Warm Vs CoolThis is one of the most basic classifications of colors, but here's actually competing theories of what qualifies as what
Everyone agrees that cool colors are colors that contain blue (green, violet, etc)
Logically if half the spectrum is cool than the other half is warm, making the warm colors be red, orange, yellow, with neutrals being red-violet and yellow-green (as well as the true neutrals black, white, brown/mud)
However, some claim that if cool colors contain blue, then warm colors contain orange. This sounds like the same thing, but yellow and red make orange, they are not made of orange. I rather prefer this classification because some pinks look cool as well as some yellows.
Whichever you agree with doesn't really matter as its all vague and gets more complicated with more complex colors than are found on the basic color wheel.
How to use warm and cool
Light/shadowUsually warm colors occur in the light, while cool colors will occur in shadow. This can be used for shading, though a more complex explanation will be found later.
Atmospheric PerspectiveAtmospheric perspective is most often used in landscapes and was created before linear perspective. Painters found that things farther away became hazy and gained an blue/gray haze. Those items in the foreground had more detail, higher contrast, and had warmer hues.
Examples:
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