Something sounds loose but can't see what I have a relatively new Boardman Pro 29er. It has around 500 miles on it. 

I'm having a sound issue at the minute where at certain speeds a very loud resonating vibration type sound starts. I'm convinced it's coming from the crank or bottom bracket but can't be sure. It almost sounds like a loose guitar string.

It seems to be related to cadence more than actual moving speed. I'd say roughly 60rpm.

I've inspected my bike with my fingers for loose nuts and bolts, cable ends rubbing, cables rattling and I can find nothing.

What could it be?
One possibility is that a bolt through the bottom bracket shell is too long and is touching the spindle of your crankset. As the crank spindle rotates, it sets this bolt into vibration, and the frame along with it, at certain speeds. 

Check to see if you have a cable guide at the bottom of your bike. If you do, see if the bolt that attaches it to the frame is long enough to reach inside the bottom bracket shell.

Some other diagnostic things you could do:

Remove the chain and coast down a hill, pedaling at different speeds. Does it persist? If not, focus on the chain. 

If you have one available, swap the rear wheel. If this cures it, focus on the wheel and cogset. 

Take off one brake rotor. Pedal at various intensities somewhere safe. Sometimes various conditions will cause a subtly dragging rotor to start vibrating. Put it back on and try the other. 

If none of that is to blame, I would concentrate on the bottom bracket bearings and the crankset/chainrings. Take them all off, clean, inspect, regrease, tighten to specs.