Take a harp, go about the city
As harlots used to do, that by their music, both vocal and instrumental, they might allure men into their company to commit fornication with them; so Tyre is directed to, or rather this is a prophecy that she should take very artful and ensnaring methods to restore her commerce and merchandise:
thou harlot that hast been forgotten; (See Gill on Isaiah 23:15):
make sweet melody;
or, "do well by striking" F11; that is, the harp in her hand; strike it well with art and skill, so as to make melody, and give pleasure:
sing many songs;
or, "multiply a song" F12; sing one after another, till the point is carried aimed at:
that thou mayest be remembered;
men may took at thee again, and trade with thee as formerly, who had been so long forgotten and neglected.