A mixture of pure tones: a base frequency f and harmonics at 2f, 3f, 4f, … . Fourier analysis says the recipe — how loud each harmonic is — determines the shape of the wave and the timbre (color) of the sound. Drag the bars below to change the recipe, and listen.
Drag a bar up or down, or use the sliders below, to set how loud each harmonic is. Set it to zero to remove it.
Two periods of the summed wave. Hover a bar above to see that single harmonic drawn on top.
The sound updates live while you drag the bars. Same recipe + different f = same timbre, different pitch.
Square-wave approximation uses only odd harmonics (1, 3, 5, …) with amplitudes 1, 1/3, 1/5, … and sounds hollow, like a clarinet. Notice the ripples near the jumps of the target square wave. As more harmonics are added, the overshoot becomes narrower but does not disappear: this is the Gibbs phenomenon. Sawtooth approximation uses every harmonic with amplitudes 1, 1/2, 1/3, … and sounds bright and brassy. Soft makes the amplitudes decrease rapidly (like 1/n²), reducing high-frequency content and making this finite sum look gentler. For infinite Fourier series, faster decay of the high-frequency coefficients is closely connected with greater smoothness of the waveform. That link between a wave and its harmonic recipe is exactly what Fourier analysis studies.
Press and glide on the pad: left–right changes the base frequency continuously, up–down changes the volume. Release to stop. The tone uses whatever harmonic recipe you set in section 1.
The pitch axis is logarithmic: each octave (a doubling of frequency) has the same width. Turn on White-noise beat to add a simple repeating pulse. The beat frequency is the number of pulses per second.
Audio uses the Web Audio API — works in any modern browser. No data leaves your device.