I just installed new furnance and AC

My furnace used to be up on the main level in the utility room, just off of the listening room. Very audible. I bought a new higher efficiency furnace and had it placed in the basement. Much better.

If it bothers you that much shut it down when you are listening to your music! My furnace is real loud but luckily it is on the other end of my house! You would think in this day and age they would make things like that quiet!

Any noticeable noise in the listening room is undesirable. If you live where AC is a necessity in the summer, and you don't have a silent source, the problem is compounded. Electric heat is impractical cost-wise, unless you live where electric rates are less than $0.10/kwh. I heat with wood that comes from my land; other than my labor, it's free and quiet. In summer, I use the AC as little as necessary, turning it off for serious listening. There is no easy answer.

My furnace is in the basement but still noise of the blower and moving air comes thru. Shutting it down for the time of listening session, as Yogiboy suggested, can be done but not when temperature outside is very low or it will get chilly real fast. I have small fireplace but it is for entertainment only. It produces radiated heat but also sucks warm air from the room. I've noticed that furnace works harder (longer) when fireplace is used. I consider replacing it with the one that takes air from outside and has glass door. It moves air from the room around/behind fireplace box. That is perhaps the most efficient type.

Common problem. High eff furnaces with 2 motors (combustion and blower) can make more noise. There are quiet ones but they get expensive. Sometimes it's just a question of setup and getting fan speed/deltaT to 60 degrees or manufacture's spec's. Sometimes I recommended using flexible duct connections on both return and supply to isolate vibration. Been a long time since I did residential.