This is a general problem that I'm sure many people have thought about
for years.  While it seems like it should be easy, it doesn't work out
that way.  Why?  Here's a relatively easy explanation:

Suppose you are listening to two flutes.  The sound of a flute can be
represented as a sine wave.  The sound of two flutes each playing a
note at the same time is "sine A" plus "sine B".

However, back in high school, we learned (and mostly forgot) that:

    sine A + sine B = cosine of (A X B)

Great.  Since a cosine is just a sine 180 degrees out of phase, that
means that a computer doesn't "hear" the two notes A and B, it hears
the note "A times B" (whatever frequency that is).

Sigh.

Jim Cook
Bolton, MA