Gargoyle: There are SOME musical applications. My program HARMONY generates random tunes in the style of jigs and reels, complete with chords.

But here, we are almost all talking about Pseudo-Random numbers, the series of which is totally predictable if you know the seed and the algorithm (and the arithmetic precision used). It takes the white-noise generator approach to get close to real Random numbers. The UK Premium Bonds draw from the 1950's used "ERNIE", which stood (Still does?) for Electronic Random Number Indicator, working on that principle.

HARMONY uses the built-in random number generator in Visual Basic, seeded from the system clock. I have no idea how random these numbers are, but I have never seen the same tune generated twice!