1. This was present in my previous system as well and I'd hoped to eliminate it
2. More noticeable at higher (but not excessive) volumes.
3. Occurs through speakers and headphones
This rules out everything, leaving only the ears. Like I said, its tinnitus.
If there was just one wish the Genie could grant me it would be to stop people from posting absolute blather as if they knew anything about it. Tinnitus is most definitely NOT always worse with no sound. Tinnitus can manifest in a whole lot of different ways. Unlike the blatherer I know what I'm talking about having actually lived through it!
There's so many different forms of tinnitus this is total coincidence but what I had was exactly what the OP described. No ringing or funny noises at all, except with certain notes or sounds. I even had the problem first start to show up after making some changes, causing me to waste a lot of time and money trying to track down in my system what was actually in my ears.
When I noticed the exact same "noise" listening to iPod and ear phones I knew for sure it wasn't the system. So for sure that is what you have. Really sorry to say.
Tinnitus can have many causes. In my case it was long term use of pain killers for chronic back pain. Got the pain down, got off the meds, and it took a while but the ringing pretty much went away. Your case may well be different but its worth taking a look.
Like a lot of things its easier to handle once you know what it is. Even if it won't go away (which it probably won't) at least you know what it is now and can disregard it and stop chasing down phantoms in your system.