The tartan is a colorful woven cloth that traditionally denotes allegiance to or membership of a family clan in the Celtic world. The pattern of a tartan is made up of four basic elements. The first and most important is the "sett," which is the basic set of colored threads used in the design. The "reverse" is the mirror image of the sett, and the "repeat" starts the pattern over again. The "pivot" is the point in the pattern where the sett meets the reverse and the reverse meets the repeat. This pattern is woven horizontally into the vertical pattern to produce the tartan pattern.
Identify the first pivot. You should look at a larger piece of cloth and find the point where a mirror image is created. It doesn't matter if it is the pivot between the sett and the reverse or the reverse and the repeat. They can be labeled appropriately later.
Identify the second pivot. Starting at the pivot you have already identified, follow the pattern until the next mirror image is identified. This may appear identical to the first pivot if the sett and reverse are identical---that is, if the sett's mirror image is the same as the sett.
Count the colored threads in the sett or reverse. If you have them interchanged, it will be easy to correct when you look it up.
Look up the sett pattern in a tartan weaver's reference. This will tell you the exact number of each colored thread required in the sett to weave a certain pattern, which is usually identified by clan name. If you do not have a reference like this available, you can visually match the sett and reverse against pictures of tartans.