NEW YORK, NYZ.- A key relic of the genesis of Giacomo Puccini’s two operas set in Asia can be found not in Italy, where both works premiered, nor in China or Japan, where they are set, but — of all places — in Morristown, New Jersey.

There, in the Morris Museum’s collection of mechanical musical instruments and automata, is a music box from around 1877. During a visit to the museum in 2012, musicologist W. Anthony Sheppard happened upon the box and, listening to it, was surprised to find that it contained melodies present in those Puccini operas, “Madama Butterfly” (1904) and “Turandot” (left unfinished at his death in 1924).

Sheppard and other scholars came to believe that the box — made in Switzerland, exported to China, returned to Europe and owned in Italy before it was acquired by the brewing heir and prodigious collector Murtogh D. Guinness and donated to the Morris Museum — may have been the exact one that Puccini encountered at a friend’s home and quoted in his classic works.

This plain brown music box is therefore central to the ambivalence that lately surrounds Puccini, “Madama Butterfly” and “Turandot,” and the amorphous label of appropriation that has been applied to both. It reminds us that Puccini, who was always searching to endow his scores with “local color,” didn’t just compose exotic-seeming, faux-Asian tunes for his operas, but also sought out actual Asian examples. These works are tributes to the curiosity about other cultures — the desire to blend your traditions with others’ and tell stories about more than just yourself — that has animated art for as long as humans have been making it.

“When the heart speaks, whether in China or Holland,” Puccini wrote to one of his “Turandot” librettists, “it says only one thing, and the outcome is the same for everyone.”

But the box, with its reed organ that tinklingly plays six Chinese tunes off a cylinder, is a testament, too, to the messiness of cultural borrowing; it is clear, for example, that Puccini had no problem using melodies from China and Japan in his depiction of Cio-Cio-San, the Japanese protagonist of “Madama Butterfly.”

He was interested in authenticity — but only to a point. He and most of his audience didn’t (and still don’t) know or care about the specifics of this material much beyond it being identifiably “Oriental.” Joseph Kerman, in his influential 1956 book “Opera as Drama,” lambasted the “bogus Orientalism” of “Turandot” that is “lacquered over every page of the score.”

So what are we to make of “Madama Butterfly” and “Turandot”? These two sumptuously dramatic operas remain among the most popular in the world; both are playing at the Metropolitan Opera this spring.

With increased sensitivity in recent years to the dynamics of cross-cultural representation — who gets to tell which stories, and how — the works have come under new scrutiny for propagating stale racial tropes and for using musical styles that weren’t Puccini’s to take. The announcement of an upcoming Opera Philadelphia run of “Butterfly” seems to apologize for the production’s very existence, offering fretful assurances in the very first sentence that the staging “illuminates and ultimately transcends harmful stereotypes.”

Other American companies have anxiously adjusted “Butterfly” to make it obvious that they are aware of this discourse. Last year, Cincinnati Opera framed the work as the imaginative leap of a video-game-playing young man, to suggest that both the male lead and Puccini are white men fantasizing about Japan. New Orleans Opera rewrote the ending entirely in an effort to empower the main character, who lives instead of killing herself. Some European productions of “Turandot” have dispensed with its legendary-times setting in favor of starker, tougher, more overtly anti-Orientalist aesthetics.

“Madama Butterfly,” though, is hardly credulous about the power imbalance in the encounter it depicts: A caddish American naval officer marries Cio-Cio-San, then swiftly abandons her to go back to his country, returning to Japan three years later to take their young son. With “The Star-Spangled Banner” blaring in ironic fanfare near the start, this is an anti-imperialist, even anti-American tragedy.

Puccini isn’t ambiguous about the relative morality of his heroine and villain. Indeed, he cloaks Pinkerton, the American officer, in the seductive musical armor of the traditional tenor lover, a Rodolfo to Cio-Cio-San’s Mimì, as if to implicate the whole Italian opera genre in the man’s grotesque actions.

Of course, even sympathetic depictions of cultural “others” can participate in stereotyping them, and perpetual victimization is its own stereotype; just because “Butterfly” shows an Asian woman being betrayed doesn’t mean it truly empathizes with her. But in Cio-Cio-San, there is more than just a reinforcement of the trope of the demure, passively abused geisha; she has, as musicologist Arthur Groos wrote in 2016, “a complexity of character unmatched in fin-de-siècle Italian opera.”

