Imagine administrators and Rajput princes riding on elephants through the arcade as far as the Naqqar Khana (Drum House), where the imperial band played and visitors were obliged to dismount.
The imperial band would follow the princes as they played. 
mnli hypothesis: The imperial band would follow the princes as they played.  premise: Imagine administrators and Rajput princes riding on elephants through the arcade as far as the Naqqar Khana (Drum House), where the imperial band played and visitors were obliged to dismount.