Where on God's earth is the GFCI? You have a switch controlling 8 outlets? Overhead lights or switch controlled lights should not be on the same circuit with GFCI protected outlets.

texasredhead - it is located a by a garden tub in a master bathroom which has a window that faces out the front to the house.

This was part of a window candle package that the electrician put in when the house was built. Basically 1 switch controls outlets installed by each window in the front of the house so that candles can put in the windows and plugged in with the ability to turn all on and off by one switch. The only things plugged into these outlets are window candles.

They had to put a GFCI for the one in the master bath because the tub is too close to the window.

Now about the hum? :-)

Can you name the tune?

Seriously, my guess would be an interaction between the electronic in the X10 and the GFCI. Try replacing the X10 with a standard switch and see if it goes away (or if the tune changes :)

Unless the X-10 has a contactor and NOT a thyristor, it is likely the cause of the hum.
Even when full on a thyristor controlled circuit still distorts the AC waveform (it has a turn on threshold of at least 0.5 V and sometimes as high as 1-2 V).
This distortion can cause vibration in any transformer on the circuit, and a GFCI uses a coil as a pick up transformer to measure current balance.

Thanks all for the replies.

Therefore if it is the X10 switch can I assume all is safe and no need to change anything or do I have a concern?

It could damage the GFCI.
Sound means vibration, and that will eventually break the wiring on the pick up coil.
It can also interfere with the response time of the GFCI.