Symbolism, Imagery, Allegory
This play is chock full of music and singing, and it's not just there for our listening pleasure. Throughout Pericles, music is associated with sexual and familial relationships, which can either be harmonious or full of discord.
The first time we hear music is when Antiochus's daughter gets trotted out and displayed to Pericles before our hero takes a crack at solving the riddle (1.1.5). When Pericles solves the riddle and finds out Antiochus's daughter has been having an incestuous affair with her father, he compares her to a musical instrument (a "viol") that gets "finger'd" and "play'd upon":
You are a fair viol, and your sense the strings;
Who, finger'd to make man his lawful music,
Would draw heaven down, and all the gods, to hearken:
But being play'd upon before your time,
Hell only danceth at so harsh a chime. (1.1.81-85)
So, making music is totally a metaphor for sex. Basically, Pericles says that if Antiochus's daughter were married and engaged in a "lawful" sexual relationship with a husband, their lovemaking would be heavenly, instead of "hell[ish]" and sinful. (By the way, in Sonnet 8, Shakespeare makes a famous comparison between harmonious music and healthy family relationships.) Here, Pericles associates the incestuous relationship between Antiochus and his daughter with musical discord.
By the time we get to the end of the play, where Pericles is reunited with his virginal daughter, he swears he hears "heavenly music": "Oh heavens bless my girl! [...] The music of the spheres! List, my Marina"(5.3.223-229). Clearly, this heavenly music is associated with family harmony. It also signals that mournful Pericles has been healed by his reunion with Marina.
By the way, the healing power of music totally reminds us of how Cerimon revives Thaisa with a combination of potions and music: "The viol once more. How thou stir'st, thou block! / The music there! I pray you give her air" (3.2.90-91). Pretty impressive, don't you think?
It's almost as if music is a symbol for life itself: it's there in happy families, it's there in healthy sexual relationships, and it's there when people are brought back to life.