Who has solved the HVAC air noise problem?

Why not just turn the HVAC system off when you are doing critical listening?

The biggest reason for a noisey HVAC system is generally a poor return system. Many will try to use 1 return air duct which is centrally located in the house. The better alternative is to put 2 in and try to keep them in hallways if possible. This is the way I did my house and I cannot tell when it is running. Another problem may be an air handler too big for the system.
If you use a separate system you will have to put a return air duct in the room which is not desireable. A better alternative is to increase the size of the existing system (heat pump I pressume) and install another return air duct. An experienced HVAC contractor should be able to remedy this noise problem for you. Also DO NOT use duct board unless you like breathing in fiberglass particles. You probably cannot find it anyway. I haven't seen it used for years and it is probably against code also. Metal trunk lines with flex duct is the way. Trunk lines should be wrapped with insulation. HVAC should not be noisey. Good luck

Several things:
1. not all blowers are created equal; shop around.
2. keep the blower as far from the room as possible.
3. make the ducts as big as possible; the drop in noise from doubling the size of the duct will astonish you and is probably more effective than anything else you can do. I cannot emphasize this enough.
4. Mechanically decouple the ducting from the pump/blower unit with a flexible coupling to eliminate vibration transmission.

There is tons of good info in F. Alton Everest's Master Handbook of Acoustics, around $40 in paperback. It is well worth getting a copy before you really start planning.

I would like to call attention to the central unit itself, the working part of the system. This is often located on the same floor level, and even worse if situated near the listening room.

Since this houses the electronics, blower motor and fan assembly, it is a major source of mechanical noise and vibration. Installing sound absorbing fiberglass within the walls of this utility closet will go a long way toward killing these noises.

I went one step farther. Had a custom (extra thick) solid core exterior door and frame with threshold built for my utility closet. It was then weather-stripped with the rubber gasket system for severe weather. Made an unbelievable difference by closing up the last cracks and vents that leaked noise into the space.

The previous suggestions coupled with mine can reduce the various sources of noise to almost inaudible levels.

For return ducting, internally lined sheet metal ductwork would be my first choice for noise reduction, followed by ductboard. By the way, ductboard IS code approved for residential and commercial HVAC systems. I'm not crazy about the fiber from ductboard either. Internal insulation lining is MUCH better. Wrapping the outside of metal ductwork with insulation is done primarily to prevent condensation and avoid energy losses through the duct walls. In my experience wrapping the outside of metal ductwork with insulation does little to reduce or dampen air noise inside the ducts-which is what Bill wants to accomplish.
Make sure any metal ductwork is heavy gauge. This will help prevent ductwork noise often experienced when the blower first comes on and pressurizes the duct system.
As to filtration, an Aprilaire Space Gaurd media type filter installed by the blower does a great job and adds to noise reduction due to its thickness and composition. Some electronic air filters will marginally outperform the Space Gaurd but require maintainance and make some noise.
Hope this helps.
Roger