Special meetings of the Council may be called by the City Clerk on the written request of the Mayor or any three members of the Council on twenty-four hours written notice to each member of the Council, designating the purpose of such meeting and served personally or left at his usual place of residence by the Clerk or someone designated by him; but any special meeting at which all members of the Council are present or have waived notice in writing shall be a legal meeting for all purposes without such notice.