Magic is, without a doubt, among the strongest themes in The Tempest. Every major plot point in the play is either officiated by Prospero's potent art or set up with the assistance of magic, resulting in such a supernatural force being the main impetus with which the play moves. You will see it everywhere in any reading of the play (that is, if you're actually reading it). Magic and the Supernatural as a theme encompasses both the influence on elements of the natural world and events through some form of mysterious ability and the occurrences of mysterious events by some seemingly arcane or extramundane influence.
As stated previously, the play is heavily reliant on Magic and the Supernatural. As a matter of fact, the play begins with an event incited by Prospero's magic (although it isn't learned to be so until the following scene). The titular 'tempest' in the first scene is actually an illusion fabricated by Prospero's magic and executed in part by his servant spirit Ariel:
"Now in the waist, the deck, in every cabin
I flamed amazement. Sometime I'd divide
And burn in many places - on the topmast,
The yards and bowsprit would I flame distinctly,
Then meet and join. Jove's lightning, the precursors
O'th' dreadful thunderclaps, more momentary
And sight-outrunning were not; the fire and cracks
Of sulphurous roaring, the most mighty Neptune
Seem to besiege and make his bold waves tremble,
Yea, his dread trident shake."
Magic is also seen in other spectacles throughout the play, such as when Ariel descends upon the banquet table (brought in earlier) to condemn the "three men of sin" there from a falsified position of authority as an agent of destiny. The group of hunters and dogs which chase Caliban and his trio offstage are also a magically-fabricated illusion.
Ariel's invisibility is another aspect of magic in the play, allowing Prospero to direct the spirit to spy on the noblemen on the island or manipulate them from the guise of invisibility.
The common thread among these seemingly unrelated spectacles in the play is Prospero's painstaking hand in all of them. His magic is used almost exclusively in the manipulation of the other characters in the play, either in affecting their mental states or forcing them to fall into the machinations of his plan for revenge.
Prospero's Magic
Prospero’s magic, frequently referred to as his “Art,” represents an overwhelming power which holds both his servants to his command as well as fabricates the impetus with which the play moves. Armed with his magic garment, staff and wealth of esoteric knowledge garnered from his books, he is the most objectively powerful being in the play.
One of the most considerable uses Prospero employs for his magic is in the discipline of his servants. The assured potency of his “Art” guarantees him manipulation of the elements and natural world. Thus, when Ariel becomes impatient about his promised freedom, he can threaten imprisonment of the spirit akin to that from which he was freed.
In the same vein of manipulation and discipline of his servants, Prospero regularly uses his magic to persecute the often rebellious and abrasive Caliban- “for every trifle,” as he says. Caliban’s acknowledgment of Prospero’s formidable ability to set his spirits upon him and reduce him to a throbbing mass of aches and pains (communicated through an aside) shows the authority/power Prospero is able to maintain through his magic:
"I must obey. His art is of such power it would control my dam's god Setebos."
Of course, Prospero does not only use his magic to persecute his servants, but also in manipulating the courtiers on whom he plans to exact his revenge. For example, he makes himself invisible to observe the trio of traitors while Ariel impersonates the authority of destiny to persecute them. His magic is also used when Ferdinand draws his sword on him to charm him to momentary paralysis. The masque starring Iris, Ceres and Juno for the blessing of Miranda and Ferdinand's bond is also a use of his magic, though it is as an exhibition of his art in celebration of their love.
Ariel as as Instrument of Magic
Ariel is the magical being through which Prospero is able to create the iconic spectacles and manipulations throughout the play, working as a faithful servant- apt to carry out every task he is given.
The airy spirit assumes invisibility to all but Prospero for most of the play, and it is through this small magical detail that much of Prospero’s contrivances are realized: the song that he sings to Ferdinand to cause the lonely son despair, the song he sings to wake Gonzalo to prevent the king’s death, the song he sings to lead Caliban and his party astray, and even the comedic use of Trinculo’s voice to stir up conflict among the prospective usurpers are all done while the spirit is invisible.
Ariel also uses song throughout the play from his conveniently invisible state to influence the actions and mental dispositions of those on the island according to his master’s instruction.
In this way, Ariel’s songs are simultaneously a dramatic technique in and of their own musical significance, but also through the interesting dramatic irony created by the different meanings the songs have to the oblivious victims and the informed audience.
The most notable of Ariel’s uses of magic in the play are the two spectacles which represent the play’s most climactic points; the first being the tempest, and the second being Ariel’s appearance as a harpy in Act 3 Scene 3.
In creating the tempest, Ariel ‘flamed amazement,’ fabricating the lightning, thunder and flames of the storm to make their wreckage more believable.
At the ‘banquet,’ Ariel’s sudden descent upon the table, coupled with the lightning, thunder and harpy-like appearance created by way of magic, is able to convince the courtiers that some supernatural force truly aims to recompense them for their perfidy.
Devices Portraying Magic and the Supernatural
Dramatic Irony
Dramatic Irony is the device seen to most commonly aid in the portrayal of Ariel’s magic. In the play, Ariel is given orders to make himself invisible to everyone besides Prospero. Because of this, only Prospero and the audience are aware of Ariel's presence and interference in the events of the play whilst the other characters remain oblivious.
Act 3 Scene 2: Ariel mimics Trinculo’s voice while Caliban attempts to explain the details of his plot to Stephano, repeating “Thou liest” at spaced intervals to stir up conflict within the trio. The usurping trio is unaware of Ariel’s interference, leading to Stephano and Caliban’s increasing annoyance with the jester.
Music/Song
Act 1 Scene 2: Ariel’s song “Full fathom five thy father lies” is sung from his guise of invisibility, driving the recently bereaved son further into despair and grief.
Spectacle (with Light and Sound)
The most impressive feats of magical and supernatural manipulation come in the form of Shakespeare’s use of spectacle, ostentatious supernatural éclats fabricated by the magic of Prospero and Ariel. Spectacle involves the use of sound effects, lighting, and occasionally costume to convey the potency of magic within the play.
In Act 1 Scene 1, the titular ‘tempest’ is an example of spectacle portraying magic. The stage directions indicate “a tempestuous noise of thunder and lightning heard.” When combined with the chaotic shouting and mortal peril of the scene, a spectacle, which we later learn has been fabricated by Prospero with the help of Ariel, is created to propel the play into a climactic and tense protasis.
Act 3 Scene 3- Ariel descends upon the banquet table and rebukes the ‘three men of sin’ in a spectacular display of costume, lighting and thunderous sound effects. This supernatural occurrence is meant to trigger the guilt of those at the table, convincing them that the forces of destiny aim to persecute them for their perfidy. This is also an example of dramatic irony, as Ariel’s words are undoubtedly at Prospero’s command, delivered by the spirit only to make the supernatural aspect of this condemnation more believable.
In Act 4 Scene 1, Prospero creates a masque with the help of Ariel's "meaner spirits," staging a performance of mystical dance and song to pronounce his blessing on the marriage of his daughter and Ferdinand.