Obama fiddled while Rome burned.

WASHINGTON — Michelle and Barack Obama sat one table over from J. Lo and Marc Anthony, and all four of them were rocking in their seats as Sheila E. shook the house — well, really the tent.

The latest installment of the White House music series was too big for the East Room, so a high-wattage assortment of Latin musicians sent pulsating, can’t-help-but-bob-along rhythms tumbling out of a giant tent on the mansion’s South Lawn.

As it happens, music of all sorts — rock, jazz, country, classical — has been busting out of the White House all year long.