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Duke of Perth has never been an official Scottish or British title. It was granted to James Drummond, then Earl of Perth, by the deposed and exiled King James II and VII in 1701, although some sources give 1695. The Drummonds remained loyal to the Stewart cause and the 2nd Duke was, as they say, »out« with the Old Pretender in 1715. Both of his sons were with Bonnie Prince Charlie in 1745. The 3rd Duke died on board a ship fleeing after Culloden and his brother, the 4th Duke, died in fighting in Holland in 1747.

The family tree gets very complicated after the 4th Duke but John Drummond, currently 9th Earl of Perth is accepted as the Jacobite 15th Duke of Perth. 
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If you have a spare 39 seconds, here is an interesting clip of the Duke of
Perth being danced in Glasgow circa 1964   Only one time through, alas.
<<http://ssa.nls.uk/film/3270>>  The caption says Highland dancing. . .but it lies.  It's SCD.