THE LAST LOOK we got at the Textile Museum's collection of some of the world's oldest carpets was in 1972. At that rate, the current exhibition of their 12th- through 17th-century Spanish masterpieces probably will be our last chance at them in the 20th century.

"Our two main missions are to preserve our fabrics and to present them, and there's a built-in conflict," says Carol Bier, curator of the museum's Eastern Hemisphere collections. "We're showing these carpets for seven months this time, which is pushing it a little past what our conservators recommend. Eventually the strain starts to become stretch, and it's time to retire them again."

It is remarkable that these carpets have survived for so long; it's astonishing that many retain textures and colors almost as rich and fine as when the Muslim weavers produced them, knot by tiny knot, in the era when Spain was Islam's last western outpost. While most probably were produced in workshops rather than by women working at home, the formal traditions within which the works are cast are relieved by myriad personal touches that catch the eye and heart; it is plain that the weavers regarded themselves as artists.

Although "fine old carpets" brings Persia and Turkey to mind, most of the finest surviving examples are Spanish. And most of those are in this Textile Museum collection by founder George Hewitt Myers. So fierce was the tugging and hauling among rival collectors that several pieces split down the middle: Three panels from a 15th-century wheel design from Alcaraz went to a Swiss collector, and a piece of another is in Philadelphia.

To the untutored eye the lush fruit of the Spanish looms is very similar to the Persian and Turkish examples the museum has mounted for comparison, but the provenance of the Spanish pieces is indisputable. Spanish weavers, alone in all the world, used single-warp knots rather than gathering several warp threads; the pattern is apparent at a glance, and the difference in feel is such that you can tell them apart in the dark.

Or so they say. One of the trials of a visit to the exhibition is that we must keep hands off these enticing fabrics, which is almost more than a body can bear. The Textile Museum assumes that its visitors will respect the rules and allows a much closer approach to its exhibits than most institutions. So clasp your hands behind your back as you bend close to these carpets; it will make you look sagacious and will keep you out of trouble. SPAIN'S CARPET HERITAGE -- Through October 2 at The Textile Museum, 2320 S Street NW. Open 10 to 5 Tuesday through Saturday and 1 to 5 Sunday; closed Mondays. 667-0441.