When I use the Mixer brush in Photoshop CC, banding occurs on the background(s). It was suggested that I add a bit of noise but I dont want noise in hte image. Suggestions to fix this.
First of all you need to work in 16 bit color depth. In 8 bit depth you will get banding, since you only have 256 discrete steps.
Any banding you see in 16 bit files is in your display system. The monitor still works in 8 bits (usually), but with a good display those steps should be evenly distributed. If they aren't, the problem is either the panel itself, any calibration tables in the video card, or a bad display profile.
It doesn't take much noise to break up banding. Keep in mind that any photograph, however fine grained, will have enough noise to conceal banding. It takes a very bad display indeed to show banding in a photograph.