Steering head wobble but only at particular speed

New one for me. Between about 45 and 58 mph I'll get front end wobble with hands off the bars. Just touch the bars with a single finger it stops.

No changes to bike recently, pre-load set high. Did it with warm and cold. Lowered the windscreen and it seems to take a little longer to start the wobble.

Never noticed it before.
Could it be I have just the right magical combination and in another few thousand miles it'll not happen?

I'm guessing front or rear tire wear or type.

I have found this to be true with a few tires on the front. What brand do you have on there now?

Running double dark.

Pirelli Demon (rear) on the front. About 2/3 through the tread. Running 42#'s normally but I was down to about 39 cold this time out, climbed to 42 when warmed.

My 1100 had a little head shake when I started out for WeSToc on a new BT023 rear and a 1/2 gone Storm2 front. 4 days and 1700 miles later it was gone. Anyway, IMO these things come and go so don't sweat it.