According to the latest Cruise Answerbook from Princess, the normal pattern for a seven-night cruise is two formal nights, one semiformal night, and four casual nights -- but the actual number of semiformal and casual evenings may vary. In particular, an extra semiformal night is likely on cruses that draw a large number of repeat passengers, requiring two separate "Captain's Circle" receptions to accommodate all of the repeaters.
Princess's Cruise Answerbook provides the following guidance for dress (omitting only the misplaced sentences about rental of formalwear aboard ship).
[i] When you're in port, evening dress is casual; slacks, sweaters, blouses, open-neck shirts, etc., are typically worn. Shorts, cut-off T-shirts, "torn" jeans, and bare feet are not permitted in the dining room. For semiformal evenings, passengers dress as they would for a fine restaurant at home, with ladies in skirts/dresses/pantsuits and gentlemen wearing a sportcoat or suit.... On formal nights, ladies prefer evening gowns or cocktail dresses and men turn out in tuxedos, dinner jackets, or dark suits. See chart to the right for a general dress code schedule."
By way of clarification, I should add that the Princess Patter aboard MV Royal Princess specifically stipulated a suit or sportcoat and tie for gentlemen on semiformal evenings during my last cruise, which ended last Sunday.