No ordinance shall be enacted except upon two readings thereof at separate regular or special meetings (which need not be consecutive) with at least one week intervening between the meetings; provided, however, that at any regular or special meeting of Council, with all members present, an emergency ordinance may be passed at one reading by a unanimous vote of the members of Council declaring the same to be an emergency ordinance. In all cases where it is required by the general law of the State, a proposed ordinance shall be published, as required by law, at least ten days before final passage, and any interested party shall have the right to appear and be heard with respect to the proposed ordinance at a meeting of Council before such final passage. No material amendment may be made in a proposed ordinance after its publication. In addition, Council may also determine, by a majority vote of all the members then in office that ordinances and resolutions with respect to particular subjects (other than those as to which publication is required by law) shall be advertised and that resolutions with respect to particular subject shall not be adopted without a second reading; any resolution containing such a determination shall not be rescinded except by the majority vote of all the members of Council then in office.