Puccini’s Madame Butterfly, derived from a play by the American author David Belasco, has a disturbingly true-to-life story. In the wake of the opening of Japan to trade with the United States in the 1850s, a cynical young naval officer, Lieutenant Pinkerton, marries a naïve fifteen-year-old geisha, Cho-Cho-San, whom he calls “Madame Butterfly.” He then sails away with no intention of honoring the Japanese ceremony. Cho-Cho-San persists against all evidence in hoping he will return; but when he eventually does, he brings his “real” American wife with him, and Cho-Cho-San, now mother of Pinkerton’s child, kills herself.

During Act II, in response to her maid’s doubts, Cho-Cho-San sings the opera’s most famous number, “Un bel dì,” spinning a fantasy about Pinkerton’s return. From the hills (she imagines) they will first see a little wisp of smoke, as the gunboat appears on the horizon. She sings this vision to a memorable melody that has a floating, disembodied quality in keeping with the fantasy it portrays — partly because it begins high in the soprano’s range and slowly descends, partly because of its delicate orchestration.

After this melody, the aria takes on a freer formal cast. Cho-Cho-San sings varied music that mixes full-fledged melody (at “Poi la nave bianca . . .”) with something closer to a recitative-like declamation (at “Mi metto là sul ciglio . . .”).

But when she comes in her fantasy to the moment of remeeting Pinkerton (“Per non morire . . .”), she sings her heart out to a reprise of the aria’s opening melody, now louder and with redoubled, brass orchestration. It is a stroke of almost unbearable pathos, for it dramatizes the helpless growth of her fantasy. Originally linked to the hope that Pinkerton’s ship would return, now the main melody expresses her joy at his reunion with her — which is sheer delusion. Puccini underscores the pathos when, at Cho-Cho-San’s last words, the orchestra takes up the intensified melody once more to end the aria.