An Etymological Dictionary of the German Language/Annotated/Gaden
Gaden, Gadem, masculine and neuter, ‘room, cottage, storey,’ from Middle High German and Middle Low German gaden, gadem, neuter, ‘house containing one room only,’ then generally ‘apartment, chamber,’ Old High German gadum, gadaum, neuter; originally a merely Upper German word, which found its way, however, even into Low German. Akin to Gothic *gatm (from ga- and tmo-, the latter related to Greek δόμος, μεσό-δμη, and High German Zimmer)?. Less probably allied to Anglo-Saxon geat, English gate (compare Dutch gat, ‘opening,’ under Gasse). At all events, the connection with Greek χιτών, ‘garment,’ is impossible.