When Henry Tudor became England’s King Henry VII in 1485 after decades of civil war, his claim to the throne was shaky. To polish his reputation he spared no expense filling his palaces with art, just like the European monarchs he saw as his peers. It was the beginning of a family tradition. The Tudors, who occupied the throne for a little over a century, left a richer artistic legacy than any previous English monarchs. A brilliant collection of works they commissioned, including tapestries, metalwork, ceramics and illuminated manuscripts, is on display in “The Tudors: Art and Majesty in Renaissance England,” an exhibition opening on Oct. 10 at New York’s Metropolitan Museum of Art.