It seems there is an increased interest in dying fabric to get specific desired colors. So a brief tutorial about the art and science of dying. Technique varies by product and base fabric so I won't be getting into that. But there is a basic knowledge set that is helpful to understand.
First of all, if you are matching colors on the internet you are on a fool's errand. The chromatic reproduction on a digital screen is subject to a number of variables you have absolutely no control over. Color reproduction depends on the style/quality/make and settings of you monitor. If you want a specific color use _only_ properly standardized color chips that you can hold in your hand.
Colors are standardized according to the Pantone Matching System (PMS). There is a different set of formulas for inks and dyes. The Pantone Textile system is what you want for fabric colors. The other system will give you ink formulas for printing. But the PMS color numbers are the same in each system. Only the formula changes.
Pantone colors are used by printers and artists to make sure the color reproduced is the same color desired. The mixture of different colors in the proper proportion is the science behind dying or printing. Thus it is the formula that is important to the manufacturer or artist.
Once you have the Pantone number you can begin the process of trying to find a dye that will produce that color. Dye manufacturers and distributors should be of assistance in this regard if you ask the right questions. Rit has a formula calculator that will approximate any particular pantone color. But, that calculator is linked to the Rit dyes and may not be transferable to other manufactures. Dye formulas are often very proprietary. Different products will give different results unless the Pantone color is stated on the packaging.
Pantone color numbers can be found from the companies who publish logo charts. Or any printshop should have the latest Pantone color chips which can be matched to a sample. But always do so under the predominant light where the item will be used. For normal gear purposes that would probably be natural lighting. Beware of Fluorescent or incandescent lighting as they have their own unique color shift.
There's the science behind the process. The art comes in the form of technique and knowledge and usually can only be achieved by practical experience.
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