Keep the original tone control as it is then add another potentiometer and capacitor for the bass cut control. Adding a DPDT on/on/on switch gives you the choice of A) Bass cut alone B) Both tone controls working C) Treble cut alone.
This has the advantage of keeping the original tone control exactly as it is. The disadvantage of this circuit is it requires you to drill 2 holes in your guitar. Also, I am unsure about the potentiometer value. From what I've read about bass cut circuits, the pot value, its taper and the capacitor value all make a huge difference. Please contribute any suggestions you may have.
OK, wolf, I'll sign off on that latest diagram. According to the Truth Table published in the first post, the above diagram works as advertised.
As to values, those run the gamut of possibilities. I think it's going to boil down to two things: what kind of pickups are in place, and what the user/player wants to hear. In my original published circuit, I used a 0.005µfd, across a 1MΩ pot. But that was for a single coil pup of average design. For certain, most of us have expanded that parameter way beyond the original guitar builder's intent.
Unlike the standard tone control (a treble cut), where we have a narrow range of probably useful values, the bass cut is much more sensitive to changes, and therefore has a wider range of action. No, I don't mean within one pair of values, I mean that either the cap, the pot, or both can be of such a wide range of possible values, when it comes to setting up the guitar for use. Like I said, it's what (how much) effect the player wants to hear that will control the final selection of parts values.
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Your bass-cut cap value seems to be in the usual ball park, at 0.0022uF. I also worked out that if you went to an even smaller cap, like 560pF to 820pF, you can carve the response of a full humbucker to make it look like a single-coil, at least on a frequency response plot.
The bass cut resistor value needs a large pot if you want to have the max bass cut, and 1M seems the go. A linear pot seems like the best taper. Nothing much happens in the first few k except for a slight volume drop, then the bass cutting starts to happen. One of the key parameters is the relationship between the bass cut and volume pot. It is the volume pot resistance that make the load that allows the bass cut to work. So with a 250k volume pot, the bass cut does more with a given set of values, than with a 500k volume.
I like your switch, but a PTB system, if you have a no-load treble cut pot, can also get completely out of circuit. The bass cut at minimum, causes no loss.