Starting with Dioclesian in 1690, Purcell began to increase the significance and length of the musical sections of the plays to the point that they required as much time as the spoken portions. This prompted Purcell's contemporary Roger North to call Purcell's works "semi-operas." Purcell's incidental music for "The Tempest" was part of an already established tradition of reinventing Shakespeare's plays for the musical stage. In 1667, poet John Dryden made modifications to "The Tempest," adding characters and augmenting it with incidental music. Thomas Shadwell revised Dryden's version in 1674, inserting two masques with musical contributions from several composers, most importantly, Matthew Locke. This seems to have been the preferred version until sometime in the 1690s, when it was supplanted by a new, Italianate setting, anonymous but ultimately attributed to Purcell.
In recent years, serious doubt about Purcell's authorship of the music for The Tempest have arisen. Much of the string writing resembles that of Arcangelo Corelli more than anything else Purcell composed. The complete da capo arias in the Italian style are unlike those composed by Purcell at the end of his life. Scholars agree, however, that the song, "Dear pretty youth," is indeed by Purcell. It is thought that most of the music was composed by Purcell's student, John Weldon, in or around 1712. There are similarities between some of the music in The Tempest and other examples of Weldon's music for the stage; however, some find The Tempest to be of far greater quality than anything else Weldon composed. It may never be known for certain who wrote most of The Tempest.
The vocal sections of Purcell's semi-operas were often cast as self-contained "scenes," enabling coherent performance outside the theater. The overture to The Tempest is a contrapuntal delight, with fugal entries featuring an inverted version of the subject. The incidental music begins with the masque of devils in the second act, containing the most famous number of the piece, the da capo aria, "Arise, ye subterranean winds," with the word "Arise" set to upward leaps. Italian influence is clear in the appearance of an instrumental interlude after the first line of text. Also, melismas are on accented syllables and set to long vowels. This Purcell also learned from Italian practice. The dance following "Arise, ye subterranean winds" is from the Prologue of Lully's Cadmus et Hermione. Four more songs appear in Act III and two dances and the song, "Dear pretty youth" take place in Act IV. Among these, "Æolus, you must appear," is notable for its instrumental symphony and "Halcyon days" is an excellent da capo aria featuring a solo oboe. In Ariel's "Dry those eyes," Purcell avoids the potential monotony of the ground bass by introducing the instruments at different points in the aria. It should be: In "Full Fathom Five," we hear an imitation of bell sounds in both the continuo and chorus. It is not certain where the two dances, "The Devil's Grand Dance" and "The Sailor's Dance," belong in the second act.