Traditional fabric printing uses a series of passes by a single color ink at one time to produce the design. Just like spot colors in printing, each ink adds to the printing costs. For that reason, if fabric is to be screen printed (you'll also hear the term "spot color" used for this), you need to keep your colors to the absolute minimum. This is in contrast to most commercial printing that produces its colors by a combination of Cyan, Magenta, Yellow, and Black inks. In photographic (or continuous tone) printing process, it isn't necessary to limit your palette. If you need to produce a limited color palette, however, you can do that most easily to choosing colors you want that can range in value from dark to light. A printing press lays down one color at a time (even in CMYK printing) and does this by creating halftones or screens that tell the press how to space the dots of color. Below, I created a black to white gradient in Photoshop and then, under, changed it to a halftone (which would be finer and more subtle in reality).
You can see how the black dots seem to separate as as the screen becomes lights. That's what occurs on press as the ink fills the image. For a 6 color print, the complete image requires 6 passes through the printer. To keep your colors clean, you don't want to mix up colors as you would in CMYK printing; you don't want them to blend on press.
So, how do you go about choosing and using a limited range of colors in Adobe Illustrator? In the video below, I show you how to choose colors off of a target image. There are so many ways to pick colors; this is just one of them. However, once I've selected a color, I then define it as Global color to get easy access to the all the tints possible from the base color. Take a look! Please ask me if you have any questions about this. I will answer all comments as soon as possible.
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