The "Original Six" is all a myth anyway because those teams weren't the original teams and the league had more than six teams prior to what is now called the "Original Six" era. The league was founded with four teams (the Canadiens, the Montreal Wanderers, the Ottawa Senators, and a team in Toronto that some years later became the Leafs), although that was reduced to three within a couple of weeks when the Wanderers folded after their arena burned down. The Quebec Bulldogs joined the next year and subsequently moved to Hamilton; that team folded after its players went on strike. Meanwhile, the Montreal Maroons and Boston Bruins joined in 1924. The Hamilton team was replaced by the New York Americans in 1925; the Pittsburgh Pirates also joined during that year. Then in 1926 the league added the New York Rangers, Detroit Cougars (later the Falcons and then the Red Wings), and Chicago Blackhawks. That gave the league ten teams.
The Depression caused financial problems. The Pirates moved to become the Philadelphia Quakers but folded after one year; the Senators suspended operations at the same time (today's franchise is not technically related to the original one), returned after one year, then became the St. Louis Eagles and subsequently folded. The Maroons suspended operations prior to the 1938 season and the league never allowed the franchise to be reactivated. The Americans tried to move to Brooklyn but lost so many players to World War II that they also wound up suspending operations; like the Maroons, the league never allowed them back in (purportedly at the behest of the Rangers' ownership) and that left the six teams now called the "Original Six."