ref the buzzing mentioned by some above
I have '60 XJ6FA and I also found it was at times both 3000rpm ish and 4500-5000 rpm ish. Riding on open road, I managed to figure out it was the front screen/black dial 'dash'.
Local dealer tried to tighten all the screen fixings - no change.
Second trial with 2 guys on the bike with me holding the revs, it stopped if they pressed the black dial 'dash' to the left & right of the dials, right at the pointed bit where it meets the screen and fairing. They have fixed by fitting some, like double sided sticky sponge, at that point and the noise has stopped - heaven!