How does additive synthesis create complex musical tones from sine waves?

Additive synthesis creates complex musical tones by combining multiple individual sine waves, which are pure tones lacking overtones. This process is grounded in the Fourier theorem, which states that any steady-state complex wave can be constructed from a series of sinusoidal components—specifically, a fundamental frequency and its associated harmonics.12

In an additive synthesizer, each sine wave component is assigned a specific frequency, amplitude, and phase. By precisely controlling the relative intensities and harmonic relationships of these individual signals, the instrument can build rich, complex timbres. This approach offers significant control over the resulting sound, allowing for the creation of tones that imitate traditional instruments or entirely new, synthetic sound colors. While other methods like subtractive synthesis start with a complex signal and remove components, additive synthesis builds the final sound from the ground up using these fundamental building blocks.231