Here is the render with the upper half using noise and the lower half not using noise. You should be able to see the bands in the lower half, but not in the upper half. Or perhaps the upper you can still see them but they are weaker. As I said, my laptop screen is not so good, so to me the upper half looks band-free.

A really good monitor produces exact and precise luminance for every pixel. A cheap or old monitor will naturally produce its own "noise" and is unable to make two pixels exactly alike given the same value. Thus, bad monitors introduce the noisy luminance automatically and hide this effect from you.

Because I know of this effect, I always (ALWAYS) use a slight bit of luminance noise on any wall that has a simple constant color on it.

If there is a pattern of any kind (color, luminance, or bump) you don't need to do this.

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Renderosity forum reply notifications are wonky. If I read a follow-up in a thread, but I don't myself reply, then notifications no longer happen AT ALL on that thread. So if I seem to be ignoring a question, that's why. (Updated September 23, 2019)