They don’t really. Capacitors have an impedance. That changes with frequency. This is why different values pass different frequencies.
At the frequency at which the RC circuit is resonant, the cap’s impedance is a lot less than the pot value. So the cap looks like a wire.
As you turn down the tone control pot from ten, the major effect is changing the resistive loading on the resonant circuit. This is because the impedance of the capacitor in the range of the resonance is a lot less than the pot value.
As the pot gets closer to zero, the capacitor becomes important, but the initial effect is just resistive loading.
So if you remove the cap you might hear a difference on 10, but you won’t hear a difference with different value caps.
In one of my basses I have a switch to chose between two different value caps or no cap. When the tone control is on 10, switching the switch does nothing to the sound. That’s with a 500k pot.
With 250k you might hear more resistance loading. If you want to remove the cap on 10, get a no load pot.
The function of the cap is to pass signal above its resonant frequency to ground. That’s your high frequency content. So your signal gets muffled. And all this talk about paper-in-oil sounding “better” than a film cap, or even ceramic is nonsense, since you never hear the signal passing through the cap.
All that matters is the value of the cap, and it shouldn’t be old and “leaky” or have a too high an ESR rating. That’s the resistance of the cap. But that’s usually pretty low. Ceramic caps have a lower ESR than film caps. But at the most it’s a couple of ohms.
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