“Book of Longing,” the latest large-scale vocal work in Philip Glass’s prolific career, received an enthusiastic reception this weekend at the Rose Theater as part of Lincoln Center Festival. The song suite, which made its premiere in Toronto last month, sets the verse of Canadian singer and writer Leonard Cohen, taking its title from Mr. Cohen’s collection published last year, from which Mr. Glass distilled 22 poems, imparting the stylistic and emotional concentration of his friend’s work.

With those poems suspended as lyrics within the composer’s nuanced repetitions (performed by Mr. Glass and his seven-piece ensemble, with a cast of four singers and a voice-over provided by a recording of Mr. Cohen), “Book of Longing” traversed themes of restless passion and unreachable opportunity — facets of the poet’s dry humor and often mordant persona — while wielding a persistent erotic charge.

The ensemble opened before a black backdrop, in what might be enjoyed as a nod to Mr. Cohen’s dress code. Mr. Glass andmusicdirectorMichaelRiesmanfaced one another across the stage at electric keyboards; manning risers were their six band mates, on percussion, violin, cello, oboe, English horn, flute and reeds, and contrabass. The prologue featured Mr. Cohen’s voice (“She’ll step on the path / She’ll see what I mean / My will cut in half / And freedom between”), as boldly amplified and metronomic as Mr. Glass’s music.

The backing curtain then rose, displayingMr. Cohen’sblack-andwhite drawings on panels forming an open-work wall: self-portraits, three female nudes shown from behind, a candlestick and salt shaker. Over the course of the 70-minute piece, the rear wall’s milky luminescence would turn lime green or warning red, with the largest panel morphing through images, sometimes injecting lurid color or cobbling together the other panels’ subjects as if they were glyphs.

The first of the evening’s singers, the polished baritone Daniel Keeling, entered and with matter-of-fact style concluded “I finally understood / I had no gift / for spiritual matters,” a reference to Mr. Cohen’s leaving the Buddhist monastery at Mount Baldy, California, after five years of training. As the early numbers progressed, Mr. Keeling alternated with mezzo Tara Hugo (who embodied Mr. Cohen’s careworn elegance), soprano Dominique Plaisant in a black gown, and tenor Will Erat. Their methodical exits and synchronized entrances were choreographed with casual precision by Susan Marshall.

Blurring boundaries between operatic breadth, pop appeal, and folk confession, the singers shared songs and lingered in chairs when not at the microphone stands, then added subtle flourishes — turning a page for one keyboardist, circling a chair before approaching the audience. At one point, Mr. Erat put an arm around Ms. Plaissant during a duet, with Mr. Keeling exiting once through the illustrated door on the panel wall. The intimate, nonnarrative approach of “Book of Longing” took structure from this piecemeal diversity. Singers who had just deployed with Broadway force across the stage might then ponder the back wall.

From his piano, Mr. Riesman audibly counted numbers off into a leisurely pulse, while the ensemble listened attentively as another member or a vocalist took the spotlight. The cellular operations of Mr. Glass’s music generated a persistently rhythmic organism, detailed with passing textures: bass clarinet accented by a soft marimba; winds that gleaned Baroque patterns pinioned by strings hocketing with minimalist motor techniques; rare jazz walking notes by the bassist Eleonore Oppenheim, who, in a late passage, bowed two notes laden with portent that were echoed more gently by the violinist Tim Fain. Figures accelerated to double time, then settled back on a dime, and cellist Wendy Sutter turned her back, her playing hinting at Persian blues-tinged modalities.

Mr. Cohen’s trenchant observations — his early influences included country greats Merle Haggard and Roy Acuff — made for an evening both bracing and personable. After a sequence of self-portraits with scrawled epigrams scrolled by too quickly to read, Mr. Glass took an office chair near the spotlight, listening intently as Ms. Oppenheim took her spare solo. A troubadour’s guitar was projected high on the back wall; the musicians stood, still playing, and house lights rose as the fitting verse, “It’s merely a song / merely a prayer,” brought “Book of Longing” to a close.