That complexity emerged from the seriousness with which Puccini approached his work on “Butterfly,” which was, as Mary Jane Phillips-Matz writes in her biography of the composer, “so different from everything he had written.” After he decided to adapt David Belasco’s play “Madame Butterfly,” which he saw in London in 1900, Puccini researched Japanese music and asked the wife of a Japanese diplomat in Rome for help with sources. He discussed matters of style with Japanese soprano Tamaki Miura, who would go on to sing over 2,000 performances of “Butterfly.”

The melody of “Echigo-Jishi,” a well-known piece for the koto, a traditional string instrument, was incorporated into the score in the passage when the marriage broker Goro announces the entrance of Cio-Cio-San and her friends in the first act. “It is played by staccato violas, cellos and bassoons in unison,” Groos writes, “gesturing toward the plucked strings of the koto and the Kabuki accompaniment of shamisen and flute that Puccini had heard when he saw Japanese actress Sadayacco perform the piece in Milan in late April 1902.”

“Turandot,” based on an ornate 18th-century fairy-tale drama by Carlo Gozzi, exists in a wholly different theatrical universe than the Belasco-esque, naturalistic 19th-century melodrama of “Butterfly.” Its playfully fabulistic setting — a magical rather than realistic Peking — has to be understood to accept what might seem like offensive oddities: a dragon-lady protagonist and three court ministers named Ping, Pang and Pong.

But even the haughty, bloodthirsty Princess Turandot explains herself and the painful sources of her rage, and the seemingly interchangeable trio of ministers gets a surprisingly tender, individualized scene at the beginning of Act 2. For the score, Puccini borrows melodies from the Guinness music box and at least one other box owned by a family he knew. A source told Phillips-Matz that Puccini wrote to Giulio Gatti-Casazza, the general manager of the Metropolitan Opera and a friend, asking him to visit Manhattan’s Chinatown and return with musical examples he could use in the opera.

Here and in “Butterfly,” the result was more sophisticated and moving than standard-issue, window-dressing Orientalism. (There’s far more authentic material in these operas than in, for example, Bizet’s “Les Pêcheurs de Perles” or Delibes’ “Lakmé,” both set in South Asia.) The intensity of curiosity in Puccini’s two operas comes through, as does their interest in using musical research to create a vision of Asia that included characters whose interiority and intricacy Western audiences would be forced to recognize and empathize with.

Puccini’s universalism was sincerely felt, even if it’s unfashionable today, and it deserves to be appreciated rather than cynically apologized for — as some opera companies seem to do while continuing to reap the ticket-selling benefits of his popularity.

It’s helpful to remember that we are dealing here with Italian operas about Asia, not with Asian operas. I think audiences understand this distance even without specific directorial strategies that emphasize it. But such techniques can be effective; the Met’s sleek and lacquer-shiny current production, originally directed by Anthony Minghella, affectingly represents Cio-Cio-San’s son with a Bunraku puppet, constantly surrounded by operators draped in black.

Something similar will be attempted in the upcoming Opera Philadelphia staging, directed by Ethan Heard, in which Cio-Cio-San will be represented by a doll, separate from the soprano. That soprano will be Karen Chia-ling Ho, who is Taiwanese; the doll’s puppeteer is Hua Hua Zhang, who was born in Beijing.

If Puccini was guilty of conceiving Asianness as a monolith, then, he isn’t alone. What is so different about a Taiwanese soprano being thought of as right for “Butterfly” versus Puccini using Chinese melodies in addition to Japanese ones in the score? (And interest in such matters is spotty: The accurate representation of Roma people is not a part of most “Carmen” stagings or casting decisions.)

I regularly hear from white audience members about their faint embarrassment at watching the glittering explosion that is Franco Zeffirelli’s Met production of “Turandot,” a staging first seen in 1987 that actualizes the fairy-tale dream of China that the opera’s creators intended.

But assuming that the whole thing is ersatz — and therefore more or less unacceptable — may itself be the ignorant position. After all, the production’s dances were created by Chiang Ching, described in The New York Times in 1979 as “a choreographer who fuses her own Chinese cultural background with the American modern‐dance currents around her.”

What’s brushed off as appropriation can be a more complicated and interesting story than the one that is told.

This article originally appeared in The New York Times.