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Bang was born into a noble family of Asserballe, on the small Danish island of Als, the son of a South Jutlandic vicar (a relative of N. F. S. Grundtvig).
The seat of the duke was Sonderburg, but parts of the domain were located in Denmark (in the Duchy of Schleswig), mainly on the islands of Als and Ærø and around Glücksburg, whilst other lands were part of the Holy Roman Empire (in the Duchy of Holstein), including the Ämter of Plön, Ahrensbök, and Reinfeld.