So I see often on here the advice that you shouldn't mix paints with black, and that art students are discouraged from buying paints that are anything but red, blue and yellow.
Today I was actually painting with acrylics for the first time in years, and so, remembering that blue is darker in value, used that to help me with the shadows. It was certainly a lesson, lol.
But what if you want a colour that's darker than the blue paint allows? And how do you stop colours from being overly bright and saturated? Is using white considered acceptable, or is it discouraged just like black?
Black and white are just colors like all the other colors you use. Once you understand that, it makes it easier to use them in your palette. Depending on the type of white or black the effect they have on the other colors shifts them so they are no longer the same hue. For example mixing yellow with ivory black in paint will darken the yellow but also shift it and give you a green hue. The problem with beginners is they see black and white everywhere even when it isn't actually there.
What you want to teach yourself then is to mix hues and achieve the desired result. Learning what all the components of color are and how they interact and affect the outcome of your mixing is what is important. Some mixes lessen chroma quickly, some slowly, learning the combinations teaches you how to control your palette and the hue, chroma and value of all your colors. The way you learn is by making color charts and value charts of all the pigments on your palette.
//Disclaimer: This user (sadly) ha close to 0 experience with oils and acrylics.//
I don't really see a problem with using black and white to mix other colors -if you use pure black or pure white though; that would be a problem. But as dpaint has said, the two are just colors like every other. As long as you know how to use them it's no issue. And to know how to use them you've gotta start working with them in the first place -right?
With acrylics if you don't use at least white you're pretty much screwed. Try mixing blacks, you can get beautiful warms and cools. Alizarin Crimson mixed with Pthalo Green makes a beautiful cool black and Ultramarine Blue with Burnt Sienna mixes to a warm black.
Dpaint gave some great advice. Acrylics can be used in so many ways, like oils, so you also need to determine how you will develop color on your surface. Directly by mixing and painting or glazing. Know how to mix is critical with both but more so with direct alla prima etc.
Once you get good I can share some real acrylic secrets with you.
Further discussion on using and not using black:
The only way not to use white paint is to paint transparently on a white surface. Some traditional watercolorists can get down right fascistic about this (disallowing any piece with opaque paint from shows and competitions, etc). This is silly.
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If you look at painters throughout history you'll find that the vast majority of them had at least one actual black pigment on their palettes. Click down to the links to individual artists on this site for tons of examples:
The instruction to not use black seems to be a hallmark of teachers who haven't learnt to think of mixing colours as moving through colour space:
While I don't have much experience with acrylics, one thing I learned with watercolor is to mix a color's opposite to achieve deep shadows. For example, if I have something red mixing the red with green will give a very distinct shadow color. Hope that helped a bit!