Can anyone tell me what this noise is?

Florescent lights.  Dimmers.  Bad cable shielding.

Top of the range cables doesn't mean there can't be a defect.
 
Sorry, that was my full load of ideas.

Did you remove the .mp3? Without hearing it, it is hard to know what it is - some kind of interference, I infer.

I encountered a problem like this when I had a polarity problem in my power lines.  Everything checked out fine, but with some equipment it created a buzz.
 
There are cheap circuit checkers available at hardware stores that will show ground faults, polarity problems and other issues. http: // www.amazon.com/GE-50542-3-Wire-Receptacle-Tester/dp/B002LZTKIA/ref=sr_1_1?ie=UTF8&qid=1448761735&sr=8-1&keywords=circuit+checker.  The pattern of lights on the device correlates to the circuit problem.  It's a handy tool and worth $5 - $8.

What you describe above e.g. doubling and the power cord would lead me to look for a ground loop. The audio sounds like electric hum that has been filtered. I don't see a 120 Hz peak on the spectral analysis. The sonitus equalizer has a Hum Removal (50 Hz) and a Hum Removal (60 Hz) preset that should get rid of most of it. You might have to play around with the frequencies but keep the stopband narrow (high Q). 

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. 

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...

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!

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. 

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.

Even with RX 5 Adv, it's very difficult to clean the noises, there're all kinds: humm, buzz, cliping, distortion, radio interference...

You only mention "plugged into the desk"  This implies an audio cable?? the power supply? 
Have you tried disconecting the USB cable? 
 
I get a crackling noise in my system , only when the audio engin is running, just like you are discribing. Every move you make with a mouse causes a buzzing too. 
I slowly eliminated each component and swapped out gear and I isolated it to my old Yamaha P 2100 Power amp. Go figure. Remove the power amp from the chain , crackling gone. 
 
But my point is you need to isolate each component.  The Drum module has a headphone output ,, right? try that in stand alone. 
Then hook up the USB cable..
Then try a different computer...on and on 
 

I had similar noise and I believe it was due to a ground loop picking up digital signals like USB packets, or other high frequency digital signals causing modulation into the audible spectrum (like AM). You can often change the sound by just moving your mouse around for instance.
 
As suggested by jpeterson and others, the best solution is probably to ground lift the audio signals using something like the Behringer MicroHD HD400 ($25 on Amazon). In my case it completely solved the problem.

You might try the trial version of Adobe Audition. Audition has pretty good noise reduction/removal, especially if used moderately for several passes over the audio rather than trying to remove all the noise in one go. I might be wrong but I think the trial version is fully featured until it expires after 30 fays.

That noise will ruin any sound so you need to track it down.  Have you unplugged EVERYTHING and added things back one by one.  This includes the power.   I've had just about every type of noise at one time or another and that strategy ALWAYS tracks down the culprit.   Its not a trivial operation but in the end, you also get the opportunity to unscramble what has likely become a mess of cables.  Also, being digital, do you need to sync it in any way?  I would say it is related to power and is exacerbated when you plug in the drum module.   Again, unplug EVERYTHING, then reconnect the most basic stuff like interface and monitor so you can hear and then start from there.  Maybe go withthe drums next as they seem to be triggering the issue and then one by one, power first , then audio connection (test each separately)