The art museum board shall consist of not to exceed seven (7) members, appointed by the mayor with the approval of the board of commissioners of the city, and not to exceed five (5) members ex officio as may be provided by ordinance. The official members of said board shall be designated by the board of commissioners of the city to serve one for a term of one (1) year, two for a term of two (2) years, two for a term of three (3) years, and two for a term of four (4) years, and thereafter as their terms expire the members of such art museum board shall be appointed and hold their offices for a term of four (4) years and until their successor or successors shall have been appointed and qualified. Ex officio members of the board shall have a voice but no vote in the deliberations of the board. Vacancies on the board shall be filled for the unexpired terms.