Now, I'm getting confused. Nearly every post on a dedicated breaker that I can remember has cautioned that a separate ground rod is a code violation? What gives?
A separate grounding electrode is legal per NEC 250.54 but ultimately the separate electrode must be connected to the ground of the main service per NEC 250.4 (A)(5).
An isolated ground receptacle basically means that the ground terminal on the receptacle is isolated from its yoke. In theory if you install an isolated ground receptacle and run the ground wire back to the breaker box, the ground wire will be isolated from the other ground wires and metal boxes on that circuit - up to a point.
Ultimately, every ground wire terminates at the same bus bar. Additionally, every single neutral wire is also eventually connected to the same ground back at the service. With that in mind, the only way for your audio system to be truly "isolated" from everything else in your home is to install a separate service.
That being said, having a dedicated circuit for your rig, as well as utilizing isolated ground receptacles, and paying mind to which circuits are connected to which phase in your breaker box can go a long way towards reducing unwanted noise, but it's not a cure-all or a magic bullet.
...take all of this with a grain of salt - I'm just a dumb electrician who builds amplifiers...