Note that changing the resistor type can slightly alter the sound characteristic of a unit, replacing a Carbon Composition with a Metal Film is likely to show the biggest change, although the effect is quite subtle.
One other comment.
I suspect
Hyperion is referring to plate swings in tube amplifiers, not solid state which operate at much lower voltage. But, in any event, if the resistor changes the sound it is adding
distortion. That may be distortion humans like, or distortions humans dislike, but it is, nontheless,
distortion, so the amplifier is no longer a straight wire with gain.
Here's what I previously wrote on that subject, somewhat edited for content and brevity.
A carbon-composition resistor (CCR) is made from a mixture of clay (non-conductive) and carbon black (conductive). The ratio determines the resistance; more carbon = less resistance, while less carbon = more resistance. This grainy mix tends to act like a jumble of diodes which causes peculiar properties. (The diodes are not aligned, so the resistor does not have directionality.) This is similar to the varistors made from copper oxides. (That work on copper oxides, BTW, leads to Bardeen and Brattain collaborating as a team, and that, in turn, led to their stealing credit for the transistor from Russell Ohl. Neglecting that it had actually been invented by others decades before, and technically wasn't patentable because of all the prior art.
Yes, this will be on the quiz.)
Anyway, the variable voltage drop of the diode effect give rises to a Vcr (Voltage Co-efficient of Resistance). The value of a CCR thus non-linearlly fluctuates with applied voltage: (If the resistance changes as the voltage fluctuates between high and low values, then resistor offers non-linear behavior, i.e. the change is lesser at the lower voltages and greater at the higher voltages.) If the voltage is relatively constant, however, which is the case for most resistors in an amplifier (dividers, bias, and the like), the resistor is just constantly out of specification, with the difference being a function of voltage and usually trivial for low (< 100 V) voltages. So it must be a plate resistor experiencing a large voltage swing, as nothing else in the amplifier has that kind of fluctuation.
The Erie Resistor Company found differences of a few percent over swings of several hundred volts. Others found 0.025% / volt for values below 1 MΩ and twice that, 0.05% / volt, for values above 1 MΩ. What that means, in practice, is at, say, 300 V the values below 1 MΩ would have about 7.5% drift and those above 1 MΩ would have about 15% drift. This is why it matters at the plate. This effect won't show up at low or constant voltages.
So all those CCR solid-state guitar amplifiers running with 35 V (or lower) rails? Nope. No benefit from distortion. And voltage dividers? They're just out of spec because the voltage across them is constant. (Neglecting trivial fluctuations in the supply, of course, for those who want to quibble.)
Solid-state uses low voltages compared to tubes, so Vcr tends to be irrelevant over the narrow swings with transistors. Yet I've seen guitar effects running on a 9 VDC battery claiming "carbon resistors for sound!" when that's simply impossible.