Distinguished SOTW Member
There are a few different ways to do that digitally, and it's fun to experiment with. Several of these BR plugs can contribute to that effect, for an example of one such possible chain.......I'm constantly on the search for one specific type of plugin, one that can achieve the sort of grainy, old school audio style recordings of the 1920s/30s. I've always wanted to be able to recreate that sound .
VPRE73 (preamp) first, input cranked a bit, output attenuated a bit, for some gentle saturation (distortion)...
VLA2A (compressor) next, mostly for color, not necessarily for dynamic control...
VEQ5 (eq) after that, tweak to your liking...
Magnetite (tape) at the end, recording level boosted and playback level attenuated (for more saturation), crank hysteresis for high-end rolloff.
You'll get a pretty grainy, old-school sound from that, after you spend some time tweaking. Ironically, on the recordings you'd be emulating, the engineers were generally going for the "cleanest" sound possible, and would probably be mortified that we'd intentionally dial in the saturation and frequency filtering they fought so hard to prevent!