Bob, yes they're all tied together at the panel, but a dedicated line means there is nothing else on that circuit but your audio, so there's no other equipment on that line between your audio gear and the power pole (except for that circuit's breaker and the main electrical cut-off switch) and so nothing (in your house at least) to introduce noise into, or reduce current in, the line used by your audio.
Clio, one thing that you could do to get the most out of your non-dedicated circuit is (first cut the power at the breaker) and rewire all the outlets on that circuit, making sure you use the screw terminals (not the push connections) and making sure all the wire and teminals are clean (you can use Caig De-Oxit) Generally, the electricians daisy-chain the outlets, so if your audio system isn't using the first outlet after the circuit breaker, then there are a lot of connections between it and the panel.
Clio, one thing that you could do to get the most out of your non-dedicated circuit is (first cut the power at the breaker) and rewire all the outlets on that circuit, making sure you use the screw terminals (not the push connections) and making sure all the wire and teminals are clean (you can use Caig De-Oxit) Generally, the electricians daisy-chain the outlets, so if your audio system isn't using the first outlet after the circuit breaker, then there are a lot of connections between it and the panel.