guitarblah:
 
My speculation is that it's interference from a power supply.  I don't think it's primarily ground noise. 
One thing to ask, do you have any laser printers powered from the same circuit?  They are particularly noisy.
 
Sorry I can't be more definitive,
Paul

Wow, that does not sound like ground noise. It could be an impending component failure of some kind. 
 
At least you've isolated it to the drum module...
 
Is it feasible to try a different sound source in place of the drums? Just to make sure it is the module and not the cables running back and forth. 

HI:)
 
Sounds exactly like when you put a Handy near a speaker or an amplifier!
 
Bassman.
 

I would have thought that if it was ground loop, it would manifest with a 60hz component. In this noise, there is none.  The fundamental frequency of this sound comes in at around 250hz.  Can you hear the sound when you plug headphones directly into the TD20.  One thing you could do is put a gate on the TD20 drum track.  Not ideal, but at least you can quieten it down a bot when there are no drum sounds playing...

The Roland support page for the TD-20 states the outputs are unbalanced. How long are the cables you are using? Are they running parallel to any power cables? The spectral analysis is almost a perfect electrical hum spectrum minus the 120 Hz fundamental. Because of the characteristics of the magnetic flux density (assuming the noise is from parallel power cables) the fundamental frequency will be twice the electrical frequency. It could be component failure or just the cables on the unbalanced outputs picking up electrical hum. There are a lot of post on the web about electric hum on the unbalanced outputs of the TD-20. The signal we are listening to has been amplified by the OP. 

Switching power supply noise due to ground loop.
To test, get an extension cord and disconnect the earth on one side.
Connect your computer to the mains through this doctored extension cord.
 
Connect only your computer with this cord, not any active monitors or any other gear you might have.
 
To be safe, don't touch any metal parts of your computer, and switch on.
If the buzz is gone, it's a ground loop.
 
NOW REMOVE THE EXTENSION CORD FROM THE MAINS AND RECONNECT THE EARTH BEFORE YOU FORGET AND USE THIS CORD SOMEWHERE ELSE!

Although the trouble shooting method stated above is something I might use in a controlled environment you could be electrocuted if you do not know what you are doing. It is never recommended to remove the ground from a piece of equipment that is designed around having one. In other words you could become the ground and the current will flow through you. Electric current cause muscles to contract and can make it impossible to let go. Your heart is a muscle and it only takes a few 1000th of an amp to cause it to contract and stop beating. 1/10th of an amp for a second or two to cause death. A switching mode power supply in a pc uses the ground from the main distribution panel for the incoming filters and that ground is also bonded to the case of the power supply which comes in contact with the case of the pc.

My question is do you still hear the noise if the Drum Module is the only thing plugged in. 
 
In other words to trouble shoot you need to test each component indavidually as possible. 
 
It could be the USB cable ( or midi) connection to your computer. SO get all that out of there and test it as stand alone. Use a little mixer to test the output leads, or at least put your interface in stand alone by disconecting the USB cable. 

Hi guys, thanks for all the responses.
 
I have done a lot of testing. Changing cords, sockets, and adapters, and plugging my headphones into different things.
 
These are the results:
The signal ONLY happens when the sound card is being accessed (by a program), and ONLY if at the same time the drum module is plugged in (to the desk). If the drum module is turned on, the signal is about 60% stronger than when it's off.
When I say accessed by a program, I mean it will happen the entire time sonar is on.
It will happen if I have windows media player open (alone).
If I adjust the windows volume using the slider in the bottom right of my computer (to create the single test beep), it will happen during the test beep duration (stopping immediately after).
Again the drum module has to be at least plugged in for the above to cause it.
 
It's not triggered by cpu use as opening/using non-audio programs doesn't trigger it.
 
 
If I'm not mistaken this is going to be too difficult to figure out though I thought I should report that here anyway.
I think I have figured out a reasonable approach to removing it with EQ..

Like everyone else, I'll say it's most likely switching psu interference of some kind. I know this sounds strange, but what happens if you plug the drum module into the interface with the module not connected to power - i.e. with it's psu not even plugged in to the mains, or the switch at the mains turned off? The idea is that the psu will be functioning and therefore emitting emf so long as it's receiving mains, even if the module itself is switched off.
 
Is there any connection from module to PC, e.g. MIDI or USB? If so, does the noise still occur if that connection isn't plugged in?
 
If noise, then suspect radio interference from something being picked up by the module or cables and a different cable length might resolve the problem. Or not. As might using a DI box and using that to lift the earth (ground) between mixer and module. If no noise, then the module's psu noise is leaking through the module. Either can be a real pain to try and sort out though :-/
 
If it's quiet enough that it's not noticeable during drum hits gating it out might be a better solution than eq. Or a combination of gating and eq.