This month at the Metropolitan Opera, audiences can see and hear, for the first time there in over a century, an opera composed by a woman — Kaija Saariaho's “L’Amour de Loin.” The milestone is shocking — and it can be explained, if not fully justified.

A composer with a desire for an audience has to be in possession of skills that have, on their surface, very little to do with music. He (it was almost always a he) needs to be capable of self-promotion, of fund-raising, of a kind of confidence that makes others follow instructions. Arguably, it’s these adjacent abilities that have been least encouraged in female composers. Then there is the notion, intractable for centuries, that women could perhaps be talented of body — with nimble fingers and a bell-like voice — but never of mind, which is, of course, where composition originates.

Even if they’ve hardly ended up household names, the women in this alternative history of composing are, quite frankly, anomalies: people for whom ambition and talent coincided with privilege and pedigree. Many had musically influential or well-connected fathers and husbands; others had the support of powerful nobles. Changes in geopolitics played a role in their success, as did quirks of history. As Anna Beer writes in “Sounds and Sweet Airs: The Forgotten Women of Classical Music”: “They did not seek out, or seek to create, a female tradition, nor did they wait for a female teacher or mentor. They invariably worked with, and within, a male-dominated musical culture.”

To read about their lives, and to listen to their music, is to mentally catalog everything that went right for them — and to imagine all the forgotten women for whom it must have gone wrong.

The Soul’s Struggle Hildegard of Bingen, circa 1151 play pause “11,000 Virgins,” “Jesu corona virginum” 2:53

By the natural light from a single window, Hildegard of Bingen wrote books on medicine, botany and theology, and corresponded with penitents and popes. Born around 1098 and one of the first known composers in the Western tradition, she spent most of her life sequestered in a remote Rhineland monastery. Dozens of her compositions survive, all with original text, along with her magnum opus: a hypnotic liturgical drama called “Ordo Virtutum,” which tells the story of a struggle for a human soul between the Virtues and the Devil.

Hildegard experienced visions from the time she was a young girl — Oliver Sacks speculated that she suffered from blinding migraines — and people across medieval Europe knew her as a prophet, “the Sibyl of the Rhine.” She claimed to have been uneducated, and her letters suggest a compositional practice inspired only by faith. “Hearing earthly music,” she wrote, “enables humans to to recall their former state.”

For a Court of Women Francesca Caccini, 1625 play pause "La Liberazione di Ruggiero,” Scene 1 1:21

February in Florence was Carnival season, and in 1625 the Medici court was celebrating a recent victory against the overextended Ottoman Empire, welcoming a visit from the Crown Prince Wladyslaw IV Vasa of Poland with opulent feasts and extravagant ceremonies. Francesca Caccini, a 36-year-old composer, was the architect of the day’s signature entertainment: “La Liberazione di Ruggiero Dall’isola d’Alcina,” a comic opera in four scenes, complete with dancing horses and other visual pyrotechnics and a fantastical plot involving warring and seductive sorceresses.

With its juxtaposed arias, canzonets and madrigals, the gynocentric and multifarious opera was the product of a historically exceptional period at the court, dominated first by Caccini’s original patron, Christine de Lorraine, the wife of Ferdinando I de’ Medici, and then by her daughter-in-law, Maria Magdalena of Austria. The original audience for “La Liberazione” was, as the musicologist Suzanne Cusick has written, well prepared to welcome the “representation of a fictional world ruled by exceptional women.”

The Composing Coquette Barbara Strozzi, 1650s play pause “Volano frettolosi” 4:21

Like that of many if not most female composers throughout history, Barbara Strozzi’s career was engineered by a man. Her adoptive father, the poet Giulio Strozzi — many assumed Barbara was his illegitimate daughter — organized salons at his Venice home, where he would invite important men to debate philosophical and often prurient topics. Between discussions, the teenage Barbara would perform suggestive musical interludes.

It wasn’t until her 30s that she began to seriously and consistently compose her own music, a professional pivot that can be read as an assertion of autonomy after a lifetime of sexualized manipulation. The music she wrote could be overtly erotic — voices interweaving to a sonic climax — and sometimes misogynistic in its lyrics. It remains uncertain as to whether or not she was ever a courtesan or even a concubine.

Private Performances and Public Humiliations Elisabeth Jacquet de la Guerre, 1694 play pause "Céphale et Procris," overture 1:02

Baptized Élisabeth-Claude Jacquet, the composer now known as Élisabeth Jacquet de la Guerre was born in Paris in 1665 to a family of artisans (her father was a master harpsichord maker) whose craft allowed them access to the French nobility. She was accepted into the court of Louis XIV as a teenager, and her education and musical practice was overseen by Madame de Montespan, the king’s most adored mistress.

As was common with many musicians at the time, Jacquet’s career depended on the whims of her patrons, for whom she performed in mostly private settings. Being at the mercy of a mistress was even more precarious. And by 1694, when Jacquet staged “Céphale et Procris,” her first opera, Madame de Montespan had been replaced by a new, more religious mistress whose conservatism was already influencing the court’s taste. Though Jacquet took the trouble to publish the work, the production itself was performed only five or six times in Paris, to a wan reception. Jacquet’s husband, himself a composer, is said to have met with attendees the day after the premiere, telling them to stifle any criticism. But she never composed another opera.

They Prefer Song Marianna Martines, 1772

The English music historian Charles Burney visited Vienna in 1772, and on a Sunday afternoon in September was greeted in a grand home by the Italian librettist Pietro Metastasio. Letters were read aloud, compliments paid to mutual friends; the conversation was pleasant and intriguing.

