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...).