Orpheus Lost, beautifully written and disturbing, takes us from earth to underworld as a mathematician and a musician repeat the roles of Eurydice and Orpheus, with a few twists.

In the Greek myth, Orpheus attempts to rescue his snake-bit wife, the nymph Eurydice. With his lyre, he charms all and uses this gift to make his way into the underworld.

Orpheus is granted permission to retrieve Eurydice on one condition: He must not look back as he leaves and she follows.

But he does look.

In Janette Turner Hospital’s version, Eurydice is Leela-May Magnolia Moore, who studies the math of music at MIT. She does not like her name and pretends it is Sanskrit, lila, which means “sport of the gods.”

She meets her Orpheus as he plays his violin and sings underground: “The violin itself was weeping music. ... The singer was singing of loss ... and the sorrow was passing from body to body like a low electrical charge.”

Mishka Bartok, earning his doctorate in composition at Harvard, beguiles the subway travelers so thoroughly that they miss their trains. He is playing Gluck’s lament of Orpheus from the opera Orfeo ed Euridice when Leela is drawn to him.

Hospital takes us into many underworlds: the “underworld of Boston’s Red Line” subway, the underworld of a beaten child, of racial attacks in (her fictional) Promised Land, S.C.; of Auschwitz, an interrogation room, the “ghost” tunnels and torture chambers of Americans in Iraq.

Leela will do the rescuing. She must charm Cobb Slaughter, her childhood friend, possessor of a “cloven paw” inflicted by his father, an alcoholic Vietnam vet.

Cobb was a soldier in Afghanistan and Iraq who now works privately, secretly. After a Boston bombing, Leela is picked up for interrogation because Cobb believes some people “needed to be shown—no, more than that, they needed to experience bodily the fact that carelessness in matters of national security had consequences, and the consequences were costly.”

Cobb is more than Cerberus, hell’s watchdog, however. He is Leela’s blood brother, a besotted friend, a misguided inquisitor who seeks a “reverse flow of energies” and finds that in surprising ways at the novel’s end.

Leela also is picked up because her lover has a double life. As a child, his life and self were split between school and his odd home life in an Australian rainforest—no father, his grandparents Holocaust survivors, music permeating all.

His grandmother calls their home the promised land. “And it was, Mishka thought: ... a river that rose and rose in its banks ... foaming and splashing him with Gluck and Mendelssohn and Uncle Otto’s violin and bird cries and fragrant night-blooming flowers.”

As an adult, Mishka has another name, after his never-met father: Mikael Abukir. He follows an overwhelming and obviously dangerous desire to hear anything about his Lebanese father, perhaps alive, perhaps a terrorist.

Underlying the plot are two refrains, the first repeated twice in the first chapter: “Obsession is its own heaven and its own hell.” The second, given the aftermath, is a question phrased in various ways but not fully answered: “What will I do without that which I cannot do without?”

Also threaded through the novel is either (you decide) magical realism or hallucinations or a kind of synesthesia, a neurological cross-wiring in which senses pair—sounds might come with colors, words might have a taste.

Mishka’s family hears music that might not be playing (you decide, too, about Uncle Otto and his locked room). He tells Leela to listen to his heart to hear “The sonatina. Before I have written it down.”

Leela can see and feel the math within Mishka’s music and has from childhood found “numbers themselves—the ciphers and cryptic symbols—strangely beautiful and full of narrative mystery.”

This is all beautifully written: the descriptions of music, the alternate realities of Mishka’s rainforest and Leela’s and Mishka’s sexual and romantic love.

And then it becomes disturbing, at times, extremely disturbing: Cobb and Benedict Boykin, a black childhood friend of Leela’s, were Special Forces and know of an Abu Ghraib-like incident.

Mishka has been attending the same mosque as a subway bomber, someone he knew, and he’s lying to Leela about how he spends his time.

Hospital is relentless in her musical and mythological references, even as the novel shifts halfway through from romance to suspense when Mishka goes missing. While the book could be tagged a literary thriller, Hospital chooses to depict not clinical gore but hallucinatory pain:

“He joined his mother at the window and they stared at the effigy wearing the costume of his body. It was swinging by its wrists from a hook. Its feet did not quite touch the floor. Apart from the hood, it was naked. ... He could hear the screams.”

As Hospital has shown in “Oyster” and “Due Preparations for the Plague,” she is fascinated by religious and political fundamentalism, psychological and physical terror—and who succumbs or resists.

Published in May in Australia and this October in the U.S., Orpheus Lost has reaped acclaim, as have her earlier novels, which have won numerous Australian literary awards and a place on New York Times’ Notable lists.

An Australian native who is Carolina Distinguished Professor of English at the University of South Carolina, Hospital sounds a bit tone deaf when it comes to Promised Land, S.C., where the blacks speak colloquially but their white neighbors don’t. And she’s a tad too fond of poetic language that enraptures but does not develop character.

But she deserves great and sustained attention for the fine eye and mind she turns to the problems of our times. We should listen to her music.