I see several probable problems here:
- You use the wrong "primary" colors
- The quality of your paints might be low
- You try to replicate a certain pigment without actually using this pigment
Let's look at this problem from the bottom up (from short to long):
Burnt umber is a certain pigment. It's made out of actual brown earth (I think it contains a lot of rust, but I'm not sure about it). The easiest way to get it would be buying a tube of paint with the correct pigment in it.
Replicating the same color with different pigments is possible, but difficult. Our perception of color depends on the wavelengths of light that a substance reflects. If the physical properties of 2 paints reflect less or different wavelengths, the color looks dull or has a different hue. In general mixed paints tend to be less brilliant than pure paints. If you want burned umber, you cannot get more pure than using actual burned umber.
Low quality paints
If you happen to have one of those standard boxes of school paint, the quality of each single paint is probably low (to keep costs low). One color might be composed of several different pigments, so mixing them often results in muddy or chalky colors.
If you have "studio", "college" or "artist" paints, the quality should be better. They often have only one type of pigment in the paint, a higher amount of pigments and the pigments are much finer than in low quality paints.
But even the highest quality paints don't act exactly like shown in the color wheel, because they contain additives and binders that bind the lose pigment in a usable paint. Especially light colors like yellow often contain additives to make them more opaque. The pigments themselves are colorful dust particles, so mixing one dust with another dust won't yield a perfectly brilliant color. You always lose some brilliance by mixing paints, so using pure paints in the desired hue is generally considered the better option.
The only medium pure enough to mix all colors of the color wheel is ink (given you have the right primary colors...), because it doesn't contain additives to make it opaque. Even the highest quality of paint is by definition too low to mix all colors in a pure and brilliant way.
Wrong "primary" color
This is a very typical error, not only for beginners. In school teachers tell us that the primary colors are red, blue and yellow. Paint boxes contain red, blue and yellow. Collor wheels show red, blue and yellow.
And all of them are wrong!
The real primary colors when using paints are Magenta, Cyan and Yellow.
White light is a composition of every visible color. If you shine a red light at a spot, then add a blue light and finally a green light, the center where all colors add up, is white. This is called additive color. This applies to all TV or computer displays and anywhere where color is made by mixing light.
If you mix red, blue and green paint on a paper, you end up with black, though. Your paints don't work the same way as light. You need to take color away (subtract from the mix) to end up with white. This is called subtractive color. This applies to all printers or paints and anywhere where color is made by mixing substances.
The primary colors of additive colors are: red, green, blue. (RGB)
The primary colors of subtractive colors are: cyan, magenta, yellow. (CYM or CYMK)
(Image source and more detailed information)
And here is another example of CYM color wheel that displays how adjacting colors mix:
You see brown at the center of the wheel, half way between magenta and red. You need to keep in mind that the actual center point of the wheel is black, but wasn't displayed here. So, how do you get to brown?
- Start with magenta and add a little yellow to shift it towards red. This shift will happen at the outer margin of the wheel, because you mix adjacent colors.
- Add in the complementary color (cyan) to shift it towards the center of the wheel. The more cyan you add, the more you shift the color towards the center, which is black.
It might read trivial and you might not understand why magenta is so important if all we did was basically mix green and red to get brown, but the "pure" red already contains too much yellow and adding green puts even more yellow into the mix. If red is your "primary" color, you cannot mix it with anything to remove the yellow from it. Adding more "pure" blue to the mix shifts it further into the black center of the wheel. You have no chance to hit the sweet spot of a warm brown because this portion of the color wheel between red and blue is not available to you.
That's also the reason why you cannot mix violet from red and blue. Red contains a little bit of yellow, which is exactly opposite of blue. By mixing both together you shift the hue towards the black center and end up with an ugly, muddy violet instead of the very brilliant one shown halfway between magenta and blue. You need pure magenta without a hint of yellow to get a beautiful violet without a hint of muddy brown or grey.
Have a look at this Youtube video (sorry it's only in German and her voice is kind of annoying, but she shows the difference between the wrong and right primary colors in action).
At 10:00 minutes, she makes a color wheel with red, blue and yellow and shows how muddy and ugly the colors look.
At 12:00 minutes, she repeats the same process with magenta, cyan and yellow. Look at the difference!