Electrical Panel Grounding

All grounds must be bonded together at the service panel. This is for safety reasons, and to ensure that breakers will trip properly under fault.

Is the sub panel in the same building as the main panel or is it in an unattached garage?

What do you mean "with its own earth ground"? You cannot -- in the same building -- run a separate grounding conductor from a sub panel to a location other than where the house service is grounded. If there is a grounding conductor from a sub panel to, say, a water pipe that is more than 5 feet where the water pipe enters the house, the house water piping could be energized in the event of a fault. 

The sub panel must have a ground bar that is bonded to the sub panel and the circuit grounds get attached to the bar. That ground bar must be bonded to the main service panel ground at the point of entry by either a separate wire or metallic conduit to the sub panel from the main panel.

The sub panel must have an isolated neutral bus that prevents the sub panel circuit neutrals from being grounded upstream of the service panel, resulting in neutral currents raising the potential on the sub panel metallic parts and ground.

If the sub panel is in an unattached building and fed from a breaker in the main panel, then the sub panel needs its own earth ground (to a ground rod) and does not need a grounding conductor to the main panel.  

Earth "grounds" at different physical locations can have several volts of difference in potential. Depends on lots of factors. Only way to ensure it is at 0 Volts relative to AC is to tie them together. :)

Also, important, while you may have multiple grounds tied together, and even loop them, you may ONLY tie the neutral and ground together at one place, the service entrance. The service panel does not necessarily equal main. :)

So, the plan was to put a half dozen copper clad ground rods outside in the earth and run 6 separate ground leads to the sub panel. This should allow for an easier electrical noise pathway by lowering potential. If I connect this ground field back to the service panel, then I will connect with the noise from other home electrical devices, such as dimmers, etc. What I'm reading above is that 1) A separate ground field may cause breakers to not activate correctly and 2) cause a differential neutral voltage. I'm not clear on why multiple ground fields only makes sense for a separate building.

The sub panel powers primarily the stereo, but my neighborhood electrical is really noisy until about 10 PM. I do use PS Audio power regenerators, one on the front end and one on the amps. But they can't handle all the noise. 

So, does anyone have a different opinion on what appears to be good advice above? And I do appreciate you guys taking the time to try and teach me some power grounding fundamentals. But I am a slow learner.

Wguts, none of this is necessary nor will it improve anything.

What matters is that it all be referenced to a single point, where the neutral is bonded to it. Putting in a single, or 20 ground rods won’t help this at all.  Follow the NEC, and local codes which may now require 2 rods.

I’d focus on your room acoustics. :)

The point of the ground is to act as an earth safety, which it can only do well if bonded to the neutral at 1 location.

Now if you want to run isolated grounds from the panel, that's fine.