Thanks for your input, guys!
Jazzyvee - heh, I used to use one of those planetwaves cables a while back and had exactly the same experience as you, so I don't use it any more! But that was a very different problem to what I've got now - it's difficult to explain clearly, but the cable is securely in the jack socket and the volume is there, no crackles etc - but there's no top end in the sound - it sounds like an old P-bass with flats - until I 'twang' a string, at which point, the treble comes through loud and clear and it's back to sounding like an Alembic again. It feels like there's some kind of 'gate' on the upper frequencies, until I play an upper frequency sound loud enough to 'open' the gate and it then stays open. It's very weird.
JBY - you might be right: I use the same cable all the time. But that said, I use the same cable with all my basses, and only the Alembic does this. But there again, I use the Alembic much more than the others . . . and maybe it's the combination of a dirty jack socket and dirty cable . . . so I'll take at look at both and see if I can fix anything there.
Cheers,
K.