I would like to share my experience with Iberia airlines.
I recently had a few concerts in Madrid with a friend of mine who plays ney.
We were allowed to carry our instrument in the cabin without any additional cost.
The plane crew even propose us spontaneously to store the instruments in an apart cabinet instead of the usual overhead one.
So, overall a very good experience.
I hope it is useful to know.
Iberia seems to proud themselves to do that. I have had the same experience with a handcrafted flamenco guitar from Madrid.
No additional costs, not even necessary to register beforehand. Just brought the guitar with me and it was stored in a special cabinet in the cabin.
Great service!