Good one!Very little of the music content will be at 400Hz, what do you want to do with the rest of the audio spectrum ?
FWIW, tuning pitch has been all over the place thru the centuries. Wikipedia has a good overview of it if you search "Concert Pitch".
My old Kenwood turntable was set for 50Hz, but came with an extra pulley (the spindle on the motor that the belt goes round) for use with 60Hz mains.
No, I couldn't resist!
With the "wrong" pulley installed for a few weeks (or was it months), we had the choice of playing LPs either too fast or too slow (to the annoyance of my housemates). IMO some stuff e.g. Madonna actually sounded better at the "wrong" speed. (Other stuff, like Jackie Frisco, sounded better played backwards, but that's another story).
It's amazing how one gets used to something like that, though. One of my housemates also had a turntable, but with a busted tonearm (some knucklebrain had stood on it). When I finally got round to fixing that for her, she complained that it didn't sound right. We'd all gotten so used to playing our music on my system, that it sounded "wrong" at the correct speed.