Had the same on my A4 at 163k – I was convinced it must be a wheel bearing at that mileage.
However, I took it for a service at the local Audi specialists and the guy from the garage drove me to the train station in it. After about 2 minutes, he said to me :
“Have you got Avons on this?”
Me: “Er, yes” ( ZZ3s)
Him: “Thought so.”
Anyway, to cut a long story short, a new set of Dunlops and the car is silent again. If your tyres are getting worn, I’d wager it’s them. Certain tread patterns seem prone to the ‘sawtooth’ effect described above, i.e. some tread blocks seem taller than others as you feel around the circumference of the tyre and it creates that drumming effect.