When I hook a device to the monitor input of my digital piano, I get a very noticable 50Hz hum.

I understand that the monitor input doesn't have to be particuarly good quality, but it really is annoying.

I'd know what to look for if the attached device had a ground connection, but it happens even with battery powered products such as an ipad.

The cable is a cheap 3.5mm-jack to 3.5mm-jack thing.

I've done some experimenting:

 * ipad attached to piano, electrically insulated from everything else --> **hum**

 * ipad attached, touching ipad screen --> **even more hum**

 * Unplug the cable from the piano--> **no hum**

 * Cable pluged into piano, other side unplugged -> **no hum**

 * Cable pluged into piano, touch exposed jack parts for left and right channel -> **hum** (on the according side)

 * Cable pluged into piano, touch exposed jack ground part -> **a little hum**

 * Cable pluged into piano, shorten all three terminals on exposed jack with a bit of wire -> **no hum**

 * Cable pluged into piano, shorten all three terminals on exposed jack with a bit of wire and touch the wire -> **hum**
 

I first suspected the cable to act as an antenna, but the cable alone is quiet.

Looks like it happens only if an antenna is attached to the cable. Both ipads and humans seem to be effective antennas. 

What I don't understand how this can work with everything shortend to the ground part of the jack. With a low-impedance path to ground, how can I still inject the 50hz signal?