Many wave - beat frequencies.

I'm modelling a system that (at the most simple level) is a sum of superimposed waves with different amplitudes.

I'll spare all the details but I'd like a nice "rule of thumb" for a beat pattern of multiple waves.

The 2-wave beat pattern is obviously nice and easy, but when I was trying to expand for N waves it went a bit complex.

I don't need exact, just something to quickly tell if my results are making sense - a small calculation for the order of the beat pattern would be fine (though obviously exact would be better).

My frequencies span a range of about 2pi (in units of 1/(units I'm plotting time in)) with a quite even spread so I can't rely on small angle formulae.

The number of frequencies changes from a minimum of 5 to about 360 so far (and will probably increase as I progress) so a number independent rule would be nice.

Thanks for any replies

Happle