Thanks for the comments, guys - much appreciated. And thanks for the copyright info. To be honest, I did wonder about this when I put the clip up there, but I did a few searches and realised there are millions of other such violations up there - I'm pretty sure I spotted a few uploads that were rips of the original audio, which I can understand is blatant disregard of copyright - suggesting that Soundcloud doesn't police this stuff as strongly as they seem to imply. Anyway, I figured that since I'm not making money off the recording, and I'm not making it available as a download, it was probably OK. I'll happily take it down if the Beatles' label or Soundcloud ask me to. As a recording artist myself (albeit not in the same league as the Beatles!) I would be flattered if I saw other artists posting up arrangements of my work like this. In any case, I bought a download of the Beatles' original (ashamed to say I didn't have any Beatles tracks in my record collection!) in order to listen to it and work out how I could re-arrange it. And hopefully my recording will remind people what a funky little number Come Together is and go buy the original version for themselves!
Now how does all this work on Youtube? I put up a video of the same performance on Youtube (
http://youtu.be/i9NNfDbxjP4), so am I likely to get into trouble for that, or does Youtube have some other system in place whereby they pay the royalties owed to record labels in these cases? The sheer number of videos of folks in their bedrooms explaining 'This is how you play (insert copyrighted song name here)' is mindboggling - difficult to imagine that Youtube are accounting for all of these!