Fourier Wave Composer

Compose complex waveforms programmatically from sine wave harmonics. Connect continuous algebraic equations directly to sound synthesis.

Interactive Widget

Phasor Circle & Oscillation plot

Click a preset to approximate standard waveforms, or customize the amplitudes of individual harmonics. Turn on the Sound Synthesizer (Web Audio API) to hear how adding higher frequencies changes the timbre of the tone!

Synthesizer Pitch 220 Hz

Fourier Series Summation

f(t) = sin(t)

Mathematical Recipe Code

Python (NumPy)

JavaScript (Web Audio)

import numpy as np

def fourier_sum(t, amplitudes):
    y = np.zeros_like(t)
    for n, amp in enumerate(amplitudes, start=1):
        y += amp * np.sin(n * t)
    return y
                            

Square wave harmonics drop off at ratios of 1/n for odd integers (n = 1, 3, 5...).