The Kodak Workshop Series book “Using Filters” has a good explanation of how colored filters allow light of the same color as that of the of the filter to pass through the filter freely while preventing other parts of the light’s spectrum from passing through.
The contrast controlling filters, such as the Ilford Multigrade filter set, do the same thing with the light from an enlarger lamp.
So long as the paper is variable contrast and the exposing light passes through a contrast controlling filter, variations in the lamp voltage shouldn’t have any effect on the print contrast. For example, in the case of using a variable resistor to reduce the lamp voltage, and therefore the light intensity, even though the spectrum of the lamp is shifted more towards red at reduced voltage, only light of the same color as the filter (or very close to that of the filter) will pass through to expose the paper.
Therefore, we should expect that there will be little or no change in the contrast of the developed print. That was exactly what was reported by the originator of this discussion in post #56.
Whether the light reduction is accomplished using a neutral density filter, a variable resistor, or even a combination of the two, we can adjust the light intensity independently of the lens’s aperture setting. This allows us to make the print using the lens’s optimum aperture in those cases—such as this one—where the exposure time was too short for burning & dodging.