Hi all,
 
I'm just doing a bit of tracking in X3 this evening.   And I have my Roland XP synth plugged right into my Tascam US600.  When I arm a new track and turn on the Input Echo,  I'm getting this weird little 60-cycle type hum.  I've turned off every other electrical item in my basement studio, monitor, keyboard, fan, dehumidifer, etc.  and it's still there.
 
Granted, I can turn off the Input Echo and track just fine, but then I can't hear and monitor through my interface.  Am I missing a setting or troubleshooting step here?

Is the hum recorded on the track? If so suspect analog input chain, if not suspect output.

Classic ground-loop symptom
 
Do you have all gear running from a single outlet?
That's the easiest way to avoid grounding issues.

yeah it is.  But I have nothing in between my keyboard and the interface but a cord.
 

If there's a ground-loop, an unbalanced cable connecting the keyboard/audio-interface will reveal it.  
If you have a DI box with a ground-lift switch, you can use that to test.
Plug the keyboard into the DI box... and plug the DI box into the audio-interface.
If the hum disappears when using the ground-lift switch, you've got your culprit.
 
If the issue can't be solved by moving electrical cords to the same outlet, use a pair of DI boxes (as above) to solve the problem.

Yeah I probably have a ground loop.   Got all the gear plugged into a rackmount power strip which is then plugged into an outlet
 
I have a passive DI box (1/4" to XLR) or an ART Tube MP 127 preamp/DI - would either of those work?  That's all I have.
 

I do have an slightly-old SignalFlex passive DI box that I tried - doesn't have a ground lift switch on it.  But the hum has went away on the tracks.  Is that a decent enough workaround?   Seems much improved to my ears.

Sounds like the noise was introduced by the unbalanced cable that was connecting the keyboard to the audio interface.
 
DI boxes for keyboards are always used when playing live.
Eliminates numerous issues... including noise
 
On newer keyboards (those that use USB for MIDI/Audio I/O), if you connect to the PC using a poor quality USB cable, that can actually introduce noise.