Where an election is to be called as provided in Section 57-3-11, notice of such election shall be signed by the clerk of the governing body of any municipality, and shall be published once a week for at least three (3) consecutive weeks, in at least one (1) newspaper published in such county. The first publication of such notice shall be made not less than twenty-one (21) days prior to the date fixed for such election and the last publication shall be made not more than seven (7) days prior to such date. If no newspaper is published in such county, then such notice shall be given by publishing the same for the required time in some newspaper having a general circulation in such county, and, in addition, by posting a copy of such notice for at least twenty-one (21) days next preceding such election at three (3) public places in such county.