The tenor of the room shifted with the entrance of a young woman, whom Burney would later describe as “well dressed,” “graceful” and “very elegant.” It was the composer and harpsichordist Marianna Martines, Metastasio’s pupil and protégée, who even as a child was deemed skilled enough to play at the imperial court. The group of men greeted her with great respect, and she proceeded to sing two airs of her own composition. Her performance, Burney would write, surpassed all that he “had been made to expect.”

In his account of the visit, Burney praises Martines’s voice, her timing, her self-presentation. But he expressed concern that the physical demands of composition — the sitting, the neck craning — might mitigate her other talents. “It is a pity,” he wrote, “that her writing should affect her voice.”

Backstage Grandeur Louise Farrenc, 1850 play pause Nonet, Op. 38, III. Scherzo 5:08

In the middle of the 19th century, Paris audiences vastly preferred opera to instrumental music. But when Louise Farrenc’s Nonet in E-flat major had its premiere in 1850 — with Joseph Joachim, not yet 20 years old and not yet quite world famous, leading on the violin — the performance was met with ecstatic excitement. Alternating between winds and strings, the work is lively and bright; listeners enjoyed the way in which each instrument is given its own moment to shine.

Eight years earlier, Farrenc had been appointed professor of piano at the Paris Conservatory — one of the first female instrumental professors in Europe — and Farrenc parlayed her newfound public success into a pay raise, demanding that her wages be equal to those of her male colleagues. Her employers agreed, and Farrenc kept the post for another quarter-century. In addition to composing and teaching, she helped her husband, a music scholar and publisher, to research and edit books, including a 23-volume anthology of keyboard masterpieces. She continued the work after he died, organizing talks and concerts to coincide with various publications. Her strategic scholarship — intent on reviving and publicizing works of the past — was unusual at the time, but such behind-the-scenes labor has in fact been a large part of the work women have contributed over the centuries.

Touring and Torment Clara Schumann, 1837 play pause Quatre Polonaises Pour le Pianoforte, No. 2. Polonaise in C 2:53

In the winter of 1837, Clara Wieck, a German piano prodigy turned teenage touring virtuoso, came to Vienna to give a series of concerts that lasted through the spring. The shows often sold out; excited crowds grew so congested that the police were called upon; and a torte was named after her.

She was a celebrity. In addition to her work on the piano, she composed music that she would play at each recital — a rarity for both men and women at the time. The fact that she toured at all was in itself somewhat novel. By the 19th century, musicians who once performed privately for their noble employers now gave public concerts to larger, more diverse and more distant audiences, but it was not a tradition friendly to women, for whom a life onstage and constant transit were considered inappropriate if not impossible. Wieck was an exception.

By the time she married her husband, the composer Robert Schumann, and took his name, she was already world famous — and only 20. She continued to perform for decades, through relentless pregnancies and multiple miscarriages. And despite Robert’s nervous breakdowns and possible syphilis infection, she believed his opinion that she should retreat from composing.

“I once believed that I possessed creative talent, but I have given up this idea,” she wrote. “A woman must not desire to compose — there has never yet been one able to do it. Should I expect to be the one?”

A Song to Live By Ethel Smyth, 1912 play pause “The March of Women” 1:43

On the evening of March 1, 1912, dozens of British women gathered in central London, removed hammers and stones from their muffs and purses, and proceeded to smash the windows of politicians and businesses known to oppose voting rights for women.

The composer Ethel Smyth, then in her 50s, was one of them. The previous year, she had written “The March of the Women,” a soulful and optimistic song that immediately became the movement’s anthem. Smyth was arrested with over 100 of her compatriots that night and sent to Holloway Prison, where she served a two-month sentence. When her friend the conductor Thomas Beecham visited her in jail, he witnessed scores of suffragists marching inside the quad and singing the march, while Smyth herself leaned out a window, conducting with a toothbrush.

Data on the Rhine Ashley Fure, 2016 play pause “Something to Hunt” 10:49

In the summer of 2014, “Something to Hunt,” by the American composer Ashley Fure, 32 at the time, had its premiere at the prestigious Internationale Ferienkurse für Neue Musik in Darmstadt, Germany. The almost 11-minute piece for seven players is theatrically menacing, with prowling instrumental lines and surprising silences. Ms. Fure describes it on her website as “a multidimensional but unidirectional thrust that circles back and pushes forth relentlessly, obsessively, until its end. Looking for something. Hungry for meat.” It was awarded the Darmstadt festival’s grand prize that summer.

In August, Ms. Fure returned to Darmstadt for the biannual festival’s 70th anniversary. The organizers had furnished her with archival data about its history, and Ms. Fure found the underrepresentation of women to be even worse than she had expected. “How do you deal with an absence?” she wondered in a recent phone interview.

She decided to organize a panel discussion based on the dismaying statistics pertaining to such topics as compositions performed, prizes awarded, faculty members invited and CDs produced. The presentation and subsequent round table resulted in the creation of web pages, articles and interviews — all in just few days. Ms. Fure remains optimistic that merely offering this information transparently will have positive effects: on hiring considerations by ensembles, on invitations to teach master classes — at Darmstadt in 2018, but also sooner, and elsewhere.

Music, Ms. Fure emphasizes, is not unlike success in fine cuisine or architecture. Talent isn’t enough: A vast and complicated matrix of financing, promotion and patronage presents, as she put it, “many opportunities for the pressures and incongruities of culture to impact the dissemination and development of work.”