During sound generation harmonics of a base frequency might be desired in order to add brightness to the sound. By simple step wise multiplication of the wave value with itself, harmonics can be achieved easily. Each multiplication generates a wave which is shifted up by one octave.

18 Bit precise Multiplication in a DSP: There is only a loss of 2 digits in maximum per step because of the reduction of dynamics by ratio 2 and some offset correction.

Sound Exciting by adding Harmonics

16 harmonics or more can be used to create an exciter:

Exciter with even (red) and odd (blue) harmonics often named as warm and cold frequencies.