Quietest air conditioners for a listening room for the upcoming hot summer?

+1   That Midea that ghelly linked is an excellent unit.

If true, that is quiet, and it’s 115 volt if that helps.

Clever design, looks like they have isolated the front from the back with that deep slot design, helps keep the noise outside.

I’d plug the question into an AI. It says you are asking for something that is at the edge of physics. But recommends a:

 
LG 14,000 BTU Dual Inverter Window AC

The exact recommendation is often the part that can be wrong... so check up on the recommendation in several different ways. 

I'd recommend blue tooth noise cancelling headphones and the window unit. 

I got a portable that I keep in the closet in case our central ever goes out. 

Last year I bought a Bosch inverter and it sits on the other side of the wall from my listening area and I never know it’s on. I kinda miss the old compressor turning on and off it gave me comfort the cool air was on its way. So I’ve come to accept that the Bosch is working in the background and doesn’t need me to monitor and keep an eye on it. I know you're looking for a window unit but maybe Bosch has a window unit. They also sell refrigerators.

Although the older ACs were much better at removing humidity and it’s especially important for the newer ACs to have adequate airflow. The older ACs were more forgiving but not the new ACs.  So the only issue I have is the return vent probably could be larger and I do hear the return airflow but in my listening area the supply vent is quiet.

Make sure they do a static pressure test after they have it installed. And make sure you take pictures of whatever they see on their devices so you have a record of it. That’s the way to measure airflow. And make sure you know exactly how much Freon they put into your system I would highly recommend monitoring the process. Important to know the length of your freon run too.

Don’t trust the smiley sales person, keep a close eye on the installers. Also the choice of your models may qualify you for a nice rebate from the federal government. I qualified for $2000. And finally, I saved a lot of money on my electricity last summer which came at a good time since rates are so much higher than they used to be before AI became popular. Somehow playing video games is more important than low electricity rates.

The man needs a sleeve unit.  The side vents on the AC shown will NOT work.  It has to vent from the back.  The sleeve installed is made for a certain brand of AC, it's best you get the same brand to be compatible, otherwise you will severely shorten the lifespan of the units and they won't fit properly.  The best would be the AC with a small front and everything else is outside the window, but they won't work in the sleeve..