Definitely HD650 imo for jazz, however you would need better amp/dac to drive it properly. He400 is also good for jazz.
You also have to buy an amp/dac to drive those cans properly.
Maybe you can consider these thread for cans selection
Thanks, I am aware of the thread and have been using it to build my short list. Unfortunately many of the headphones are out of reach and some others, including the Fidelio, missing.
As others have already stated, the X1s might not be your best choice if you only listen to a lot of Jazz, but I find them to be more the adequate in that dept. Believe me, you could do a lot worse in the Jazz dept then the X1s. I listen to a lot of the vocal female greats with them. They sound pretty good even on my crappy PC. My Fiio E07K arrived a few days ago, so, I'm hoping it will take me to the next level.
Thank you, that is encouraging! I have found a pair of used Fidelios at an interesting price and they really look comfortable, so I would have really liked them to be Jazz-compatible!