Joseph Fourier proved any periodic waveform decomposes into sine waves. Add harmonics one by one and watch a scope trace morph into a sawtooth in real time.
In the world
Your cochlea performs a continuous Fourier analysis: thousands of hair cells each tuned to a narrow frequency band, reporting the strength of every partial to your brain in real time.
In 1822 Joseph Fourier proved that any periodic waveform, no matter how jagged, can be decomposed into a sum of sines at integer-multiple frequencies. The recipe is unique: exactly one set of amplitudes and phases per waveform.
This is not a metaphor. It is mathematically exact. Additive synthesis is Fourier's theorem running in reverse: instead of analysing a sound, you specify the recipe and the rack prints the sound.
Did you know?
Fourier originally developed his theorem to study heat conduction, not sound. He presented it to the French Academy in 1807, and the reviewers - including Lagrange - refused to believe any waveform could be built from sines. It took 15 years before the proof was published.
Explore
Thousands of rainbow particles flow through the scene in sine-wave streams - one river per harmonic. Click the indicator spheres on the right to toggle each harmonic on or off. Watch how individual sine streams combine into the complex waveform Fourier described. Unmute to hear each partial join the mix.