Fabric named for a Mideast capital (6)

I believe the answer is:

damask

(Other definitions for damask that I've seen before include "Silk or linen material woven with pattern on either side" , "heavy embossed table linen" , "Patterned table linen" , "Reversible fabric - type of rose" , "Table linen material" .)

I've seen this clue in The New York Times.

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