According to recent research, Tunder was born in Lübeck, not in Bannesdorf or Burg on the island of Fehmarn as was believed by earlier scholars.
Little is known about his early life other than that his talent was sufficient to allow him to be appointed as court organist to Frederick III, Duke of Holstein-Gottorp in Gottorf at the age of 18.
The concerts seem to have originated as organ performances specifically for the businessmen who congregated at the weekly opening of the town's stock exchange.
Along with Heinrich Scheidemann and Matthias Weckmann, Tunder was one of the most important members of the North German organ school; however, few of his works are preserved.
His surviving output suggests a marked preference for the chorale fantasia style, though he is also known for chorale versets, such as his setting of Jesus Christus unser Heiland, notable in particular for the opening pedal flourish (probably the earliest surviving example of an opening pedal solo in an organ work), a technique that was to be more fully exploited by Dietrich Buxtehude.