If you want to try Fourier Synthesis for yourself, check out this website.
It has a java applet that allows you to set the first 14 harmonics, both as
sines and cosines, then listen to the result over your speakers. You can
also start with standard forms like sawtooth or square and adjust from
there. I personally couldn't hear much difference when I removed one of
the harmonics as a sine and replaced it by an equal harmonic as a cosine.