Irrelevant as Islamic art has seemed to most Westerners until recently, the Persian and Moorish branches have tended to attract what interest there was; who connected culture with the bloody Turks? All the more welcome, then, is this graceful and learned--but not specialized--account of six centuries of Ottoman art by a distinguished historian of Western painting. Because art sprang from the sultan's patronage and changed with succeeding reigns, Levey's narrative is broadly historical; but he will stop you again and again with a specific observation--the comparison of the minaret to the campanile, for instance, which concludes: ""The pointed minaret also happens to be the ideal complement to the swelling shape of the typical mosque--a combination virtually of Gothic and Baroque which is still capable of pleasing in the humblest village version."" Equally arresting are the characterizations of Turkish carpets, miniatures, tiles--or the majestic logic of the Selimye mosque in Edirne, so different from the mysterious norm. An invitation that's its own reward.