A technical challenge...

After 40 years on various Guzzis and now 4 Months and 6000 kms on my GRiSO, I am convinced. This is by far the best and most enjoyable bike I've ever owned or driven!
It came with a functional Givi windscreen and I've done some minor changes, such as new mirrors, grip heating, led headlamp, and some electrical improvements. Even put on hand protectors and home made muffs, - not so good looking, but when temperatures go close to zero on the mountian crossings, I don't care how it looks.
The best change I did was to put back the stock muffler and install a corresponding Beetle map.
The bike suits me like a glove, pulls like a train and loves curvy roads and hills. And so do I.
Next will be a Stelvio shock with Öhlins spring and probably new bearings.

A tecnical challenge though. I get some strange vibrations on (mainly) the left foot peg between 3400 and 3700 rpm. It goes away above 3700 and comes in all gears. I can live with it, but can't really understand where it comes from. Any qualified guesses?

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Ready for a spectacular climb

Check all the engine mounting bolts for tightness, especially the ones on the front frame downtubes.

I suggest you also check the bolt that attaches the LH footrest for tightness.

Sounds like 3K to 4K rpm throttle body balancing should be done to verify no imbalance...that could easily explain the buzzing at the same rpm's regardless of gear.

I had a bolt missing from the corner of the oil cooler surround.
This caused the surround to vibrate against the motor at similiar revs you've stated.
It did make an audible buzz sound, but if your bolt is just loose & not missing then you might only get the vibration.

There you go. I'm thinking too complicated.
Thanks all for helping me to get down to earth and look at the simple and logic possibilities first...