Wall mounting on studs

Awesome. Thanks everyone for your responses! 

I mounted my TT on a shelf, into the studs.  Was great!  Then, had new siding installed, and the hammering needed for the siding caused the table and the platform to fall to the floor!  Arm broke, other parts broke.  Yikes.  Fortunately it was repairable, for about $900.  It was/is a mofi ultra deck.   Just a warning/heads-up for the future.    But the studs-mounted shelf solved the feedback problems.  Was a rec by Andrew Singer.

I have a similar set up though mine only uses 2 studs. I mounted it where the studs were and that forced my hand a little as they weren’t exactly where I was hoping thy would be but only by a couple inches. 
The one thing my audio dealer recommended, and therefore I designed around, was mounting my turntable to a foundational wall to minimize vibration. This has worked out extremely well for me. Realize this may not be an option for you but if it is it’s highly recommended. YMMV. 

If adding studs horizontally, have each horizontal stud 'rest' on short vertical studs screwed to the existing vertical studs on either side.  Then screw the horizontal stud to these extra 'shelf' studs. This will also give you some extra mass. 

Just adding horizontal studs isn't ideal.  You want some additional support.

Hope this helps.

You don’t mention how far off the stud location is vs desired mounting location. And as Feldman brought up, is this an interior or exterior wall? An exterior wall will be much more solid as an interior wall can still transfer foot fall. Another consideration is whether outlet boxes are on the side of the stud that you would be adding the new stud, also will you have horizontal runs of Romex wiring to negotiate. 
If your current studs are only a few inches off from desired location, would you consider a horizontal brace fastened to the wall and then mount the shelf to it. You could cut the length to have equally balanced extensions on each end if possible finish to match and it would appear to be part of the original design. It would also help to know the make of the shelf so we could see the design.