The sound may not be one article, but it is commonly associated with
vintage
equipment, and has been sought after in guitar amps, Ampex recording
electronics, "tube" mics, etc.

There's a reason all those "vintage" recordings used tube microphones;
transistors hadn't been invented yet. The engineers didn't sit around &
say "You know, we've got Charlie Parker coming in tomorrow. Wanna use
the tube stuff on him?" They used what was available, & that happened
to be tube gear. It also happened to be top drawer pro recording gear
because there wasn't any semi-pro stuff, there were no home studios
using mediocre equipment made in China, & the rooms tended to be large
spaces built by record labels with a lot of financial backing. Yeah, a
lot of older recordings sounded really good.

Scott Fraser