In the early part of the 19th century, the French mathematician Francois
Marie Charles Fourier proposed that any **complex**
vibration can be analyzed as the sum of simple vibrations (sine waves)
of particular frequencies, amplitudes, and phase relationships. This
idea has come to be known as FOURIER'S THEOREM, and an analysis of
a sound based upon this idea is called FOURIER ANALYSIS.

Fourier's theorem can also be applied in reverse: sine waves of
particular frequencies and amplitudes can be combined to form complex
sounds. This technique is called FOURIER SYNTHESIS, or ADDITIVE SYNTHESIS,
and is very important to designers and programmers of electronic musical
instruments.

See **Fourier
Synthesis** in Barry Truax's Handbook for Acoustic Ecology.

Check out this great site which has a REAL-TIME Fourier Synthesis
engine:

Real-time
Fourier Synthesis

See Fourier Synthesis.