This legit article discusses the voltage non-linearity for carbon resistors is negligible until substantial voltage, and even then I doubt it's audible in consumer electronics (including tube amps).
But there's also a noise aspect, which is much more likely to be audible.
All resistors have an
intrinsic thermodynamic noise, called Johnson noise. This noise is dependent on the resistance and the temperature, and is
not affected by the resistor's composition. The Johnson noise density is constant versus frequency, and is thus sometimes called "white noise". E.g., a 1MΩ resistor has Johnson noise density of 0.13 microvolts/√Hertz at room temperature. For a 10kHz bandwidth, the total Johnson noise is thus (0.13µV/√Hz)*(√10,000Hz) = (0.13µV/√Hz)*(100√Hz) = 13µV. Put some real gain on that and you'll hear it as white noise "hiss". See
https://en.m.wikipedia.org/wiki/Johnson–Nyquist_noise
But there's an additional
extrinsic noise that is
dependent on the resistor's composition, sometimes called excess noise, flicker noise, or "1/f" noise. (This 1/f noise also arises in transistors and opamps, you may have seen a datasheet where the noise rises at low frequencies.). See
https://en.m.wikipedia.org/wiki/Flicker_noise although they don't describe it's origin (it can have many). The noise density is higher at low frequencies, so it's most audible there - it's a kind of "pink noise" (if you think of red as lower frequency, then more red added to white gives pink) There is no general equation for this excess noise, as it depends on the detailed construction of the resistor. In a metal which conducts well, this excess noise is typically very low for the audible frequency range. Hence metal film resistors tend to have low excess noise, so their overall noise in the audible range is dominated by intrinsic Johnson noise. But carbon is not a good metal, there's a lot of internal electronic tunneling and hopping going on which generate excess noise. Thus carbon resistors generally have high 1/f noise, which is added on top of the Johnson noise. Add some gain on this, and you'll hear the pink noise "hiss", i.e., it has more low frequency noise than "white" noise.
Bottom line: there just is no mojo for resistors, only excess noise. So go with metal film resistors, because they're quieter.
(Edited a typo)
