What does a cathode capacitor in an amp do, exactly? What would omitting it, raising the value, or lowering the value do for the tone?
Taken from http://members.chello.nl/~m.heijligers/DAChtml/Analogue/Amplification.html

"A cathode capacitor is often used to remove the local feedback caused by Rc for audio frequencies. Capacitor Cp decouples the DC component from the signal on the plate, and an amplified output signal free of DC components is obtained (Vout). Cp and Ck should be chosen such that they have no impact on the audio frequence range. A -3dB point can be determined by the reactance Xc = 1 / (2 π f0 C) . The frequency at which Xc equals Rc , represents the -3dB point. A value of f0 = 10Hz should suffice in practice, and with this assumption a value of C can be determined as C = 1 / (63 . Rc )."

I think that takes care of your questions...if you need further explaination, let me know.
MG Free At Last
Damn, you sneaky little bastard. You slipped 4 questions into 1.

If Coke wasn't better, I'd just tell you to piss off. :p

Quote by cokeisbetter
What does a cathode capacitor in an amp do, exactly?

To answer that, you need to look at a typical "self-biased" triode and see how it works.

1 - The Grid is referenced to ground, through a large value resistor.

2 - To bias a triode properly, the idle current needs to be in the middle of the intended range of operation. the Grid needs to be Negative, with respect to the Cathode

-OR- looking at it another way, the Cathode needs to be positive with respect to the Grid.

3 - A resistor is used in series with the Cathode, so the Cathode will be at the correct (positive) voltage to maintain the proper idle current.

4 - As the signal is applied, the voltage at the cathode changes in the same direction as the input to the grid. This is because when the input signal goes more negative, there is less current from the cathode to the plate. Therefore there is also less voltage drop across the cathode resistor.

This causes the Gain (amplification) of this stage to be significantly less than what could be possible.

This process is known as Cathode Degeneration.

5 - the purpose of the Cathode Bypass capacitor is to hold the voltage steady at the cathode. We now get more gain from the circuit. The entire voltage swing of the input is in relation to a fixed voltage at the cathode.

Quote by cokeisbetter
What would omitting it, do for the tone?

Not so much tone, but Gain. It will be significantly decreased.
In some amps like the Pignose G-40v, there is a low frequency cutoff that is intentionally very high. The bass is intentionally weak so when pushed to heavy distortion, the amp doesn't sound "farty". It also causes it to sound anemic when played clean. In these amps, removing the cathode bypass cap will sacrifice gain, but restore a more normal frequency response. I've removed one of mine (C9 stock value = .047 uF) and I am more than pleased with the result.

Quote by cokeisbetter
What would raising the value, do for the tone?

Most amplifiers are designed with a low frequency roll-off that is below the frequencies that will be present in the signal. Raising the value will only improve the amplification of undesired frequencies, like sub-audio when the strings are pushed toward the pickups. This will cause the speakers to "breathe" too much of this can be unhealthy for your speakers.

In the case of the G40v it would lower the frequency response without sacrificing gain. The little piggy already has WAY more gain than necessary.

Quote by cokeisbetter
What would lowering the value do for the tone?

Lowering the value will increase the frequency of the roll-off. A little won't hurt, but too much will make the lower notes weaker than they should be.

Or in the case of the G40v push the roll-off point so high the only thing that would be normal, would be up in the treble range.

Sorry if this rambled a bit. I've been away from this stuff for long enough that my explanations might not be all that clear. Perhaps it will help a bit anyway.

SYK