Graham,
That would be very hard to take. I guess you've accidentally tuned your mast to an unhappy resonance - just when calmness is most desired at anchor, as the wind rises, the mast adds to the riot. You probably wish for the whistle of shrouds.
To silence a guitar string, a finger can dampen the vibration by touching it anywhere between its harmonic nodes. Or it can be tuned up or down to avoid the frequency that's inducing the (sympathetic) vibration. Adding mass somewhere in the mast would change its period of vibration. We're not used to having to do those things to our masts...
Even loading the boat might change the vibe...
You're going to solve it. Let us know how you do.
Cheers,
Kurt