All right, let's start with the Varitone schematic:
Now let's see how I have entered this into LTSpice:
I am using the .step simulation command to step the capacitor through the listed values. The 10 Meg resistors are there to bleed off DC from the caps to eliminate pops when switching and so I left them out from my schematic. If you put them in you'd see little difference in the results. I am also driving this with just a straight voltage source rather than one of my pickup models, because I want to focus on the Varitone response in isolation first. I left the 500k volume pot off too! I'm just terrible!
Here's the frequency response for those 5 caps:
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Now let's take a look at the effect that the series resistor R1 has on the shape of the response. In this case I set the value of C1 to 0.22u instead of the variable Cv, and made R1 track the variable Rv instead of being fixed at 100k. The step values are 1k, 10k, and 100k.
Schematic:
Note that the .step simulation command in blue has been "commented out" so it is not active for this next simulation.
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You can see that when the series resistor is 1k (green trace), the width of the notch is very small, while when it's at 100k (red trace) the notch is very wide. If you were to use a pot here, you might decide that the narrowest notch is not a useful setting. By putting a 10k resistor in series with a 100k pot, you could start the knob's effect at the 10k line (blue trace) instead of the 1k line. Circuit simulation (along with your ears) can help you dial in your guitar's wiring for the best range of tones from your controls.
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LTSPICE - The Varitone Zone