How does Shakespeare portray Macbeth as a tragic hero, specifically with reference to noble status, hamartia, and peripiteia?
Shakespeare's Macbeth is a classic example of a tragic hero as defined by Aristotle.
One characteristic of a tragic hero is that he must be a "great man," or of noble status. Macbeth is a highly regarded war hero. In Act I, Scene 2, the Sergeant describes his prowess on the battlefield to Duncan and Malcolm. Amidst the mayhem and chaos around him, the blood and death, Macbeth is totally focused — without concern for his own safety — on reaching Macdonwald, the traitor, and killing him with purpose and precision:
For brave Macbeth — well he deserves that name —
Disdaining fortune, with his brandish'd steel,
Which smoked with bloody execution,
Like valor's minion carved out his passage
Till he faced the slave,
Which ne'er shook hands, nor bade farewell to him,
Till he unseam'd him from the nave to the chaps,
And fix'd his head upon our battlements (17-25).
Macbeth is also advancing in the ranks of Duncan's court. For his valor, the King — with promise of future honors and compensation — rewards him. Macbeth is also the King's cousin and well-loved by him. He is also highly regarded in the Scottish ranks.
Another characteristic of a tragic hero is hamartia. Hamartia is a "tragic mistake, misconception or flaw."
Macbeth, easily tricked by the witches, takes matters into his own hands so that he will become king, as they appeal to his obsessive aspirations for power. He admits he has little real purpose for his bloodthirsty behavior. He has, after all, everything he could want as Duncan's subject, friend, and cousin. His tragic flaw is his "vaulting ambition."
I have no spur
To prick the sides of my intent, but only
Vaulting ambition, which o'erleaps itself,
And falls on th'other (Act I, Scene 7, lines 25-28).
Peripiteia is defined as "a sudden turn of events or an unexpected reversal, especially in a literary work."
The most obvious reversal of events takes place in Act V when Macbeth realizes the witches told him half-truths to win his soul to eternal damnation, as Shakespearean audiences believed regicide was a mortal sin. Until now, the first predictions (becoming the Thane of Cawdor and becoming king) were easily enough won. Macbeth is rewarded with his new title (Cawdor) by Duncan. Becoming king is something Macbeth and Lady Macbeth orchestrate by murdering the King while he stays at their home. While the first set of predictions lure Macbeth in, the second set of predictions give him a feeling of invincibility. He is told to beware of Macduff, which leads Macbeth to have Macduff's family killed. The second prediction notes that no man born of a woman can harm Macbeth. (In theory, that would mean no one ever born could defeat Macbeth.) The third prediction notes that Macbeth will not be vanquished until Birnam Wood moves to Dunsinane Hill. Trees don't, technically, move. The double-speak used by the witches encourages Macbeth to take what they say literally. However, the witches are speaking figuratively with the intention to trick Macbeth. Macduff was not "born" by traditional means, but delivered by Caesarian section; so he was born, but not the way most people are (Act V, Scene 8, lines 17-20). The trees do not move, but soldiers advancing while camouflaged by rough-hewn branches give the appearance of the woods moving (Act V, Scene 4, lines 6-9).
Macbeth has staked all on the witches' equivocations. Once they have tricked him into totally believing their empty promises, Macbeth is defeated. His destruction lies in the details of circumstances he perceived to be set in stone. These details bring about a complete reversal to the plans of greatness Macbeth anticipated for himself, and bring to fruition the ultimate demise of a once-stalwart hero and trusted friend. Everything rests on Macbeth's insatiable, driving ambition to be and have more.
Citing these three characteristics, Macbeth is a tragic hero in the purest sense.