[puffpastry]

You're talking about pre-emphasis and de-emphasis stages. Those are there for much of the same reason that you need an RIAA EQ for a turntable. It's a mechanical device, so the frequencies that the mechanical noise occurs in are removed by EQ. During playback, we have to EQ those frequencies back in.

Companding is a necessary evil whose need arrives from the noise involved with inductors, i.e. a tape head in this case.

As for the "tape" sound, there are a number of factors that come into play--one thing you're hearing is a very low-volume 3rd harmonic distortion that comes from the tape head itself. It's an inevitable artifact caused by the material that the head is constructed of. Add to that the distortions that are bound to arise from the tape material itself, and there you have it. A basic synopsis of "tape sound." I would say it's both medium AND machine.