O. Complex

The idea that overtones are pure sine waves is very idealistic. Many natural sounds have overtones, which are complex mixtures of several vibrations of similar frequencies. They overlap and form a wave of constantly changing phase and amplitude through interference. Their complex structure is best recognized in their Fourier transform spectrum (see pictures). Especially dirty (but lively) sounds (flute, violin, ensembles) show such complex overtone structures.

The inverse Fourier transformation can be used to produce such "dirty" (but interesting) sounds. To do this, replace pure (clean) frequency peaks in the overtone spectrum with complex peak structures (eg, of a flute or a string orchestra) and transform this new overtone spectrum back into a sound wave. The results are very interesting, complex sound sequences.