I don't see a round rug being an improvement in that space. Round rugs are also less common, so you would be limiting your choices as well.

I think bigger and darker would work better than what you have, with colors that tile into the warm red-brown of the piano.

I really like what cawaps shared. I agree -- that's going to be the best look for this space. By the way, are you going to raise the chandelier?

Oh, and gorgeous piano! Also love your idea to display your other instruments on the wall. There are a number of different display systems available with which to do that.

First of all you say the rest of your home is MCM and farmhouse? You want this room formal? These 3 styles don't "go" together. The chairs are neither. The table is neither and the chandelier is neither. Before you move forward I would decide on a style that will be cohesive through out your home. Perhaps your definition of formal, MCM and farmhouse are different than what they are? Regardless a round rug = NO. You need a rectangular rug.

It does not make sense to have a rug that will interfere with the moving of the piano stool back and forth.

The side table next to the piano makes no sense, neither does the mirror behind the piano.

The vase on the piano should be moved, it interferes with the acoustics.

As far as the stringed instruments, I wouldn't take the risk of their being dropped while taking them down from the wall.

They are just too valuable.

Furthermore, they would be so very exposed to the changing humidity in the home, and the heat and AC from your HVAC system.

Bad enough the piano is exposed to this, you can't help that.

But to do that to your smaller instruments just for show is a huge no-no.

I believe ideally the tail of the piano isn't supposed to be into the corner; the long side should be towards a wall or across the corner, and the pianist should look into the room. So if possible, turn the piano. I think having a rug under the piano is also preferable.

First the player faces the room so turn the piano and I agree the space in either of those styles needs to be a bit more simple .I have a baby grand between our LR and DR in a MCM ranch and since most of the time the player is playing after dinner we have it turned for that . I also agree no other instrumnets mounted on the wall.

Following
For some reason I can see the piano under the chandelier, in the middle of the room.

Do you need a little storage for your sheet music in this room?

Exactly my thoughts- the instrument is the star...make it center. I also like the idea of having hanging instruments on that wall. With the proper hardware, taking them down isn’t a problem, or at least I’ve never had a problem.