd harmonics falling as 1/k². Add more harmonics to sharpen the shape, and watch the Gibbs overshoot ripple at the edges.
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How it works
Every periodic waveform is a sum of sine harmonics with specific amplitudes. A sawtooth uses all harmonics falling as 1/k, a square only odd harmonics, and a triangle odd harmonics falling as 1/k². Adding more harmonics sharpens the shape but produces the Gibbs overshoot — the little ripple that never quite goes away at sharp edges.
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The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.
Yes. Additive Synthesis 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.
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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.