Mike, I'm trying to understand the exact means for which I can build the fabric wall, not the frame.
Well, I'm not Mike, but here is an answer. It's called an INSIDE OUT WALL. However, this has to do with how your studio is constructed in the first place. The reason is to keep any TWO LEAF systems intact.
Here's the deal. USUALLY, these type walls are only part of a DOUBLE WALL system, where one of the double walls has ONE leaf of drywall fastened to the room side of the studs, and the Inside Out wall, has the drywall fastened to the airgap side of the studs. This keeps the two leaf system intact while allowing the use of the stud cavitys to be filled with absorption materials, while providing the stud edge for a place to staple fabric. Most Pro studios have EITHER, an Inside out wall somewhere, or enough space to build standard double walls, with fixtures designed to hold absorption material in substantial depths for bass traps, and reflective/diffusive elements as well.
Here is a standard Double wall...
Here is a Double Wall with one leaf built as an "inside out" wall.
The problem with building an inside out wall in a Home studio, is keeping a two leaf system intact. If you are adding a partition wall within a room, then it has to be a double wall with one inside out leaf. If you simply add an inside out wall parallel and adjacent to an existing partition wall, the existing partition wall is most likely already a two leaf system...that is...drywall on both sides of a wood frame. (SEE NEXT POST) To make the inside out wall maintain the two leaf system, you would have to REMOVE the drywall from the existing wall(on the side facing the new inside out wall, and then erect your new inside out wall, which btw, is NOT an easy task,(and dumb in the first place unless you want double walls) as usually, you have to build a precision wall on the floor, sheath it with drywall, and then lift it into place, as it is almost impossible to drywall it while IN PLACE. That's the problem with doing this in rooms that already have exisiting two leaf system assemblies .
Which essentially means...if you don't want to remove the drywall, and then build ANOTHER WALL, then you simply build a FRAME the size you want, against the existing drywall. fill it with insulation, and staple fabric over it. However, the maximum width of your fabric will tend to define where you have to provide a stapling surface. This is why MOST HR enthusiasts...simply build broadband PANELS. Besides, when you have a bunch of panels placed in a quasi checkerboard fashion or such, as a byproduct you get a modicum of diffusion as well.
HOWEVER..you said this as well.
I'm treating my vocal booth and I'm going to have to build a wall.
Without seeing exactly what it is and where you are building this "wall", it's difficult to tell you how or what to do. Got a drawing of what your intentions are? That would certainly help.