The Four Classic Waveforms
Every synthesizer starts with the same four basic waveforms: sine, square, sawtooth, and triangle. These shapes are not arbitrary — each represents a specific harmonic recipe. The sine wave is the purest possible sound: a single frequency with no overtones. Add odd harmonics at 1/n amplitudes and you get a square wave. Add all harmonics at 1/n and you get a sawtooth. Add only odd harmonics at 1/n² and you get a triangle wave. From these building blocks, subtractive synthesis creates any sound imaginable.
Fourier Analysis in Action
Joseph Fourier proved in 1807 that any periodic waveform can be decomposed into a sum of sine waves. This simulation makes this abstract theorem visual: watch how the composite waveform changes shape as you switch between wave types, each with its characteristic harmonic spectrum displayed below. The frequency spectrum (bar chart) shows exactly which harmonics are present and at what amplitude.
Amplitude Modulation
When the modulation depth is increased, the carrier wave's amplitude varies periodically, creating tremolo at low modulation rates. At higher modulation frequencies, amplitude modulation generates sideband frequencies at f +/- f_mod, enriching the spectrum. This AM synthesis technique was the basis of the famous Yamaha DX7 synthesizer and remains fundamental to sound design. Watch the spectrum display to see sidebands appear as you increase modulation depth.
From Waveforms to Music
These simple waveforms are the starting point for all electronic music synthesis. Subtractive synthesis begins with harmonically rich waveforms (sawtooth, square) and removes harmonics with filters to shape timbre. Additive synthesis builds complex sounds by combining many sine waves. FM synthesis creates rich spectra by modulating one wave's frequency with another. Understanding these basic waveforms is the foundation for all sound design and electronic music production.