An audio signal that cannot be analyzed as a sum of sinusoids can, alternatively, be characterized as noise.  (These two possibilities, sums of sinusoids and noise, aren’t exhaustive but are rather two extremes with many other intermediate possibilities.)  Measuring a noisy signal’s short-time power spectrum will give a random result whose average is the power spectrum of the noise.  If this is a constant independent of frequency, the noise is characterized as white, in analogy with the visible spectrum.

White noise can be synthesized as a sequence of independent random amplitudes (samples).  Noise that is not white can be derived from white noise by filtering.  Noise generators and oscillators make up the traditional palette of synthesis options in electronic music.