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Special potentiometer

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I'm in need of a special kind of potentiometer, but I'm unable to find one that does exactly what I need. Does anyone know where I might find one, or how I might modify an existing potentiometer to do the same thing?

Here's what I need. I have two audio sources, and I want to be able to control the mix with a single pot. I was planning to use a 500kΩ logarithmic stereo pot, but I need it to approach zero resistance at the half position. For example, when the pot position is between the 0% and 50%, resistance should be close to 0. But when the position is between 50% and 100%, resistance should range between 0Ω and 500kΩ, respectively. This way, when the pot is in the middle position, both signals are allowed to pass at full volume, and by turning the pot all the way in either direction, I can block one signal and allow the other to pass at full volume. (This would be achieved by connecting the wires for the two sources to the terminals on opposing sides of the stereo pot.)

I thought about wiring some resistors in parallel with the pot, but that doesn't seem to be what I need. Does anyone have any ideas?
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