Thanks very much for the suggestion Steve, but I checked that and it's definitely not even close to touching, even when crossed to 39-14 (third smallest cog.)

It doesn't make any audible sound, it's just a faint rough feeling I can sense through my shoes (and perhaps also in the handlebars.)

I've also checked the chain slack, and none of the pulleys are rubbing anywhere, even when crossed to 39-12 (which I never do.)